Honors Calculus Courses for Academic Credit Online
HONORS New Course Sequence
In Summer 2023, Distance Calculus introduced the HONORS sequence of courses geared towards those students who wish to go to that next level of academic engagement in their calculus sequence courses. Unlike traditional Honors Calculus courses, these Honors courses are not "more rigorous" in the sense of an axiomatic development of lower Calculus, but they definitely are even more challenging than their main sequence sibling courses, with more breadth of topics, and a new, exciting writing curriculum culminating 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 Title: | Honors STEM Calculus I |
Catalog Number: | DMAT 254 |
Credits: | 5 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors STEM Calculus I |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 254 - Honors STEM Calculus I |
Course Title: | Honors STEM Calculus II |
Catalog Number: | DMAT 264 |
Credits: | 5 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors STEM Calculus II |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 264 - Honors STEM Calculus II |
Course Title: | Honors Multivariable Calculus and Vector Analysis |
Catalog Number: | DMAT 356 |
Credits: | 5 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors Multivariable Calculus and Vector Analysis |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 356 - Honors Multivariable Calculus and Vector Analysis |
Course Title: | Honors Computational Differential Equations |
Catalog Number: | DMAT 322 |
Credits: | 4 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors Computational Differential Equations |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 322 - Honors Computational Differential Equations |
Course Title: | Honors Computational Linear Algebra |
Catalog Number: | DMAT 336 |
Credits: | 5 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors Computational Linear Algebra |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 336 - Honors Computational Linear Algebra |
Course Title: | Honors STEM Calculus I |
Catalog Number: | DMAT 254 |
Credits: | 5 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors STEM Calculus I |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 254 - Honors STEM Calculus I |
Roger Williams University Course Catalog Listing: DMAT 254 - Honors STEM Calculus I
Course: DMAT 254
Course Title: Honors STEM Calculus I
Transcript Course Title (30 Characters Max:): Honors STEM Calculus I
Course 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. [5 Semester Credits]
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
PDF Course Syllabus: Detailed Course Syllabus in PDF for DMAT 254 - Honors STEM Calculus I
DMAT 254 - Honors STEM Calculus I - 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.
- Honors Additional Topics:
- 20.* To investigate data interpolation and algebraic modeling of data sets using polynomial and trigonometric functions
- 21.* To investigate Preditor-Prey differential equations modeling
- 22.* To investigate numerical limits error analysis, the need for Lagrange, Newton, L'Hopital, Extrapolation methods
- 23.* To understand and compute integrals with the Monte-Carlo method
- 24.* To understand the concept of algebraic integration in Finite Terms
- 25.* To develop mathematical technical writing skills, culminating in a term paper on an approved topic.
- * = Additional topics for Honors course
DMAT 254 - Honors STEM Calculus I - 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
Course Title: | Honors STEM Calculus II |
Catalog Number: | DMAT 264 |
Credits: | 5 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors STEM Calculus II |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 264 - Honors STEM Calculus II |
Roger Williams University Course Catalog Listing: DMAT 264 - Honors STEM Calculus II
Course: DMAT 264
Course Title: Honors STEM Calculus II
Transcript Course Title (30 Characters Max:): Honors STEM Calculus II
Course 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. [5 Semester Credits]
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
PDF Course Syllabus: Detailed Course Syllabus in PDF for DMAT 264 - Honors STEM Calculus II
DMAT 264 - Honors STEM Calculus II - 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
- Honors Topics:
- 15.* To understand the concept of integration in finite terms and its connection to integration techniques
- 16.* To understand and compute basic solutions of differential equations in relation to integration techniques.
- 17.* To understand and compute polynomial approximations to solutions of differential equations.
- 18.* To understand and compute near-finite-term integrals and their expression in power series.
- 19.* To understand and compute integrals using complex integration techniques
- 20.* To understand and compute numerical integration techniques of Newton, Midpoint, and Runge-Kutta, and higher RK approximations.
- 21.* To understand and explore higher integral functions, such as those defined by elliptical and hyperbolic integrals
- 22.* To explore initial topics in Analytical Number Theory
- 23.* To understand higher special functions defined by either series or integral formulations
- 24.* To understand and compute more advanced polynomial and rational polynomial approximation techniques (Chebyshev, et al)
- 24.* To develop mathematical technical writing skills, culminating in a term paper on an approved topic
DMAT 264 - Honors STEM Calculus II - 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
Course Title: | Honors Multivariable Calculus and Vector Analysis |
Catalog Number: | DMAT 356 |
Credits: | 5 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors Multivariable Calculus and Vector Analysis |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 356 - Honors Multivariable Calculus and Vector Analysis |
Roger Williams University Course Catalog Listing: DMAT 356 - Honors Multivariable Calculus and Vector Analysis
Course: DMAT 356
Course Title: Honors Multivariable Calculus and Vector Analysis
Transcript Course Title (30 Characters Max:): Honors Multivar Calculus IV
Course 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. [5 Semester Credits]
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
PDF Course Syllabus: Detailed Course Syllabus in PDF for DMAT 356 - Honors Multivariable Calculus and Vector Analysis
DMAT 356 - Honors Multivariable Calculus and Vector Analysis - 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
- 7. To understand and compute path integrals of vector fields
- 8. To understand, compute, and graph sources, sinks, and singularities of vector fields
- 9. To understand and compute the divergence of a vector field, and its associated computations
- 10. To understand and compute the rotation and curl of a vector field, and its associated computations.
- 11. To understand and compute path integrals in the presence of singularities
- 12. To understand and compute multiple integrals, and their associated geometrical interpretations
- 13. To understand and utilize Fubini's Theorem for reordering integrations
- 14. To understand and compute Jacobian transformations of multiple integrals
- 15. To understand and compute cylindrical, spherical, and other coordinate systems, and their associated measurments with derivatives and integrals
- 16. 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.
- Honors Topics:
- 17.* To understand and compute curves with dictated curvature
- 18.* To understand and compute examples in data fitting by polynomials and trigonometric functions
- 19.* To understand and compute higher dimensional optimizations using multivariable derivatives
- 20.* To understand and compute potential functions as antiderivatives of gradient functions
- 21.* To understand an introduction to Electric and Hamiltonian Fields
- 22.* To understand and compute 3D path integrals and surface integrals, both directly and using the reductions afforded by the Generalized Fundamental Theorem of Calculus
- 23.* To develop mathematical technical writing skills, culminating in a term paper on an approved topic
DMAT 356 - Honors Multivariable Calculus and Vector Analysis - 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
Course Title: | Honors Computational Differential Equations |
Catalog Number: | DMAT 322 |
Credits: | 4 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors Computational Differential Equations |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 322 - Honors Computational Differential Equations |
Roger Williams University Course Catalog Listing: DMAT 322 - Honors Computational Differential Equations
Course: DMAT 322
Course Title: Honors Computational Differential Equations
Transcript Course Title (30 Characters Max:): Honors Comp Differential Eqns
Course 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. [4 Semester Credits]
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
PDF Course Syllabus: Detailed Course Syllabus in PDF for DMAT 322 - Honors Computational Differential Equations
DMAT 322 - Honors Computational Differential Equations - 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
- Honors Topics:
- 12.* To understand and compute the linearization and equilibrium point solution methods
- 13.* To understand and compute the classic examples of Van der Pol, Lorenz, Hamiltonian Systems
- 14.* To understand an introduction to partial differential equations
- 15.* To understand and compute solutions to the Heat and Wave Equations.
- 16.* To develop mathematical technical writing skills, culminating in a term paper on an approved topic
DMAT 322 - Honors Computational Differential Equations - 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
Course Title: | Honors Computational Linear Algebra |
Catalog Number: | DMAT 336 |
Credits: | 5 Semester Credit Hours |
Syllabus PDF: | PDF Syllabus for Honors Computational Linear Algebra |
Delivery: | Fully Online, Asynchronous, Self-Paced |
Click Here to Enroll in DMAT 336 - Honors Computational Linear Algebra |
Roger Williams University Course Catalog Listing: DMAT 336 - Honors Computational Linear Algebra
Course: DMAT 336
Course Title: Honors Computational Linear Algebra
Transcript Course Title (30 Characters Max:): Honors Comp Linear Algebra
Course 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. [5 Semester Credits]
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
PDF Course Syllabus: Detailed Course Syllabus in PDF for DMAT 336 - Honors Computational Linear Algebra
DMAT 336 - Honors Computational Linear Algebra - 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
- 7. To understand and compute bases, change of bases, spanning and linear independence, kernel and image sets
- 8. To understand and compute the diagonalization of a matrix, both with Singular Value Decomposition, and Eigenvalue - Eigenvector constructions.
- Honors Topics:
- 9.* To understand and compute interpolating polynomials and Fourier fitting and analysis
- 10.* To understand and compute the Gram-Schmidt process in relation to Singular Value Decomposition
- 11.* To understand and compute the diagonalization of a matrix when Eigenvalues are repeated and/or complex.
- 12.* To understand and compute the relationship of matrix diagonalization and dynamical systems of differential equations
- 13.* To understand and compute the Spectral Theorem
- 14.* To develop mathematical technical writing skills, culminating in a term paper on an approved topic
DMAT 336 - Honors Computational Linear Algebra - 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
Date Posted: Jan 19, 2020
Review by: William Williams
Student Email: wf.williamster@gmail.com
Courses Completed: Linear Algebra, Probability Theory
Review: I have difficulty learning calculus based math, akin to dyslexia when examining the symbolic forms, equations, definitions, and problems. Mathematica based calculus courses allowed me to continue with my studies because of the option of seeing the math expressed as a programming language for which I have no difficulty in interpreting visually and the immediate feedback of graphical representations of functions, equations, or data makes a huge impact on understanding. Mathematica based calculus courses should be the default method of teaching Calculus everywhere.
Transferred Credits to: Thomas Edison State College
Date Posted: Jul 22, 2021
Review by: Emma C.
Courses Completed: Linear Algebra
Review: This was a great course. Flexible and informative with a great professor. It's a great option if you need to fill a prerequisite fast or if you enjoy working at your own pace.
Transferred Credits to: University of Virginia
Date Posted: Aug 16, 2020
Review by: Jennifer S.
Courses Completed: Calculus I
Review: The course was intense and required a lot of hard work. Professors ready available to assist when needed. Professors presented and explained materials/course work in detail and provided explanations and resources.
Transferred Credits to: University of New Haven, West Haven, CT