Course Notes for Math 252
Course Notes for Math 252
Textbook
Zill, A First Course in Differential Equations, 11th edition
Section 1.1 Definitions and Terminology
Section 1.2 Initial-Value Problems
Section 2.2 Separable Equations
Section 2.3 Linear Equations
Video: How to use the integrating factor method (4 minutes)
Section 2.4 Exact Equations
Video: Exact DE (6 minutes) This video illustrates method 1 from the notes.
Video: Exact DE (3 minutes) This video illustrates method 2 from the notes.
Section 2.5 Solutions by substitutions
Video: Homogeneous DE (8 minutes)
Section 3.1 Linear Models
Section 4.1 Preliminary Theory - Linear Equations
Section 4.2 Reduction of Order
Section 4.3 Homogeneous Linear Equations with Constant Coefficients
Section 4.4 Method of Undetermined Coefficients
Handout: Method of Undetermined Coefficients
Section 4.6 Variation of Parameters
Section 4.7 Cauchy-Euler Equations
Handout: Constant coefficients and Cauchy-Euler equations
Section 5.1 (part 1) Linear Models: Initial-Value Problems
Section 5.1 (part 2) Driven Motion
Section 5.1 (part 3) LRC circuits
External link: Applications of 2nd order DEs (it includes great examples)
Handout: Linear combination of Sine and Cosine
Section 6.1 Review of Power Series
Handout: Basic Maclaurin series
Section 6.2 Solutions About Ordinary Points
Section 7.1 Definition of the Laplace Transform
Handout: Table of Laplace transforms
Section 7.2 Inverse Transforms and Transforms of Derivatives
Math 250A review: Section 8.5 Partial Fractions
Handout: Partial fractions
Section 7.3 Operational Properties I
Desmos graph of the current in example 11
Section 7.4 Operational Properties II
Transform of a Periodic Function (won't be tested, it's for electronics students)
Proof of the convolution theorem
Section 7.5 The Dirac Delta Function
External link: Dirac delta function
Section 8.1 Preliminary Theory - Linear Systems
Math 251 review: Section 4.1 Introduction to Eigenvalues and Eigenvectors
Section 8.2 Homogeneous Linear Systems
Section 8.3 Nonhomogeneous Linear Systems