Skip to main content

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

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

DMAT 462 - Learning Outcomes

  1. To understand the initial topics of Numerical Analysis as a springboard into Data Science and other related fields
  2. To understand the concept of approximation and error analysis
  3. To understand the techniques and necessities of numerical differentiation
  4. To understand the solution techniques for non-linear equations
  5. To understand the numerical issues of large-scale matrix algebra
  6. To understand the concepts of interpolation
  7. To understand the numerical issues involved with statistical regression
  8. To understand the numerical approach to integration
  9. To understand the numerical solution techniques for differential equations
  10. To understand the numerical approaches to optimization
  11. 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:

Agnes Scott College • Aiken Technical College • Albany College of Pharmacy and Health Science • Alma College • American Graduate University • American Public University • American University • Andrews University • Arizona State University • Armstrong Atlantic State Univeristy • Athens State University • Auburn University • Auburn University MBA Program • Augusta State University • Austin Peay State University • Azusa Pacific University • Babson College • Baruch College • Baylor University • Belmont University • Beloit College • Bentley University • Berklee College of Music • Berry College • Bethany College • Binghamton University • Bloomsburg University • Bluefield State College • Bluegrass Community and Technical College • Borough of Manhattan Community College • Boston Conservatory • Boston University • Bryant University • Buena Vista University • California Lutheran University • California Polytechnic State University, San Luis Obispo • California state University • California State University Channel Islands • California State University, Dominguez Hills • California State University, Sacramento • Carleton College • Carnegie Mellon University • Cedarville University • Central Michigan University • Central Washington University • Champlain College • Chapman University • Charter Oak State College • Chicago State University • Clark University • Clarkson University • Clemson University • Cleveland State University • Coastal Carolina University • College of Santa Fe • College of William & Mary • Colorado Mesa University • Colorado State University • Columbia University • Columbia University School of Business • Cornell Univeristy • Cornell University • Covenant College • CUNY Medgar Evers College • Denison University • DePaul University • Drexel University • Duke University - Fuqua School of Business • Duke University School of Law • Duke University, Durham NC • Duke University, Fuqua School of Business, Law School, Graduate Programs • East Stroudsburg University • Eastern Illinois University • Eastern Kentucky University • Eastern Mennonite University • Eastern Nazarene College • Elon University • Embry Riddle Aeronautical University • Embry Riddle University • Endicott College • Evangel University • Excelsior College • Fairifield University • Fairleigh Dickenson University • Ferris State University • Florida A & M University • Florida Agricultural and Mechanical University • Florida Atlantic University • Florida Institute of Technology • Florida International University • Florida State College, Jacksonville • Florida State University • Fordham University • Fox Valley Technical College • Franklin University • Freed-Hardamen University • Fresno State University • Friends University • Gannon University • George Mason university • George Washington University • George Washington University School of Business • Georgetown University • Georgia Institute of Technology • Georgia State • Georgia State University • Georgia Tech • Gordon College • Governor's State University • Green Mountain College • Griffith University • Grinnell College • Grove City College • Hamline University • Hampshire College • Hampton University • Harvard University, Kennedy School of Government • Harvard University: Kennedy School of Government, Medical Schools • Hillsdale College • Hillsdale University • Hiram College • Hofstra University • Howard University • Huntingdon College • Illinois Institute for Technology • Illinois Institute of Technology • Indiana University • Iowa State University • Jacksonville State University • James Madison University • Jeff State Community College • Johns Hopkins Univerisity • Johns Hopkins University • Kalamazoo College • Kansas State University • Kaplan University • Kennesaw State University • Kentucky State University • Kettering University • Kings College, University of London • La Sierra University • Lebanon Valley College • Lee University • LeTourneau University • Liberty University • Lincoln University of Pennsylvania • Lipscomb University • Loma Linda University • London School of Economics • Loyola Marymount University • Luther College • Macon State College • Marian University • Marquette University • Mars Hill College • Marshall University • Mary Baldwin College • Massachusetts Maritime Academy • McHenry County College • Mercer University • Mercyhurst College • Meredith College • Mesa State College • Messiah College • Miami University • Michigan State University • Michigan Technological University • Middle Tennessee State University • Middlebury College • Millersville University • Missouri University of Science and Technology • Montana State University • Montana Tech • Montclair University • Morehead State University • Murray State University • Naval Post Graduate School • New Mexico Military Institute • New Mexico State University • New York University • North Carolina Agricultural and Technical State Univerisity • Northeastern University • Northern Arizona University • Northern Michigan University • Northwest Nazarene University • Northwestern University • Oberlin College • Occidental College • Oglethorpe University • Oklahoma Baptist University • Old Dominion University • Olympic College • Orange Coast College • Oregon State University • Pacific Lutheran University • Penn State University • Pennsylvania State University • Pepperdine University • Pomona College • Portland State University • Princeton University • Purdue University • Quinnipiac University • Randolph-Macon College • Regent University • Regis University • Rensselaer Polytechnic Institute • Rhode Island School of Design • Rice University • Robert Morris University • Rochester Institute of Technology • Roger Williams Univerity • Roger Williams University • Roosevelt University • Rowan University • Rutgers University • Saint Anselm College • Saint Joseph's University • Saint Louis University • Saint Michael's College • Salve Regina University • Samford University • San Diego State University • Santa Fe Community College • Shepherd University • Smith College • South Dakota School of Mines and Technology • Southern Adventist University • Southern Methodist University • St. Anselm College • St. John's College • St. Mary's College of Maryland • Stanford University • Stanford University, MBA • State University at Buffalo Law School • State University at Buffalo, Law School • State University of New York • Stevens Institute of Technology • Strayer University • SUNY Binghamton • Swarthmore College • Syracuse University • Texas A&M University • Texas A&M • Texas A&M University • Texas Tech University • The Art Institute of Atlanta • The Catholic University of America • The Citadel • The Citadel, Military College of South Carolina • The College of New Jersey • The College of St. Scholastica • The George Washington University • The Master's College • The New England Institute of Art • The Ohio State Universtity • The University of Alabama • The University of South Carolina • The University of Texas at Austin • The University of Virginia • Thomas Edison State College • Trinity University • TUI University • Tulane University • Union University • United States Air Force Academy • United States Military Academy • Univeristy of Puget Sound • University of Alabama, Huntsville • University of Arizona • University of Arkansas, Little Rock • University of Auckland, New Zealand • University of California, Berkeley • University of California, Los Angeles • University of California, Santa Barbara • University of California, Santa Cruz • University of Central Florida • University of Central Oklahoma • University of Central Texas • University of Chicago • University of Cincinnati • University of Colorado • University of Colorado, Boulder • University of Colorado,Colorado Springs • University of Connecticut • University of Dallas • University of Findlay • University of Florida • University of Georgia • University of Hartford • University of Hawai'i-Manoa • University of Illinois • University of Kentucky • University of La Verne • University of Maine • University of Maryland • University of Massachusetts • University of Massachusetts, Amherst • University of Memphis • University of Michigan • University of Michigan: MBA, Medical Schools, Graduate Programs • University of Minnesota • University of Minnesota, School of Public Health • University of Minnesota, Twin Cities • University of Minnesota-Twin Cities • University of Mississippi • University of Missouri • University of Missouri, Columbia • University of Montana • University Of Mount Union • University of Nebraska • University of Nevada • University of New Hampshire Law School • University of New Haven • University of New Orleans • University of North Carolina • University of North Carolina at Chapel Hill • University of North Carolina, Chapel Hill • University of North Carolina, MBA • University of North Dakota • University of North Texas • University of Northern Iowa • University of Notre Dame • University of Oklahoma • University of Otago • University of Pennsylvania • University of Pennsylvania Architectural School • University of Pennsylvania, Wharton School of Business • University of Phoenix • University of Pittsburgh • University of Portland • University of Redlands • University of Richmond • University of San Francisco • University of South Carolina • University of Southern California • University of Southern Indiana • University of Sussex • University of Tampa • University of Tennessee • University of Texas • University of Texas at Austin • University of Texas, Arlington • University of Texas, Austin • University of Texas, Brownsville • University of Texas, Dallas • University of Texas, Houston • University of Utah • University of Virginia • University of Warwick • University of West Alabama • University of West Florida • University of West Georgia • University of Wisconsin • University of Wisconsin, Madison • University of Wyoming • University West Florida • US Air Force Academy • Utah State University • Utah Valley University • Valdosta State University • Valley Forge Military College • Vanderbilt University • Villanova University • Virginia Military Institute • Virginia Tech • Walla Walla University • Washing State University • Washington and Lee University • Washington State University • Webster University • West Chester University • West Virginia University • West Virginia Wesleyan College • Western Governors University • Western Kentucky University • Western Michigan University • Westminster College • Wharton School of Business, University of Pennsylvania • Wheaton College • Wheaton College (IL) • Wheaton College Illinois • Whitman College • Whittier College • Widener University • William and Mary • William Jewell College • Winthrop University • Woodbury University • Wright State University • Yale University • Yeshiva University • Yonsei University





Distance Calculus - Student Reviews

Joe★★★★★
Posted: Jan 13, 2020
Courses Completed: Calculus II
This is the most interactive and productive online course I have ever taken. I had taken calculus before but never understood some of the underlying concepts until I took this course.
If you want to really learn calculus in a way that will stay with you for the rest of your life, take this course.
Transferred Credits To: The college of New Jersey
Lauren B.★★★★★
Posted: May 5, 2025
Courses Completed: Linear Algebra, Probability Theory
You don’t just learn in this course you understand. As someone who has always struggled with math taking advanced courses was intimidating. Dr. Curtis and his TAs made math manageable and framed the questions in a way they were applicable to real world. Thanks again!
Jennifer S.★★★★★
Posted: Aug 16, 2020
Courses Completed: Calculus I
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
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
Video Player