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.

Overview

Mathematics 376 covers basic concepts, methods and techniques for solving ordinary Differential Equations (ODEs), and considers applications of ODEs in different areas.

Outline

Mathematics 376 consists of three main parts covering particular differential equations topics in 15 units. The main objective in each unit is to identify the corresponding type of equation or system of equations and to learn techniques for solving them.

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

Learning outcomes

Upon successful completion of this course, you should be able to

demonstrate understanding of the meaning of an ordinary differential equation (ODE), its order, its general solution, and its particular solution.

recognize and solve different types of first-order ODEs, including separable, exact, homogeneous, linear and Bernoulli equations.

solve simple applied initial value problems (IVPs) modelled with first-order ODEs, including population models, Newtonian mechanics problems, and heating and cooling problems.

apply the methods of undetermined coefficients, variation of parameters, and Laplace transform, to solve systems of linear ODEs with constant coefficients, higher-order differential equations, homogeneous and nonhomogeneous equations, and IVPs for systems of first-order linear equations and single higher-order linear equations with constant coefficients.

apply concepts of power series and reduction to linear ODEs to solve differential equations with variable coefficients, including Cauchy-Euler equations.

demonstrate understanding of concepts related to phase plane analysis, such as autonomous systems, phase plane, critical (equilibrium) points, and their stability and classification.

Evaluation

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

Activity

Weight

Assignment 1 (Part I)

5%

Assignment 2 (Part II)

5%

Assignment 3 (Part III)

5%

Assignment 4

5%

Midterm Examination

30%

Final Examination

50%

Total

100%

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

Materials

Nagle, R. K., Saff, E. B., & Snider, A. D. (2018). Fundamentals of Differential Equations (9th ed.). Pearson. (eText)

Maymeskul, V. (2018). Student’s Solutions Manual (7th ed.). Pearson. (eText)

Nagle, R. K., Saff, E. B., & Snider, A. D. Student Access Kit: MyLab Math for Fundamentals of Differential Equations. Pearson MyLab. (eText)

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.