Notation:
B = the book Introduction to Differential Equations (2nd edition) by Michael E. Taylor
N = Online Notes by Pichkitti Bannangkoon
| Date | Topic | References | Lecture Notes |
|---|---|---|---|
| M 01/24/2022 | Introduction to course; Classification of Ordinary Differential Equations (ODE); Solutions of ODE. | N - Sections 1.1, 1.2 | Lecture1 |
| W 01/26/2022 | The exponential and trigonometric functions; First order linear equations; | B - Sections 1.1, 1.2 N - Section 2.1.3 | Lecture 2 |
| M 01/31/2022 | Examples on first order ODE; General solution and Initial Value Problem; Implicit and Explicit solutions; Separable equations; | B - Sections 1.2, 1.3 N - Sections 2.1.1, 2.1.3 | Lecture 3 |
| W 02/02/2022 | 2nd order differential equations x''=f(t,x,x'); Special cases when f is independent of x and f is independent of t; Physics application. | B - Sections 1.4, 1.5 N - Section 3.8 | Lecture 4 |
| M 02/07/2022 | Second order constant-coefficient linear equations-homogeneous (two distinct real roots and repeated real roots cases) | B - Section 1.9 N - Sections 3.2.1, 3.2.3 | Lecture 5 |
| W 02/09/2022 | Second order constant-coefficient linear equations-homogeneous with two complex conjugate roots | B - Section 1.9 N - Section 3.2.2 | Lecture 6 |
| M 02/14/2022 | Nonhomogeneous equation. Finding a particular solution using the method of undetermined coefficients. | B - Section 1.10 N - Section 3.6.1 Handout | Lecture 7 |
| W 02/16/2022 | Finding a particular solution using the method of undetermined coefficients. Mechanical vibrations. | B - Section 1.10 N - Section 3.6.1, 3.7 Handout - Mechanical Vibrations | Lecture 8 |
| M 02/21/2022 | Undamped free vibrations; Damped free vibrations. | B - Sections 1.12, 1.9 N- Sections 3.7.1, 3.7.2 | Lecture 9 |
| W 02/23/2022 | Undamped forced vibrations (beat and resonance); Higher order linear homogeneous equations with constant coefficients; Wronskian determinant. | B- Sections 1.12, 1.9, 1.17, 1.14 N- Sections 3.7.3, 4, 3.1 | Lecture 10 |
| M 02/28/2022 | Abel's theorem; Use Wronskian to solve a second order linear homogeneous equation. Laplace transform | B - Sections 1.15, 1.18 N - Sections 3.5, 5.1 | Lecture 11 |
| W 03/02/2022 | Laplace Transform and Inverse Laplace Transform; Step Functions. | B - Section 1.18 N - Sections 5.3, 5.4.1, 5.5 Handout - Partial Fraction Decomposition Handout - Laplace Transform for solving ODI | Lecture 12 |
| M 03/07/2022 | Step Functions. | N - Section 5.5 | Lecture13 |
| W 03/09/2022 | Midterm | ||
| M 03/14/2022 | Spring Break - no class | ||
| W 03/16/2022 | Spring Break - no class | ||
| M 03/21/2022 | Vector spaces; Linear transformations. | B - Sections 2.1, 2.2 | Lecture 14 |
| W 03/23/2022 | Definitions of injective, surjective, isomorphism, invertible for linear transformations; A basis for a subspace of a vector space. | B- Section 2.3 | Lecture 15 |
| M 03/28/2022 | Coordinates; Properties of a basis. Isomorphism with R^n of a vector space with a basis with n vectors in it; Examples on how to use linear systems to answer questions on span, linear independence, basis, etc. | B- Section 2.3 | Lecture 16 |
| W 03/30/2022 | Examples on how to use linear systems to answer questions on span, linear independence, basis, etc. (continue). Linear transformations and their matrix representation. | B - Section 2.4 | Lecture 17 |
| M 04/04/2022 | The simple form of a linear transformation if we can choose bases for domain and codomain; Rank-Nullity Theorem; Eigenvalues and eigenvectors. | B - Sections 2.4, 2.6 | Lecture18 |
| W 04/06/2022 | Algorithm to find eigenvalues and eigenvectors; Why having a basis of eigenvectors is useful? Diagonal matrices. | B - Section 2.6 | Lecture 19 |
| M 04/11/2022 | Diagonalization; Linear algebra interpretation of linear differential equation; | B - Sections 2.6 | Lecture 20 |
| W 04/13/2022 | Rewrite a system of linear differential equations as a system of first order linear differential equations. | B - Section 3.3 | Lecture 21 |
| M 04/18/2022 | How to compute the matrix exponential; Change of basis. | B - Sections 2.4, 3.1 | Lecture 22 |
| W 04/20/2022 | Diagonalization of a matrix and computing matrix exponential; Nonhomogeneous equations and Duhamel's formula; RLC circuit example as application. | B - Sections 3.1, 3.4, 3.5 | Lecture 23 |
| M 04/25/2022 | Method of undetermined coefficients for linear systems; Power series method; Existence and uniqueness theorems. | B - Sections 3.10, 4.1 | Lecture 24 |
| W 04/27/2022 | Existence and uniqueness theorem for the first order differential equation. The version for the linear equation. | B - Section 4.1 N - Section 2.2 | Lecture 25 |
| M 05/02/2022 | Proof of the existence and uniqueness theorem | B - Section 4.1 | Lecture 26 |
| W 05/04/2022 | Review | ||
| Tu 05/17/2022 | Final Exam |