MATH 308 - Differential Equations

MATH 308 - Differential Equations teaser image

Ordinary differential equations, solutions in series, solutions using Laplace transforms, systems of differential equations.

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Section 7.1 to 7.9 (Modules 10-12) require some knowledge about linear algebra (matrices, eigenvectors, eigenvalues, etc.). The VMLC has a workshop, Linear Algebra for MATH 308, that covers the linear algebra necessary for those sections. You can use that workshop as an introduciton or review of all those linear algebra concepts.

Sections

Module 1

Section 1.1 - Some Basic Mathematical Models; Direction Fields Section 1.2 - Solutions of Some Differential Equations Section 1.3 - Classification of Differential Equations

Module 2

Section 2.1 - Linear Equations; Method of Integrating Factors Section 2.2 - Separable Equations Section 2.3 - Modeling with First Order Equations

Module 3

Section 2.4 - Differences Between Linear and Nonlinear Equations Section 2.5 - Autonomous Equations and Population Dynamics Section 2.6 - Exact Equations and Integrating Factors

Module 4

Additional Exam 1 Problems Section 3.1 - Homogeneous Equations with Constant Coefficients Section 3.2 - Solutions of Linear Homogeneous Equations Section 3.3 - Complex Roots of the Characteristic Equation

Module 5

Section 3.4 - Repeated Roots; Reduction of Order Section 3.5 - Nonhomogeneous Equations; Method of Undetermined Coefficients Section 3.6 - Variation of Parameters

Module 6

Section 3.7 - Mechanical and Electrical Vibrations Section 3.8 - Forced Vibrations

Module 7

Section 6.1 - Definition of the Laplace Transform Section 6.2 - Solution of Initial Value Problems [via Laplace Transforms] Section 6.3 - Step Functions

Module 8

Section 6.4 - Differential Equations with Discontinuous Forcing Functions Section 6.5 - Impulse Functions Section 6.6 - The Convolution Integral Exam 2 Review

Module 9

Section 5.1 - Review of Power Series Section 5.2 - Series Solutions Near an Ordinary Point I

Module 10

Section 5.3 - Series Solutions Near an Ordinary Point II Linear Algebra Workshop for MATH 308 Section 7.1 - Introduction [to Systems of 1st Order Equations]

Module 11

Section 7.4 - Basic Theory of Systems of First Order Linear Equations Section 7.5 - Homogeneous Linear Equations with Constant Coefficients Section 7.6 - Complex Eigenvalues Section 7.7 - Fundamental Matrices

Module 12

Section 7.8 - Repeated Eigenvalues Section 7.9 - Nonhomogeneous Linear Systems

Module 15

Final Exam Review