Mathematics (MATH) 376

Ordinary Differential Equations (Revision 5)

MATH 376 Course cover

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Mathematics Diagnostic Assessment. This online test contains 70 questions that will help you assess your mathematical skills. Based on your score we will recommend which Athabasca University mathematics course you are likely ready to take successfully.

Delivery Mode: Individualized study

Credits: 3

Area of Study: Science

Prerequisite: MATH 265, MATH 266 and MATH 270 or their equivalents.

Centre: Centre for Science

MATH 376 is not available for challenge.

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MATH 376 covers basic concepts, methods and techniques for solving ordinary differential equations (ODEs), and considers applications of ODEs in different areas.


Part I: First-order Differential Equations

  • Unit 1: Introducing Ordinary Differential Equations
  • Unit 2: Directly Integrable Ordinary Differential Equations Resolved in Terms of the Derivative
  • Unit 3: Reduction to Separable Equations
  • Unit 4: Reduction to Exact Equations: Integrating Factors
  • Unit 5: First-order Equations not Resolved with Respect to the Derivative: Parametric Solutions
  • Unit 6: Initial Value Problems for a Single First-order Differential Equation

Part II: Systems of Ordinary Differential Equations with Constant Coefficients

  • Unit 7: The Basic Theory of Systems of Linear Ordinary Differential Equations
  • Unit 8: Systems of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients
  • Unit 9: Particular Solutions for Nonhomogeneous Linear Ordinary Differential Equations
  • Unit 10: Laplace Transforms
  • Unit 11: Initial Value Problems from the Perspective of Laplace Transforms

Part III: Beyond Linear Equations with Constant Coefficients

  • Unit 12: Some Cases of Reduction for Linear Ordinary Differential Equations
  • Unit 13: Power Series Solutions to Ordinary Differential Equations with Analytic Coefficients
  • Unit 14: Non-analytic Coefficients: The Method of Frobenius
  • Unit 15: Autonomous Systems of Two Equations and Numeric Approximations to Solutions of Initial Value Problems for Systems of Ordinary Differential Equations


To receive credit for MATH 376, you must achieve a grade of at least “50” per cent on the final examination, and a course composite grade of at least (50 percent). The weighting of the composite grade is as follows:

Assignment 1 (Part I) Assignment 2 (Part II) Assignment 3 (Part III) Final Exam Total
13% 14% 13% 60% 100%

To learn more about assignments and examinations, please refer to Athabasca University's online Calendar.

Course Materials


Nagle, R. K., Saff E. B., and Snider A. D. Fundamentals of Differential Equations, 7th ed. Boston: Pearson/Addison Wesley, 2008.

Maymeskul, V. Student's Solutions Manual to Accompany Fundamentals of Differential Equations 7th Edition and Fundamentals of Differential Equations and Boundary Value Problems 5th Edition. Boston: Pearson/Addison Wesley, 2008. (Electronic copy)

Other Materials

The course materials include a study guide, a student manual and an assignment manual.

Athabasca University reserves the right to amend course outlines occasionally and without notice. Courses offered by other delivery methods may vary from their individualized-study counterparts.

Opened in Revision 5, October 19, 2010

View previous syllabus

Updated May 20 2016 by Student & Academic Services