Numerical Analysis Online Course for Academic Credit
Numerical Analysis covers numerical methods including interpolation, numerical integration, solution of nonlinear equations, and numerical linear algebra using Mathematica.
Course
DMAT 462 - Introduction to Numerical Analysis
Credits
4 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
RWU Course Catalog - DMAT 462 • Introduction to Numerical Analysis
Course
DMAT 462
Course Title
Introduction to Numerical Analysis
Transcript Title
Numerical Analysis
Credits
4 Semester Credit Hours
Description
An introductory course on Numerical Analysis with emphasis on the computational and visual aspects of the subject. Topics include approximation and errors, numerical differentiation, nonlinear equations, numerical linear algebra, interpolation, regression, numerical integration, numerical solutions of differential equations, and numerical optimization techniques.
Prerequisite
Successful completion with grade B or higher in Linear Algebra and Multivariable Calculus or equivalent, or consent of instructor.
E-Textbook
Numerical Methods with Applications by Kaw et al. and Elements of Numerical Analysis with Mathematica by Loustau
Software
Mathematica and LiveMath
Syllabus PDF
DMAT 462 - Learning Outcomes
- To understand the initial topics of Numerical Analysis as a springboard into Data Science and other related fields
- To understand the concept of approximation and error analysis
- To understand the techniques and necessities of numerical differentiation
- To understand the solution techniques for non-linear equations
- To understand the numerical issues of large-scale matrix algebra
- To understand the concepts of interpolation
- To understand the numerical issues involved with statistical regression
- To understand the numerical approach to integration
- To understand the numerical solution techniques for differential equations
- To understand the numerical approaches to optimization
- To understand and utilize software tools to investigate visualization and computational aspects of the subject
DMAT 462 - 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. Approximations and Errors
2.1 Introduction to Scientific Computing
2.2 Measuring Errors
2.3 Sources of Error
2.4 Binary Representation of Numbers
2.5 Floating Point Representation
2.6 Propagation of Errors
2.7 Taylor Series Revisited
3. Numerical Differentiation
3.1 Primer on Differential Calculus
3.2 Differentiation of Continuous Functions
3.3 Differentiation of Discrete Functions
3.4 Finite Differences and Vector Fields
3.5 Finite Difference Explicit Method
3.6 Neumann Stability Analysis
3.7 Finite Difference Implicit Method and Crank Nicolson
4. Nonlinear Equations
4.1 Solving Quadratic Equations Exactly
4.2 Solving Cubic Equations Exactly
4.3 Bisection Method
4.4 Newton-Raphson Method
4.5 Secant Method
4.6 False Position Method
5. Simultaneous Linear Equations
5.1 Vectors
5.2 Binary Matrix Operations
5.3 Unary Matrix Operations
5.4 System of Equations
5.5 Gaussian Elimination Method
5.6 LU Decomposition Method
5.7 How does Gauss-Seidel method work?
5.8 Adequacy of Solutions
5.9 Eigenvalues and Eigenvectors
5.10 Cholesky and LDLT Method
6. Interpolation
6.1 History of Interpolation
6.2 Direct Method
6.3 Newton Divided Difference Method
6.4 Lagrange Method
6.5 Spline Method
6.6 The lurking dangers of extrapolation!
6.7 Why is higher order interpolation a bad idea?
6.8 Why do we need spline interpolation?
6.9 How choice of points of interpolation affects approximations!
6.10 How splines can help in developing a shorter path for a robot!
7. Regression
7.1 Primer on statistical terminology
7.2 Introduction to Regression
7.3 Linear Regression
7.4 Nonlinear Regression
7.5 Adequacy of Regression Models
8. Integration
8.1 Primer on Integral Calculus
8.2 Trapezoidal Rule
8.3 Simpson 1/3 Rule
8.4 Romberg Rule
8.5 Gauss-Quadrature Rule
8.6 Discrete Data Integration
8.7 Improper Integration
8.8 Simpson 3/8 rule
8.9 Monte-Carlo Integration
9. Ordinary Differential Equations
9.1 Primer on Ordinary Differential Equations
9.2 Euler method
9.3 Runge-Kutta 2nd order method
9.4 Runge-Kutta 4th order method
9.5 On solving higher order and coupled ordinary differential equations
9.6 Shooting Method
9.7 Finite Difference
10. Optimization
10.1 Golden Section Search Method
10.2 Newton Method
10.3 Multidimensional Direct Search Method
10.4 Multidimensional Gradient Method
10.5 Simplex Method
Distance Calculus Referenced Colleges & Universities (29 Years - 393+ Institutions)
Distance Calculus students have transferred course credits to these colleges and universities:
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Distance Calculus - Student Reviews
Posted: May 21, 2020
Courses Completed: Calculus I, Calculus II
I did not enjoy Calculus I at my school. I retook Calculus I, and then Calculus II, over the summer via Distance Calculus and it was awesome. I started my sophomore year back on track and ready for my physics classes. I struggled with the MathLive software but I guess it was alright.
Transferred Credits To: University of North Carolina
Posted: Apr 5, 2020
Courses Completed: Calculus I
Calculus I from Distance Calculus was wonderful! I took AB Calculus in high school, but I didn't take the AP Calc exam. Instead I took Calculus I with Distance Calculus, and it was so much better! It was a little review of topics, but not really. I really understood calculus when I finished!
Transferred Credits To: University of Chicago
Posted: May 18, 2025
Courses Completed: Probability Theory
A great way to learn probability theory through visualizations, code, and math. Rather than just solving equations through pencil and paper, this course helped me to see how how probability distributions form and behavior through simulations and visuals. I would recommend this course to anyone looking for a way a more interactive way to learn mathematics and at their own pace.
Transferred Credits To: none yet
Posted: Jun 25, 2026
Courses Completed: Multivariable Calculus
The professor as well as the TAs give great feedback when you need help with problems and the videos are great at explaining concepts. Return time on work is good and the work is not too much to handle.
Transferred Credits To: University of Wisconsin
Posted: Jun 24, 2026
Courses Completed: Linear Algebra
This course gives a perspective on Linear algebra that no traditional course does. I’d say i gained much more intuition for this subject from the DC course than my friends who took traditional courses elsewhere. As a cs major, this version of learning with visualization has helped me a lot in understand ML models. However the course doesn’t have videos for the last 2 chapers so i had to self learn with the mathematica notebooks. Response times are a little slow but since it’s a remote class, i guess it’s justified. Overall amazing course and definitely take this over traditional lin alg classes.
Posted: Jun 24, 2026
Courses Completed: Calculus I
As a full-time business owner completing an Executive MBA, I needed to satisfy a calculus prerequisite without putting my work on hold. Distance Calculus made that possible. The fully self-paced structure let me work early mornings and weekends around an unpredictable schedule, which a fixed-semester classroom course never would have allowed.
The course covered the core business calculus material thoroughly — derivatives, optimization, integration techniques including u-substitution, the Fundamental Theorem of Calculus, improper integrals, and numerical methods. The LiveMath computer algebra environment was central to the experience: it forced me to build each step explicitly rather than just arriving at an answer, which actually deepened my understanding of the mechanics.
Communication through the student portal was responsive when I had questions. For working professionals who need a rigorous, accredited calculus course on a flexible timeline, I'd recommend it.
The course covered the core business calculus material thoroughly — derivatives, optimization, integration techniques including u-substitution, the Fundamental Theorem of Calculus, improper integrals, and numerical methods. The LiveMath computer algebra environment was central to the experience: it forced me to build each step explicitly rather than just arriving at an answer, which actually deepened my understanding of the mechanics.
Communication through the student portal was responsive when I had questions. For working professionals who need a rigorous, accredited calculus course on a flexible timeline, I'd recommend it.
Transferred Credits To: MIT Ebma
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