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Mathematics (MATH) 376

Ordinary Differential Equations (Revision 4)

MATH 376 Course cover

Revision 4 closed, replaced by current version.

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:Reading course - Science

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

Centre:Centre for Science

MATH 376 is not available for challenge.

Overview

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

Outline

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: Limitations of Previous Methods (Optional)
  • Unit 6: First-order Equations: Parametric Solutions
  • Unit 7: Initial Value Problems for a Single First-order Differential Equation
  • Unit 8: Numerical Solutions to Initial Value Problems for a Single First-order Differential Equation

Part II: Systems of Ordinary Differential Equations and Higher-order Linear Equations with Constant Coefficients

  • Unit 9: Reducing Systems of First-order Linear Differential Equations to Higher-order Linear Equation
  • Unit 10: Linear Differential Equations
  • Unit 11: Homogeneous Systems with Constant Coefficients
  • Unit 12: The Undetermined Coefficients Method for Finding yp
  • Unit 13: Variation of Parameters
  • Unit 14: Equations Reducible to Linear Equations with Constant Coefficients
  • Unit 15: Solving Initial Value Problems and Boundary Value Problems on the Basis of General Solutions
  • Unit 16: Initial Value Problems from the Perspective of Laplace Transforms

Part III: Beyond Linear Equations with Constatnt Coefficients

  • Unit 17: Linear Equations with Nonconstant Coefficients: Reduction of Order
  • Unit 18: Power Series; Taylor's Series; Radius of Convergence; Analytic Functions
  • Unit 19: Power Series Solutions to Ordinary Differential Equations with Analytic Coefficients
  • Unit 20: Non-analytic Coefficients: The Method of Frobenius
  • Unit 21: Beyond Linear Ordinary Differential Equations: Some Special Cases
  • Unit 22: Numerical Solutions to Equations of Higher than First Order by the Vectorized Runge-Kutta Method
  • Unit 23: Autonomous Systems of Two Equations and the Phase Plane

Evaluation

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 “D” (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

Textbooks

Nagle, R. K., Saff E. B., and Snider A. D. Fundamentals of Differential Equations, 6th ed. Boston: Pearson/Addison Wesley, 2004.

Maymeskul, V. Student’s Solutions Manual to Accompany Fundamentals of Differential Equations Sixth Edition and Fundamentals of Differential Equations and Boundary Value Problems Fourth Edition. Boston: Pearson/Addison Wesley, 2004.

Other Materials

The course materials include a study guide, student manual and an assignment manual. For additional help, visit our math lab site.

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 4, May 9, 2008.

View previous syllabus

Last updated by SAS  09/10/2013 12:09:42