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Honors Calculus Courses for Academic Credit Online

HONORS Course Track

Distance Calculus offers an HONORS sequence (introduced in Summer 2023) for students who want to engage their calculus coursework at the next level. Our Honors courses are not "more rigorous" in the traditional sense of an axiomatic re-derivation of lower Calculus. They are more challenging than the standard sequence - broader in topic coverage, deeper in problem sets, and accompanied by a distinctive technical writing curriculum that culminates in a 10-20 page course term paper.

Nationally, "Honors" courses usually are centered on a mathematically rigorous development of the concepts of calculus, bringing many advanced topics from upper division courses such as Advanced Calculus and Real Analysis into the freshman honors calculus courses. While this may be a worthwhile approach for students who seek to become mathematics majors, it creates, for many students, an inflated level of course difficulty of questionable benefit to related fields of study.

Our approach to Honors courses is built upon a distinctly different educational philosophy:

  • Freshman & Sophomore Calculus is NOT the correct math level to increase rigor
    We believe that mathematical rigor is learned after exposure to the calculus, in the upper division, after some time and maturing of mathematical thought is allowed to organically develop. No student ever understood the concept of a derivative because the natural numbers were first axiomatically developed.
  • Honors means DEEPER, not just HARDER
    In mathematics, the potential for making any course harder is a rather simple proposition. Work SMARTER, not HARDER mandates that an honors course should not be more difficult just to say it is. A true honors student wants to go deeper into the topics, not flirt with academic demoralization via some mathematical bootcamp experience.
  • Technical Writing Curriculum
    While axiomatic development has its place in upper division math, core improvement of technical writing skills will benefit all students in all disciplines with immediate effect. If calculus is supposed to be mathematical preparation for science, technology, and engineering related fields, then development of technical writing skills should be as important as computational prowess.
  • Course Term Paper
    Each Honors course student will write a 10-20 page term paper on a topic chosen in collaboration with the course instructor, empowering the student to simultaneously improve technical writing skills and deepen knowledge in the student's chosen academic field via a uniquely creative exercise that will transcend the traditional course boundaries.

In summary, our Honors courses go deeper and broader in the curriculum, offer a notch more challenging course work set, and featuring a technical writing curriculum that truly prepares the student for further academics in the sciences.

Course
DMAT 254 - Honors STEM Calculus I
Credits
5 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
Download PDF Syllabus
Click Here to Enroll in DMAT 254
Course
DMAT 255 - Honors Calculus I+II for Data Science
Credits
5 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
Download PDF Syllabus
Click Here to Enroll in DMAT 255
Course
DMAT 264 - Honors STEM Calculus II
Credits
5 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
Download PDF Syllabus
Click Here to Enroll in DMAT 264
Course
DMAT 356 - Honors Multivariable Calculus and Vector Analysis
Credits
5 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
Download PDF Syllabus
Click Here to Enroll in DMAT 356
Course
DMAT 322 - Honors Computational Differential Equations
Credits
4 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
Download PDF Syllabus
Click Here to Enroll in DMAT 322
Course
DMAT 337 - Honors Computational Linear Algebra for Data Science
Credits
5 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
Download PDF Syllabus
Click Here to Enroll in DMAT 337
Course
DMAT 336 - Honors Computational Linear Algebra
Credits
5 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
Download PDF Syllabus
Click Here to Enroll in DMAT 336
RWU Course Catalog - DMAT 254 • Honors STEM Calculus I
Course
DMAT 254
Course Title
Honors STEM Calculus I
Transcript Title
Honors Calculus I
Credits
5 Semester Credit Hours
Description
An honors-level first course introduction to differential and integral calculus for engineering and science students, with emphasis on a modern, empirical exposition of the classical subject. Topics include a study of the algebraic, numerical, and graphical aspects of polynomial, exponential, logarithmic, and trigonometric functions, limits, function growth, derivative analysis and optimization, introduction to differential equations, methods and applications of integration, numerical computations of integrals including the Monte-Carlo method, and the Fundamental Theorem of Calculus. Honors courses will include greater breadth and depth of topics, and develop technical writing skills, culminating in a mathematical term paper on an approved topic.
Prerequisite
Successful completion with grade B or higher in Precalculus with Trigonometry or equivalent, or consent of instructor.
E-Textbook
Calculus & LiveMath by Robert R. Curtis, Ph.D., adapted from Davis/Porta/Uhl Calculus&Mathematica courseware series
Software
LiveMath
Syllabus PDF
Download Detailed Syllabus (PDF)

DMAT 254 - Learning Outcomes

  1. To identify, manipulate, and understand the algebraic, numerical, and graphical fundamentals of linear, polynomial, exponential, logarithmic, rational polynomial, and trigonometric functions;
  2. To understand and compute algebraic, numerical, and graphical limits at finite and infinite values;
  3. To understand and compute the fundamental concept of the derivative;
  4. To understand and compute various measurements of growth of a function
  5. To algebraically compute derivatives of common functions using summation, product, quotient, and chain rules for derivatives;
  6. To formulate and understand introductory analytical proofs in application to the concepts of limits and the derivative;
  7. To understand and compute optimization of functions using derivatives, finding critical values;
  8. To understand and compute the second derivative;
  9. To understand and compute the Mean Value Theorem and related concepts;
  10. To understand and compute first order differential equations;
  11. To understand and compute implicit differentiation and related rates;
  12. To understand and compute parametric equations, including projectile motion;
  13. To understand and calculate numerically and graphically the core concepts of the integral for applications to signed area measurements;
  14. To compute numerically, algebraically, and graphically integrals of a variety of functions;
  15. To algebraically compute integrals of basic polynomial, exponential, and trigonometric functions, with an introduction to the algebraic substitution technique;
  16. To use of tools of differential and integral calculus in various applications
  17. To understand and compute the Fundamental Theorem of Calculus
  18. To understand and compute an integral functions, including inverse trigonometric and logarithmic integrals that do not algebraically resolve;
  19. To utilize computer algebra and graphing software to amplify traditional manual computation techniques.
  20. Honors Additional Topics:
  21. *To investigate data interpolation and algebraic modeling of data sets using polynomial and trigonometric functions
  22. *To investigate Preditor-Prey differential equations modeling
  23. *To investigate numerical limits error analysis, the need for Lagrange, Newton, L'Hopital, Extrapolation methods
  24. *To understand and compute integrals with the Monte-Carlo method
  25. *To understand the concept of algebraic integration in Finite Terms
  26. *To develop mathematical technical writing skills, culminating in a term paper on an approved topic.
  27. * = Additional topics for Honors course

DMAT 254 - Syllabus of Topics

1. Getting Started
1.1 Email and Chat
1.2 Learning About the Course
1.3 Required Hardware
1.4 Software Fundamentals
2. Growth: Preparing for the Derivative
2.1 Growth of Linear Functions
2.2 Growth of Power Functions
2.3 Growth of Exponential Functions
2.4 Dominance of Growth of Functions
2.5 Percentage Growth of Functions
2.6 Global Scale: Infinite Limits
2.7 Data Functions and Interpolation
2.8 Approximation of Functions by Linear Functions
3. Continuity
3.1 Limits
3.2 Continuous Functions
3.3 Jump Discontinuities
3.4 Piecewise Functions and Continuity
3.5 Limit Rules
4. Exponential Functions and Natural Logarithms
4.1 e = Euler’s Number
4.2 Natural Logarithm
4.3 Growth Analysis
4.4 Applications: Carbon Dating
4.5 Percentage Growth and Steady Growth of Exponential Functions
4.6 Data Functions and Logarithmic Analysis
4.7 Inverse Functions
4.8 Applications: Compound Growth Rates
4.9 Applications: World Population
5. The Derivative of Polynomial, Exponential, Logarithmic, and Fractional Powers
5.1 Instantaneous Growth Rates
5.2 Definition of the Derivative
5.3 Computing the Derivative Graphically
5.4 Computing the Derivative Algebraically
5.5 Computing the Derivative Numerically
5.6 Average Growth Rate vs. Instantaneous Growth Rate
5.7 Applications of the Derivative: Spread of Disease
5.8 Finding Maxima and Minima of Functions
5.9 Relating a Function and Its Derivative
6. Computing Derivatives
6.1 Sum, Difference, Product, Quotient Rule
6.2 Chain Rule
6.3 Instantaneous Percentage Growth
6.4 Growth Dominance
7. Using Derivatives
7.1 Finding Maxima and Minima
7.2 Finding Good Representative Plots
7.3 Applications: Maximizing Volume
7.4 The Second Derivative
7.5 Applications: The Space Shuttle Challenger
8. Differential Equations
8.1 Linear Differential Equations
8.2 Logistic Equations
8.3 Rate Track Principal
8.4 Approximations - Introduction to Taylor's Theorem
9. Integration
8.1 Measuring Area Under a Curve
8.2 Definition of the Integral
8.3 Properties of Integrals, Symmetry
8.4 Integrals of Data Functions
8.5 Numerical Methods: Rectangles, Trapezoids
8.6 Undefined Integrals
8.7 Numerical Calculation of Integrals
8.8* Monte-Carlo Method of Integration
9. Fundamental Theorem of Calculus
9.1 Derivative of an Integral
9.2 Integral of a Derivative
9.3 Fundamental Formula
9.4 Distance, Velocity, and Acceleration
9.5 Improper Integrals
9.6 More Properties of Integrals
9.7 Applications: Measure Accumulation Totals
9.8 Indefinite Integrals and Antiderivatives
9.9 u-Substitution
9.10 Inverse Circular and Hyperbolic Trigonometric Functions
10.* Limits Revisited
10.1* Limitations of Numerics with Limits
10.2* Lagrange, Newton, Extrapolation Numerical Methods
10.3* L'Hopital's Rule for Limits
10.4* Introduction to Polynomial and Rational Polynomial Approximation
11.* Preditor-Prey Systems
11.1* Parametric Solutions of Differential Equations
11.2* Preditor-Prey Models
11.3* Applications
12.* Data Interpolation
12.1* Linear and Quadratic Approximations
12.2* Polynomial Approximations and Interpolation
12.3* Trigonometric Function Interpolation
12.4* Taylor's Theorem
13.* Integration in Finite Terms
13.1* Machine Integration Engines
13.2* Finite Terms
13.3* Quadrature and Limitations
14.* Mathematical Writing
14.1* Cogent writing
14.2* Mathematical Presentation
14.3* Term Paper Topic and Research
RWU Course Catalog - DMAT 255 • Honors Calculus I+II for Data Science
Course
DMAT 255
Course Title
Honors Calculus I+II for Data Science
Transcript Title
Honors Calc I+II for Data Sci (Combined)
Credits
5 Semester Credit Hours
Description
An honors-level single course introduction to differential and integral calculus for data science students, with emphasis on a modern, empirical exposition of the classical subject, condensing the essential topics from first year calculus. Topics include a study of the algebraic, numerical, and graphical aspects of polynomial, exponential, logarithmic, and trigonometric functions, limits, function growth, derivative analysis and optimization, introduction to differential equations, methods and applications of integration, the Fundamental Theorem of Calculus, calculus of data sets, numerical issues of derivative and integral computations, Monte-Carlo method, Taylor's Theorem and spline approximations, and methods of integration. Honors courses will include greater breadth and depth of topics, and develop technical writing skills, culminating in a combination programming project and mathematical term paper on an approved topic.
Prerequisite
Successful completion with B grade or higher in Precalculus with Trigonometry or equivalent, or consent of instructor; experience with a computer programming language.
E-Textbook
Calculus&Mathematica by Davis/Porta/Uhl
Software
LiveMath
Syllabus PDF
Download Detailed Syllabus (PDF)

DMAT 255 - Learning Outcomes

  1. To understand and compute algebraic, numerical, and graphical limits at finite and infinite values;
  2. To understand and compute the fundamental concept of the derivative;
  3. To understand and compute various measurements of growth of a function
  4. To algebraically compute derivatives of common functions using summation, product, quotient, and chain rules for derivatives;
  5. To understand and compute optimization of functions using derivatives, finding critical values;
  6. To understand and compute the second derivative;
  7. To understand and compute first order differential equations;
  8. To understand and compute parametric equations, including projectile motion;
  9. To understand and calculate numerically and graphically the core concepts of the integral for applications to signed area measurements;
  10. To compute numerically, algebraically, and graphically integrals of a variety of functions;
  11. To algebraically compute integrals of basic polynomial, exponential, and trigonometric functions, with an introduction to the algebraic substitution technique;
  12. To use of tools of differential and integral calculus in various applications
  13. To understand and compute the Fundamental Theorem of Calculus
  14. To understand and compute an integral functions, including inverse trigonometric and logarithmic integrals that do not algebraically resolve;
  15. To utilize computer algebra and graphing software to amplify traditional manual computation techniques.
  16. To understand spline interpolation with polynomial functions; points of contact
  17. To understand Taylor's Theorem, error analysis
  18. To understand convergences and divergence concepts of sequences, series, polynomial approximations
  19. To understand and compute double integrals
  20. To understand and compute 3D vector analysis, dot product, planes, and cross products
  21. To understand and compute partial derivatives and tangent planes to a surface
  22. Honors Additional Topics:
  23. *To investigate data interpolation and algebraic modeling of data sets using polynomial and trigonometric functions
  24. *To investigate numerical limits error analysis, the need for Lagrange, Newton, L'Hopital, Extrapolation, more advanced polynomial and rational polynomial approximation methods.
  25. *To understand the concept of algebraic integration in Finite Terms
  26. *To understand and compute integrals using complex integration techniques
  27. *To understand and compute numerical integration techniques of Newton, Midpoint, and Runge-Kutta, and higher RK approximations.
  28. *To understand and explore higher integral functions, such as those defined by elliptical and hyperbolic integrals
  29. *To explore and analyze Preditor-Prey systems of differential equations
  30. *To develop mathematical technical writing skills, culminating in a term paper on an approved topic
  31. *To utilize programming-based computer algebra software to make investigations for a programming term project in application to data science
  32. * = Additional topics for Honors course

DMAT 255 - Syllabus of Topics

1. Getting Started
1.1 Email and Chat
1.2 Learning About the Course
1.3 Required Hardware
1.4 Software Fundamentals
2. Growth: Preparing for the Derivative
2.1 Growth of Linear Functions
2.2 Growth of Power Functions
2.3 Growth of Exponential Functions
2.4 Dominance of Growth of Functions
2.5 Percentage Growth of Functions
2.6 Global Scale: Infinite Limits
2.7 Data Functions and Interpolation
2.8 Approximation of Functions by Linear Functions
3. Continuity
3.1 Limits
3.2 Continuous Functions
3.3 Jump Discontinuities
3.4 Piecewise Functions and Continuity
3.5 Limit Rules
4. Exponential Functions and Natural Logarithms
4.1 e = Euler’s Number
4.2 Natural Logarithm
4.3 Growth Analysis
4.4 Applications: Carbon Dating
4.5 Percentage Growth and Steady Growth of Exponential Functions
4.6 Data Functions and Logarithmic Analysis
4.7 Inverse Functions
4.8 Applications: Compound Growth Rates
4.9 Applications: World Population
5. The Derivative of Polynomial, Exponential, Logarithmic, and Fractional Powers
5.1 Instantaneous Growth Rates
5.2 Definition of the Derivative
5.3 Computing the Derivative Graphically
5.4 Computing the Derivative Algebraically
5.5 Computing the Derivative Numerically
5.6 Average Growth Rate vs. Instantaneous Growth Rate
5.7 Applications of the Derivative: Spread of Disease
5.8 Finding Maxima and Minima of Functions
5.9 Relating a Function and Its Derivative
6. Computing Derivatives
6.1 Sum, Difference, Product, Quotient Rule
6.2 Chain Rule
6.3 Instantaneous Percentage Growth
6.4 Growth Dominance
7. Using Derivatives
7.1 Finding Maxima and Minima
7.2 Finding Good Representative Plots
7.3 Applications: Maximizing Volume
7.4 The Second Derivative
7.5 Applications: The Space Shuttle Challenger
8. Integration
8.1 Measuring Area Under a Curve
8.2 Definition of the Integral
8.3 Properties of Integrals, Symmetry
8.4 Integrals of Data Functions
8.5 Numerical Methods: Rectangles, Trapezoids
8.6 Undefined Integrals
8.7 Numerical Calculation of Integrals
8.8* Monte-Carlo Method of Integration
9. Fundamental Theorem of Calculus
9.1 Derivative of an Integral
9.2 Integral of a Derivative
9.3 Fundamental Formula
9.4 Distance, Velocity, and Acceleration
9.5 Improper Integrals
9.6 More Properties of Integrals
9.7 Applications: Measure Accumulation Totals
9.8 Indefinite Integrals and Antiderivatives
9.9 u-Substitution
9.10 Inverse Circular and Hyperbolic Trigonometric Functions
10.* Limits Revisited
10.1* Limitations of Numerics with Limits
10.2* Lagrange, Newton, Extrapolation Numerical Methods
10.3* L'Hopital's Rule for Limits
11.* Preditor-Prey Systems
11.1* Parametric Solutions of Differential Equations
11.2* Preditor-Prey Models
11.3* Applications
12.* Data Interpolation
12.1* Linear and Quadratic Approximations
12.2* Polynomial Approximations and Interpolation
12.3* Trigonometric Function Interpolation
13.* Algebraic Integration Theory
13.1* Machine Integration Engines
13.2* Integration in Finite Terms
13.3* Integratability and Limitations
13.4* Defining advanced special functions using integrals or series
14. Taylor’s Expansion of a Function
14.1 Splines and Smooth Splines
14.2 Points of Contact
14.3 Application: Landing an Airplane
14.4 Taylor Expansion
14.5 Recognizing Familiar Expansions
14.6 Using Expansions for Approximations
14.7 Derivatives and Integrals of Expansions
14.8 Expansions At Other Points
14.9 Newton’s Method
14.10 Convergence Intervals and Barriers
14.11 Calculating Limits: L’Hopital’s Rule
14.12* Expansions and Solving Differential Equations
14.13* Complex Exponentials
14.14* Euler, Midpoint, Runge-Kutta Integral Estimates
15.* Differential Equations
15.1* Types of Differential Equations
15.2* Linkage to Algebraic and Numerical Integration Theory
15.3* Power Series Solutions to Differential Equations
15.4* Elliptical and Hyperbolic Integration Functions
15.5* Exploring Special Named Functions
16. Polar Coordinates
16.1 Basic Graphing
16.2 Recognizable Curves
16.3 Differentiation and Integration in Polar Coordinates
17. Vector Analysis
17.1 Vector Arithmetic
17.2 Dot Product, Cross Product
17.3 Planes
17.4 Partial Derivatives
17.5 Tangent Planes
18.* Mathematical Writing
18.1* Cogent writing
18.2* Mathematical Presentation
18.3* Term Paper Topic and Research
RWU Course Catalog - DMAT 264 • Honors STEM Calculus II
Course
DMAT 264
Course Title
Honors STEM Calculus II
Transcript Title
Honors Calculus II
Credits
5 Semester Credit Hours
Description
An honors-level second course in the differential and integral calculus for engineering and science with emphasis on computational techniques, graphical analysis, and algebraic methods. Topics include integration theory, algebraic methods of integration, integral functions and transformations, improper and numerical integrals, applications of integration to geometry and physics, double integrals, integration over regions with parametric boundary, splines, barriers, Taylor's Theorem, L'Hopital's Rule, infinite sequences and series. Honors courses will include greater breadth and depth of topics, and develop technical writing skills, culminating in a mathematical term paper on an approved topic.
Prerequisite
Successful completion with B grade or higher in Calculus I or equivalent, or consent of instructor.
E-Textbook
Calculus & LiveMath by Robert R. Curtis, Ph.D., adapted from Davis/Porta/Uhl Calculus&Mathematica courseware series
Software
LiveMath
Syllabus PDF
Download Detailed Syllabus (PDF)

DMAT 264 - Learning Outcomes

  1. To understand and compute algebraic integrals using a variety of symbolic techniques, including substitution, integration by parts, integration via differentiation, iteration methods
  2. To understand and compute with the Fundamental Theorem of Calculus
  3. To understand and compute solutions to applications problems involving integrals
  4. To compute measurements of volumes of geometric objects using integrals (slides, surfaces of rotation
  5. To understand and compute with Green's Theorem
  6. To understand and compute parametric and Polar function integrals
  7. To understand and compute double integrals
  8. To understand and compute splines and polynomial approximations
  9. To understand and compute with Taylor's Theorem
  10. To understand and compute with L'Hopital's Rule and using expansions to compute limits
  11. To understand and compute sequences and series
  12. To understand and compute convergence or divergence of sequences and series using various tests (Ratio, Integral, p-Test)
  13. To understand and compute 3D vector analysis, dot product, planes, and cross products
  14. To understand and compute partial derivatives and tangent planes to a surface
  15. Honors Topics:
  16. * To understand the concept of integration in finite terms and its connection to integration techniques
  17. * To understand and compute basic solutions of differential equations in relation to integration techniques.
  18. * To understand and compute polynomial approximations to solutions of differential equations.
  19. * To understand and compute near-finite-term integrals and their expression in power series.
  20. * To understand and compute integrals using complex integration techniques
  21. * To understand and compute numerical integration techniques of Newton, Midpoint, and Runge-Kutta, and higher RK approximations.
  22. * To understand and explore higher integral functions, such as those defined by elliptical and hyperbolic integrals
  23. * To explore initial topics in Analytical Number Theory
  24. *To understand higher special functions defined by either series or integral formulations
  25. *To understand and compute more advanced polynomial and rational polynomial approximation techniques (Chebyshev, et al)
  26. * To develop mathematical technical writing skills, culminating in a term paper on an approved topic

DMAT 264 - Syllabus of Topics

1. Getting Started
1.1 Email and Chat
1.2 Learning About the Course
1.3 Required Hardware
1.4 Software Fundamentals
2. Integration
2.1 Measuring Area Under a Curve
2.2 Definition of the Integral
2.3 Properties of Integrals, Symmetry
2.4 Integrals of Data Functions
2.5 Numerical Methods: Rectangles, Trapezoids
2.6 Undefined Integrals
2.7 Numerical Calculation of Integrals
3. Fundamental Theorem of Calculus
3.1 Derivative of an Integral
3.2 Integral of a Derivative
3.3 Fundamental Formula
3.4 Distance, Velocity, and Acceleration
3.5 Improper Integrals
3.6 More Properties of Integrals
3.7 Applications: Measure Accumulation Totals
3.8 Indefinite Integrals and Antiderivatives
4. Measurements via Slicing
4.1 Measuring Area via Slicing
4.2 Measuring Volume via Slicing
4.3 Density and Mass
4.4 Accumulation of Rates
4.5 Arc Length
5. Computing Integrals
5.1 Algebraic Antiderivatives
5.2 Integrals of Standard Functions: Polynomial, Exponential, Trigonometric, Logarithmic
5.3 Transforming Integrals: u-substitution
5.4 Measuring Area under Parametric Curves
5.5 Integrals of Polar Functions
6. Measurements via Slicing
6.1 Measuring Area via Slicing
6.2 Measuring Volume via Slicing
6.3 Density and Mass
6.4 Accumulation and Rates
6.5 Arc Length
7. Double Integrals
7.1 Measuring Area and Volume
7.2 Gauss-Green Formula
7.3 Changing Order of Iterated Integrals
8. Integration Techniques
8.1 Separable Differential Equations
8.2 Integration By Parts
8.3 Integration Patterns and Reduction Formulas
8.4 Partial Fractions Technique
8.5 Trigonometric Integrals
8.6 Trigonometric Substitution
8.7* Integration via Differentiation Technique
8.8* DeMoivre’s Theorem
8.9* Complex Integration
9. Taylor’s Expansion of a Function
9.1 Splines and Smooth Splines
9.2 Points of Contact
9.3 Application: Road Curves
9.4 Taylor Expansion
9.5 Recognizing Familiar Expansions
9.6 Using Expansions for Approximations
9.7 Derivatives and Integrals of Expansions
9.8 Expansions At Other Points
9.9 Newton’s Method
9.10 Calculating Limits: L’Hopital’s Rule
9.11* Expansions and Solving Differential Equations
9.12* Complex Exponentials
9.13* Euler, Midpoint, Runge-Kutta Integral Estimates
10. Sequences and Series
10.1 Sequences of Numbers
10.2 Series of Numbers
10.3 Convergence
10.4 Convergence of Taylor Expansions
10.5 Barriers: Radius of Convergence
10.6. Shared Convergence Intervals for Derivatives and Integrals of Functions
10.7 Applications: Drug Dosing
11. Power Series
11.1 Basic Definition
11.2 Solutions of Differential Equations
11.3 Convergence Intervals of Power Series
11.4 Ratio Test and Other Convergence Tests
11.5 Finding Series Convergence Values via Power and Taylor Series
11.6* Famous Number Theory Infinite Series Values
11.7* Near-Finite Term Integration Formulas via Power Series
12.* Differential Equations
12.1* Types of Differential Equations
12.2* Linkage to Algebraic and Numerical Integration Theory
12.3* Power Series Solutions to Differential Equations
12.4* Elliptical and Hyperbolic Integration Functions
13. Polar Coordinates
13.1 Basic Graphing
13.2 Recognizable Curves
13.3 Differentiation and Integration in Polar Coordinates
14. Vector Analysis
14.1 Vector Arithmetic
14.2 Dot Product, Cross Product
14.3 Planes
14.4 Partial Derivatives
15.5 Tangent Planes
15.* Algebraic Integration Theory
15.1* Machine Integration Engines
15.2* Integration in Finite Terms
15.3* Integratability and Limitations
15.4* Defining advanced special functions using integrals or series
16.* Special Functions and Approximations
16.1* Approximating Functions with Polynomials and Rational Polynomials
16.2* Defining advanced special functions using integrals or series
16.3* Elliptical Curves and Fermat's Last Theorem
16.4* Exploring Special Named Functions
RWU Course Catalog - DMAT 356 • Honors Multivariable Calculus and Vector Analysis
Course
DMAT 356
Course Title
Honors Multivariable Calculus and Vector Analysis
Transcript Title
Honors Multivar Calculus IV
Credits
5 Semester Credit Hours
Description
An honors-level first course in multivariable differential and integral calculus, with emphasis on computational techniques, vector field analysis, and the generalized Fundamental Theorem of Calculus giving insight to the classical theorems of Green, Gauss, and Stokes. Topics include geometric analysis of multivariable functions, partial derivatives, level curves and surfaces, optimization, properties of vector fields, gradients, potential functions, path integrals and independence, field singularities, divergence and rotation, multiple integration, integral coordinate Jacobian transforms. Honors courses will include greater breadth and depth of topics, and develop technical writing skills, culminating in a mathematical term paper on an approved topic.
Prerequisite
Successful completion with grade B or higher in both Calculus I and Calculus II or equivalent, or consent of instructor; experience with programming languages.
E-Textbook
Vector Calculus & Mathematica by Davis/Porta/Uhl
Software
LiveMath & Mathematica
Syllabus PDF
Download Detailed Syllabus (PDF)

DMAT 356 - Learning Outcomes

  1. To understand the core geometrical elements of Euclidean space
  2. To understand and compute vector operations and their geometrical interpretations
  3. To understand and compute partial derivatives and gradient functions
  4. To understand and compute curves, level curves, surfaces, and level surfaces to multidimensional functions
  5. To understand and compute vector-valued functions and their geometric representations
  6. To understand and compute the classical optimization procedure of Lagrange Multipliers
  7. To understand, compute, and graph vector fields and their associated metrics
  8. To understand and compute path integrals of vector fields
  9. To understand, compute, and graph sources, sinks, and singularities of vector fields
  10. To understand and compute the divergence of a vector field, and its associated computations
  11. To understand and compute the rotation and curl of a vector field, and its associated computations.
  12. To understand and compute path integrals in the presence of singularities
  13. To understand and compute multiple integrals, and their associated geometrical interpretations
  14. To understand and utilize Fubini's Theorem for reordering integrations
  15. To understand and compute Jacobian transformations of multiple integrals
  16. To understand and compute cylindrical, spherical, and other coordinate systems, and their associated measurments with derivatives and integrals
  17. To understand an introduction to the Generalized Fundamental Theorem of Calculus, and its variations in the Divergence Theorem, and the Theorems of Gauss, Green, and Stokes.
  18. Honors Topics:
  19. * To understand and compute curves with dictated curvature
  20. * To understand and compute examples in data fitting by polynomials and trigonometric functions
  21. * To understand and compute higher dimensional optimizations using multivariable derivatives
  22. * To understand and compute potential functions as antiderivatives of gradient functions
  23. * To understand an introduction to Electric and Hamiltonian Fields
  24. * To understand and compute 3D path integrals and surface integrals, both directly and using the reductions afforded by the Generalized Fundamental Theorem of Calculus
  25. * To develop mathematical technical writing skills, culminating in a term paper on an approved topic

DMAT 356 - Syllabus of Topics

1. Getting Started
1.1 Email and Chat
1.2 Learning About the Course
1.3 Required Hardware
1.4 Software Fundamentals
2. Vectors
2.1 Geometry of Vectors
2.2 Tangent Vectors; Velocity Vectors, Acceleration Vectors
2.3 Vector Length
2.4 Dot Products
2.5 Vector Projection
2.6 Perpendicularity
2.7 Lines
2.8 Normal Vectors
2.9 Cross Product
2.10 Planes in 3D
2.11 Normal, Binormals, Curvature, Torque
2.12* Curvature Dictating Curves
3. The Derivative
3.1 Partial Derivatives
3.2 Gradient
3.3 Level Curves and Surfaces
3.4 Linearization
3.5 Total Differential
3.6 Lagrange Multipliers
3.7* Data Fitting
3.8* Higher Dimensional Optimizations
4. Vector Fields
4.1 Plotting and Trajectories
4.2 Flow-Along and Flow-Across Curves
4.3 Differential Equations and Vector Fields
4.4 Path Integrals
4.5 Gradient Fields
4.6 Sources, Sinks
4.7 Divergence Theorem
4.8 Singularities
4.9 Rotation and Curl
4.10*Potential Functions
4.11*Electrical Fields
4.12*Hamiltonian Fields
4.13*Implicitly Defined Functions
4.14*Work
4.15*Laplacians and the Heat Equation
5. Multiple Integrals
5.1 Basic Computation
5.2 u-v Transformations; Jacobians
5.3 Measurement of Volume, Mass, Density
5.4 3D Integrals
5.5 Average Value
5.6 Fubini’s Theorem
5.7* Ribbons of Constant Width
5.8* Eigenvalues and Eigenvectors
5.9* Hypervolume
6. Other Coordinate Systems
6.1 Cylindrical Coordinates
6.2 Spherical Coordinates
6.3 Integration in Other Coordinate Systems
6.4* Tubes, Horns
6.5* Average Values, Centers of Mass
6.6* Mobius Strips
7. Gauss, Green, Stokes Theorems
7.1 Green’s Theorem
7.2 Stokes’ Theorem
7.3 Divergence Theorem ? 7.4 Generalized Fundamental Theorem of Calculus
7.5 Sources, Sinks, and 3D Gauss’s Formula
7.6 Surface Integrals
7.7* Gradient Test in 3D
7.8* Work in 3D
7.9* Parallel Flow and Irrotational Flow
7.10* curlField and rotField Connections
7.11* Laplacians
7.12* Flux and Electric Fields
8.* Mathematical Writing
8.1* Cogent writing
8.2* Mathematical Presentation
8.3* Term Paper Topic and Research
RWU Course Catalog - DMAT 322 • Honors Computational Differential Equations
Course
DMAT 322
Course Title
Honors Computational Differential Equations
Transcript Title
Honors Comp Differential Eqns
Credits
4 Semester Credit Hours
Description
A first course in the study of differential equations with emphasis on modern software computational techniques with geometrical and qualitative interpretations. Topics include first, second, and higher-order ordinary differential equations, analysis of forcing functions, Laplace Transforms, convolution integral techniques, Fast Fourier Transforms and data approximations, systems of differential equations, classical algebraic solution methods, power series solutions. Honors courses will include greater breadth and depth of topics, and develop technical writing skills, culminating in a mathematical term paper on an approved topic.
Prerequisite
Successful completion with grade B or higher in Calculus II or equivalent, or consent of instructor.
E-Textbook
Differential Equations & Mathematica by Davis/Porta/Uhl
Software
Mathematica
Syllabus PDF
Download Detailed Syllabus (PDF)

DMAT 322 - Learning Outcomes

  1. To understand the core construction of the differential equation, and its classification parts
  2. To understand the role of the forcing function in differential equations
  3. To understand, observe, and compute the steady state solutions for a differential equation
  4. To understand, observe, and compute solutions of differential equations with a variety of forcing functions, including DiracDelta, step, oscillatory, and others
  5. To understand, observe, and compute solutions of differential equations with a variety of forcing functions, including DiracDelta impulses, step, oscillatory, et al.
  6. To understand and compute solutions of second order differential equations oscillators and how forcing functions affect their solutions
  7. To understand and compute manual solutions of first and second order differential equations using classical techiques
  8. To understand and compute with the Laplace Transform method
  9. To understand and compute graphical and numerical solution methods of differential equations
  10. To understand and compute solutions of linear systems of differential equations
  11. To understand and compute polynomial approximations to solutions of differential equations
  12. Honors Topics:
  13. * To understand and compute the linearization and equilibrium point solution methods
  14. * To understand and compute the classic examples of Van der Pol, Lorenz, Hamiltonian Systems
  15. * To understand an introduction to partial differential equations
  16. * To understand and compute solutions to the Heat and Wave Equations.
  17. * To develop mathematical technical writing skills, culminating in a term paper on an approved topic

DMAT 322 - Syllabus of Topics

1. Getting Started
1.1. Email and Chat
1.2. Learning About the Course
1.3. Required Hardware
1.4. Software Fundamentals
2. Exponential Differential Equations
2.1. Unforced DEs
2.2. Forced DEs
2.3. Steady State
2.4. Personal Finance
2.5. Step Function and Dirac Delta Function
2.6. Tangent Vectors
2.7. Initial Conditions
2.8. Integration Factors
3. Second-Order Differential Equations
3.1. Overdamped and Underdamped Oscillators
3.2. Linear Forced and Unforced Oscillators
3.3. Homogeneous and Inhomogeneous Equations
3.4. Convolution Method
3.5. Characteristic Equations
3.6. Euler’s Formula
3.7 Impulse Forcing
3.8 Dirac Delta Convolutions
3.9 Springs and Electrical Charges
3.10 Higher Order Equations
4. Laplace Transforms
4.1 Laplace Transforms of First and Second Order Equations
4.2 Fourier Analysis and Fourier Fit Approximations
5. Graphical Analysis of Differential Equations
5.1 Euler’s Method
5.2 Flow Plots and Trajectories
5.3 Preditor-Prey Model
5.4 Logistic Harvesting
6. First-Order Differential Equations
6.1 Autonomous Equations
6.2 Non-Autonomous Equations
6.3 Separation of Variables Solving Method
7. Systems of Differential Equations
7.1 Flows and Trajectories
7.2 Conversion Between Higher Order ODEs and Systems
7.3 Relationship to Eigenvalues and Eigenvectors
8. Power Series Solutions of Differential Equations
8.1 Recursion Relations
8.2 Comparing Series Solution to Numerical Solution
8.3 Barriers
9.* Linearization of Nonlinear Differential Equations
9.1* Equilibrium Points
9.2* Lyapunov's Rules
9.3* Pendulum Oscillator
9.4* Linearizations and Gradients
9.5* Van der Pol Oscillator
9.6* Hamiltonian Systems
9.7* Chaos and the Lorenz Attractor
10.* Heat and Wave Equations
10.1* Examples and Calculations of the Heat and Wave Equations
10.2* Introduction to Partial Differential Equations
10.3* Fourier Analysis and Fourier Fit Approximations
11.* Mathematical Writing
11.1* Cogent writing
11.2* Mathematical Presentation
11.3* Term Paper Topic and Research
RWU Course Catalog - DMAT 337 • Honors Computational Linear Algebra for Data Science
Course
DMAT 337
Course Title
Honors Computational Linear Algebra for Data Science
Transcript Title
Honors Linear Algebra Data Sci
Credits
5 Semester Credit Hours
Description
An honors-level first course in matrix algebra and linear spaces with emphasis on computational software techniques and geometrical analysis, with applications applicable to data science. Topics include matrices, solutions of systems of linear equations, determinants, linear spaces and transformations, inner products, higher dimensional spaces, inverses and pseudoinverses, rank, Singular Value Decomposition, change of basis, Eigenvalues and Eigenvectors, matrix decomposition and diagonalization, Principal Component Analysis, image and data compression, and an introduction to numerical analysis issues in the subject. Honors courses will include greater breadth and depth of topics, and develop technical writing skills, culminating in a mathematical term paper on an approved topic.
Prerequisite
Successful completion with grade B or higher in Calculus II or equivalent, or consent of instructor.
E-Textbook
Matrices, Geometry & Mathematica by Davis/Porta/Uhl
Software
Mathematica
Syllabus PDF
Download Detailed Syllabus (PDF)

DMAT 337 - Learning Outcomes

  1. To understand the core connection between matrix algebra and a study of systems of linear equations
  2. To understand and compute measurements of vectors and their geometry
  3. To understand and compute core matrix algebra operations and their geometrical interpretations
  4. To understand and compute the fundamental properties of determinants and inverses of matrices, both for square and non-square generalizations
  5. To understand and compute Singular Value Decomposition
  6. To understand and compute the core concept of rank and its variations
  7. To understand and compute Gaussian elimination and other strategies for finding solutions or approximate solutions to systems of linear equations
  8. To understand and compute bases, change of bases, spanning and linear independence, kernel and image sets
  9. To understand and compute the diagonalization of a matrix, both with Singular Value Decomposition, and Eigenvalue - Eigenvector constructions.
  10. Honors Topics:
  11. * To understand and compute interpolating polynomials and Fourier fitting and analysis
  12. * To understand and compute the Gram-Schmidt process in relation to Singular Value Decomposition
  13. * To understand and compute the diagonalization of a matrix when Eigenvalues are repeated and/or complex.
  14. * To understand and compute the relationship of matrix diagonalization and dynamical systems of differential equations
  15. * To understand and compute the Spectral Theorem
  16. * To understand Principal Component Analysis and additional concepts in data fitting
  17. * To understand issues concerned with image compression and round-off error
  18. * To develop mathematical technical writing skills, culminating in a term paper on an approved topic

DMAT 337 - Syllabus of Topics

1. Getting Started
1.1 Email and Chat
1.2 Learning About the Course
1.3 Required Hardware
1.4 Software Fundamentals
2. Vectors
2.1. Geometry of Vectors
2.2. Perpendicular Frames
2.3. Curves in 2D: Change of Frames/Basis
2.4. Dot Products
2.5. Cross Products
2.6. Ellipses and Ellipsoids
2.7. Area and Volume
3. Matrices
3.1 Basics
3.2 Transforming Curves
3.3 Matrix Arithmetic
3.4 Translations and Rotations
3.5 Shears
3.6 Linear Transformations
3.7 Inverses
3.8 Determinants
3.9 Transposes
3.10 Matrix Decomposition: Singular Value Decomposition
3.11 Rank
3.12 Projections
3.13 Higher Dimensions
4. Linear Systems
4.1 Conversion to Matrix Notation
4.2 Gaussian Elimination
4.3 Vector Spaces and Subspaces
4.4 Numerical Considerations
4.5 Applications: Least Square Fit
4.6 Spanning Sets; Basis
4.7 Linear Independence
4.8 Pseudo Inverses
4.9 Approximate Solutions
4.10 Null Space and Image Space
4.11* Interpolating Polynomials and Trigonometric Functions: Fourier Fit
4.11* Undetermined Coefficients in Differential Equations Systems
5. Eigenvalues and Eigenvectors
5.1 Diagonalization of a Matrix
5.2 Eigenvalues
5.3 Eigenvectors
5.4 Exponential of a Matrix
6. Principal Data Component Analysis
6.1 Image and Data Compression
6.2 Round-off Error
6.3 Principal Data Component Analysis with SVD
7.* Honors Topics
7.1* Gram-Schmidt Process and Singular Value Decomposition
7.2* 4D Projections
7.3* Non-Real Eigenvalue and Eigenvectors
7.4* Applications to Dynamical Systems
7.5* Spectral Theorem
8.* Mathematical Writing
8.1* Cogent writing
8.2* Mathematical Presentation
8.3* Term Paper Topic and Research
RWU Course Catalog - DMAT 336 • Honors Computational Linear Algebra
Course
DMAT 336
Course Title
Honors Computational Linear Algebra
Transcript Title
Honors Linear Algebra
Credits
5 Semester Credit Hours
Description
An honors-level first course in matrix algebra and linear spaces with emphasis on computational software techniques and geometrical analysis. Topics include matrices, solutions of systems of linear equations, determinants, linear spaces and transformations, inner products, higher dimensional spaces, inverses and pseudoinverses, rank, Singular Value Decomposition, change of basis, Eigenvalues and Eigenvectors, matrix decomposition and diagonalization, dynamical systems and the Spectral Theorem. Honors courses will include greater breadth and depth of topics, and develop technical writing skills, culminating in a mathematical term paper on an approved topic.
Prerequisite
Successful completion with grade B or higher in Calculus II or equivalent, or consent of instructor.
E-Textbook
Matrices, Geometry & Mathematica by Davis/Porta/Uhl
Software
Mathematica
Syllabus PDF
Download Detailed Syllabus (PDF)

DMAT 336 - Learning Outcomes

  1. To understand the core connection between matrix algebra and a study of systems of linear equations
  2. To understand and compute measurements of vectors and their geometry
  3. To understand and compute core matrix algebra operations and their geometrical interpretations
  4. To understand and compute the fundamental properties of determinants and inverses of matrices, both for square and non-square generalizations
  5. To understand and compute Singular Value Decomposition
  6. To understand and compute the core concept of rank and its variations
  7. To understand and compute Gaussian elimination and other strategies for finding solutions or approximate solutions to systems of linear equations
  8. To understand and compute bases, change of bases, spanning and linear independence, kernel and image sets
  9. To understand and compute the diagonalization of a matrix, both with Singular Value Decomposition, and Eigenvalue - Eigenvector constructions.
  10. Honors Topics:
  11. * To understand and compute interpolating polynomials and Fourier fitting and analysis
  12. * To understand and compute the Gram-Schmidt process in relation to Singular Value Decomposition
  13. * To understand and compute the diagonalization of a matrix when Eigenvalues are repeated and/or complex.
  14. * To understand and compute the relationship of matrix diagonalization and dynamical systems of differential equations
  15. * To understand and compute the Spectral Theorem
  16. * To develop mathematical technical writing skills, culminating in a term paper on an approved topic

DMAT 336 - Syllabus of Topics

1. Getting Started
1.1 Email and Chat
1.2 Learning About the Course
1.3 Required Hardware
1.4 Software Fundamentals
2. Vectors
2.1. Geometry of Vectors
2.2. Perpendicular Frames
2.3. Curves in 2D: Change of Frames/Basis
2.4. Dot Products
2.5. Cross Products
2.6. Ellipses and Ellipsoids
2.7. Area and Volume
3. Matrices
3.1 Basics
3.2 Transforming Curves
3.3 Matrix Arithmetic
3.4 Translations and Rotations
3.5 Shears
3.6 Linear Transformations
3.7 Inverses
3.8 Determinants
3.9 Transposes
3.10 Matrix Decomposition: Singular Value Decomposition
3.11 Rank
3.12 Projections
3.13 Higher Dimensions
4. Linear Systems
4.1 Conversion to Matrix Notation
4.2 Gaussian Elimination
4.3 Vector Spaces and Subspaces
4.4 Numerical Considerations
4.5 Applications: Least Square Fit
4.6 Spanning Sets; Basis
4.7 Linear Independence
4.8 Pseudo Inverses
4.9 Approximate Solutions
4.10 Null Space and Image Space
4.11* Interpolating Polynomials and Trigonometric Functions: Fourier Fit
4.11* Undetermined Coefficients in Differential Equations Systems
5. Eigenvalues and Eigenvectors
5.1 Diagonalization of a Matrix
5.2 Eigenvalues
5.3 Eigenvectors
5.4 Exponential of a Matrix
6.* Honors Topics
6.1* Gram-Schmidt Process and Singular Value Decomposition
6.2* 4D Projections
6.3* Non-Real Eigenvalue and Eigenvectors
6.4* Applications to Dynamical Systems
6.5* Spectral Theorem
7.* Mathematical Writing
7.1* Cogent writing
7.2* Mathematical Presentation
7.3* Term Paper Topic and Research




Distance Calculus - Student Reviews

Bill K.★★★★★
Posted: Dec 20, 2019
Courses Completed: Calculus I, Calculus II, Multivariable Calculus, Linear Algebra
I took the whole calculus series and Linear Algebra via Distance Calculus. Dr. Curtis spent countless hours messaging back and forth with me, answering every question, no matter how trivial they might seem. Dr. Curtis is extremely responsive, especially if the student is curious and is willing to work hard. I don't think I ever waited much more than a day for Dr. Curtis to get a notebook back to me. Dr. Curtis would also make videos of concepts if I was really lost.

The course materials are fantastic. If you are a student sitting on the fence, trying to decide between a normal classroom class or Distance Calculus classes with Livemath and Mathematica, my choice would be the Distance Calculus classes every time. The Distance Calculus classes are more engaging. The visual aspects of the class notebooks are awesome. You get the hand calculation skills you need.

The best summary I can give is to say, given the opportunity, I would put my own son's math education in Dr. Curtis's hands.
Transferred Credits To: None
James Holland★★★★★
Posted: May 3, 2018
Courses Completed: Calculus I, Calculus II
I needed to finish the Business Calculus course very very very fast before my MBA degree at Wharton started. With the AWESOME help of Diane, I finished the course in about 3 weeks, allowing me to start Wharton on time. Thanks Diane!
Transferred Credits To: Wharton School of Business, University of Pennsylvania
Daniel Marasco★★★★★
Posted: Jan 13, 2020
Courses Completed: Multivariable Calculus
This course was more affordable than many, and the flexible format was terrific for me, as I am inclined to work very diligently on tasks on my own. It could be dangerous for a person who requires external discipline more, but it works well for self-starters, allowing you to prioritize when you have other pressing work. I was a full time teacher adding a math certification, and this course allowed me to master the math while working around my teaching schedule and fitting work into moments here and there when I had time. I was able to transfer the credits to Montana State University, Bozeman for my teaching internship program without a hitch. The instructors were all very helpful and patient, even when I failed to see a ridiculously simple solution on one problem after 20 emails back and forth. Overall, I was more pleased with my experience in this class than I was with any of my other 9 courses.
Transferred Credits To: Montana State University, Bozeman
M M.★★★★★
Posted: Feb 8, 2026
Courses Completed: Precalculus, Calculus I
The courses were excellent. Very flexible and engaging and the platform offers a lot of upper-level courses. Dr. Curtis is an outstanding professor and very responsive. I would take again.
Transferred Credits To: None yet
Tanja B.★★★★★
Posted: Jan 28, 2026
Courses Completed: Calculus I
After two failed attempts at my university, this course helped me understand Calculus. The live maths tool along with Dr. Curtis were especially helpful, allowing me to visualize concepts and expand my understanding. The explanations were clear, the examples practical, and I could learn at my own pace, which built my confidence. Thank you.
Transferred Credits To: University of Namibia
Henry F.★★★★★
Posted: Dec 18, 2025
Courses Completed: Differential Equations
Transferred Credits To: Saint Joseph High School

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