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Differential Equations + Linear Algebra - Combined Course

Differential Equations + Linear Algebra is a combined 5-credit course covering ordinary differential equations and linear algebra, emphasizing the deep connections between the two subjects, using LiveMath.

Thomas Attractor
Thomas Attractor

Why a Combined Course?

DMAT 346 is a single sophomore-level course covering the standard topics of both Differential Equations and Linear Algebra. We offer it because many colleges and universities across the USA structure these as one combined course rather than two separate ones, usually to lighten the load on engineering and physics students who would otherwise be taking two full courses in the same semester.

The content of DMAT 346 is exactly the same as our standalone DMAT 335 - Linear Algebra and DMAT 321 - Differential Equations courses. Same curriculum, same depth, same mastery standard. It is just packaged together for students whose degree plans expect the combined version.

How DMAT 346 Is Structured

The course is built as 15 modules that alternate between the two subjects. You complete one module from the Linear Algebra side, then one module from the Differential Equations side, and back again, all the way through:

  • Module 1: Linear Algebra
  • Module 2: Differential Equations
  • Module 3: Linear Algebra
  • Module 4: Differential Equations
  • ... continues alternating ...
  • Module 15: final module

By the time you finish the 15th module, you have completed the full content of both subjects, in lockstep with each other.

A Long Course - Plan Accordingly

By its very nature DMAT 346 is the longest course we offer, eclipsing even the marathon Calculus II course. This is not a course that can be done quickly or on a fast-track schedule.

  • If you need a faster route through one or both subjects, the standalone DMAT 335 (Linear Algebra) and DMAT 321 (Differential Equations) courses are better choices, since each can be sized to its own schedule.
  • If your transfer plans include a school whose curriculum requires the combined course, then DMAT 346 will articulate more cleanly than transferring two separate courses, and the longer timeline is worth it for the transfer fit.

The Mathematical Payoff: Where Linear Algebra and Differential Equations Meet

Linear Algebra and Differential Equations are deeply related, and the combined course leans into that connection in a way that two separate courses never can.

In the last part of the Differential Equations content - when you reach flows and phase portraits of systems of linear differential equations - the work starts to feel much more like a Linear Algebra course:

  • You use eigenvalues and eigenvectors to characterize the behavior of solutions.
  • You diagonalize matrices as a technique for solving systems of differential equations.

At the same time, in the Linear Algebra portion of the course you are marching toward exactly those sections: eigenvalues, eigenvectors - all a payoff of starting the Linear Algebra course with a thorough study of SVD analysis - so you reach the concluding material together like two asymptotic curves joining smoothly. So when you hit those sections in the Linear Algebra side, you are simultaneously seeing the same topic on the Differential Equations side.

That is a wonderful blending. Instead of two separate courses with overlapping mathematical themes, you watch a single subject reveal itself in both algebraic and dynamical form. By the end, you have become a master of both Linear Algebra and Differential Equations through one large 5-credit course.

Course
DMAT 346 - Differential Equations & Linear Algebra
Credits
5 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced

RWU Course Catalog - DMAT 346 • Differential Equations & Linear Algebra
Course
DMAT 346
Course Title
Differential Equations & Linear Algebra
Transcript Title
Differential Eqns + Linear Algebra (Combined)
Credits
5 Semester Credit Hours
Description
A combined course in differential equations and 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, bases, Eigenvalues and Eigenvectors, matrix decomposition and diagonalization; 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.
Prerequisite
Successful completion (C- or higher) of Calculus II or equivalent, or consent of instructor.
E-Textbook
Differential Equations + Matrices, Geometry & Mathematica by Davis/Porta/Uhl
Software
Mathematica and LiveMath
Lorenz Attractor
Lorenz Attractor

DMAT 346 - 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
  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 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 via SVD and Eigenvalue-Eigenvector constructions
  10. To understand orthogonalization and the Gram-Schmidt process
  11. To understand the core construction of the differential equation and its classification
  12. To understand the role of the forcing function in differential equations
  13. To understand, observe, and compute steady state solutions for differential equations
  14. To understand, observe, and compute solutions with various forcing functions including DiracDelta, step, oscillatory
  15. To understand and compute solutions of second order differential equations and oscillators
  16. To understand and compute manual solutions using classical techniques
  17. To understand and compute with the Laplace Transform method
  18. To understand and compute graphical and numerical solution methods
  19. To understand and compute solutions of linear systems of differential equations
  20. To understand and compute polynomial approximations to solutions of differential equations
Laplace Transform
Laplace Transform

DMAT 346 - 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, Rotations, Shears, Rigid Motions
3.5 Linear Transformations
3.6 Inverses
3.7 Determinants
3.8 Transposes
3.9 Singular Value Decomposition and Geometry
3.10 Rank and Nullity
3.11 Projections
3.12 Higher Dimensions: 2D, 3D, 4D
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 Orthonormal Bases and Gram-Schmidt Process
5. Eigenvalues and Eigenvectors
5.1 Diagonalization of a Matrix
5.2 Eigenvalues
5.3 Eigenvectors
5.4 Exponential of a Matrix
5.5 Dynamical Systems
5.6 Trace, Determinant
5.7 SVD Analysis and Eigenvalue Decomposition Connection via Transposes
6. Exponential Differential Equations
6.1 Unforced DEs
6.2 Forced DEs
6.3 Steady State
6.4 Personal Finance
6.5 Step Function and Dirac Delta Function
6.6 Tangent Vectors
6.7 Initial Conditions
6.8 Integration Factors
7. Second-Order Differential Equations
7.1 Overdamped and Underdamped Oscillators
7.2 Linear Forced and Unforced Oscillators
7.3 Homogeneous and Inhomogeneous Equations
7.4 Convolution Method
7.5 Characteristic Equations
7.6 Euler Formula
7.7 Impulse Forcing
7.8 Dirac Delta Convolutions
7.9 Springs and Electrical Charges
7.10 Higher Order Equations
8. Laplace Transforms
8.1 Laplace Transforms of First and Second Order Equations
8.2 Fourier Analysis and Fourier Fit Approximations
9. Graphical Analysis of Differential Equations
9.1 Euler Method
9.2 Flow Plots and Trajectories
9.3 Predator-Prey Model
9.4 Logistic Harvesting
10. First-Order Differential Equations
10.1 Autonomous Equations
10.2 Non-Autonomous Equations
10.3 Separation of Variables Solving Method
11. Systems of Differential Equations
11.1 Flows and Trajectories
11.2 Conversion Between Higher Order ODEs and Systems
11.3 Relationship to Eigenvalues and Eigenvectors
12. Power Series Solutions of Differential Equations
12.1 Recursion Relations
12.2 Comparing Series Solution to Numerical Solution
12.3 Barriers
Aizawa Attractor
Aizawa Attractor

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
Flow Plots
Flow Plots





Distance Calculus - Student Reviews

I.★★★
Posted: May 5, 2025
Courses Completed: Calculus II
The course material was well explained through the videos and notebooks, and it was nice to receive feedback on each assignment and correct any mistakes. However, the software required for the course was ridiculously outdated, to the point where I had to reinstall a very old operating system on my computer to even be able to run it. It was annoying and tedious to use, and it sometimes crashed. The graders were also sometimes overly picky about the way that concepts had to be explained to be considered correct (specific wording, etc), but it wasn’t too bad. Having multiple final exams seemed a bit excessive but again was not too bad. Overall, the main strength of this course is that it is completely asynchronous and self-paced, so I do recommend it if that is the most important factor to you. You will learn all of the material thoroughly, but you must be willing to deal with the more annoying aspects of the course (primarily the outdated technology).
Laura T.★★★★★
Posted: May 18, 2025
Courses Completed: Linear Algebra
I completed the Linear Algebra course as a prerequisite to an M.Ed program in Mathematics. I worked entirely at my own pace, it was cheap, I actually learned the material. This was not a "pay your fee, take your B" type of class. I had to demonstrate true understanding in order to earn credit. Dr. Curtis was responsive and helpful when I had questions. All in all I would recommend this course and any other Distance Calculus course.
Transferred Credits To: James Madison University
Aileen C.★★★★★
Posted: Dec 8, 2020
Courses Completed: Differential Equations
This course may be more difficult than your average differential equations course, which better prepares you to use these skills in your degree. The self-learning does make learning some of the concepts challenging, but you get the help you need to understand these concepts.
Transferred Credits To: Johns Hopkins University
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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