Mathematics (MATH) 376

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:

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