Linear Algebra and Differential Equations

Differential Equations and Linear Algebra Class Notes

Keywords: differential equations notes, linear algebra notes, Edwards and Penney, Euler method, eigenvalues, vector spaces, Laplace transform, linear systems, power series.

As an instructor for linear algebra and differential equations, I prepared these class notes as a review of the sections in Differential Equations and Linear Algebra by Edwards and Penney. They include example problems which have been worked out in some detail. I hope you find these useful.

Class Notes In-Class Exercises Solutions
1.1 Differential Equations and Mathematical Models Exercises 1.1 Solutions 1.1
1.2 Integrals as General and Particular Solutions Exercises 1.2 Solutions 1.2
1.3 Slope Fields and Solution Curves Exercises 1.3 Solutions 1.3
1.4 Separable Equations Exercises 1.4 Solutions 1.4
1.5 Linear First-Order Equations Exercises 1.5 Solutions 1.5
1.6 Substitution Method, Exact Equations Exercises 1.6 Solutions 1.6
2.1 Mathematical Models and Numerical Methods Exercises 2.1 Solutions 2.1
2.2 Equilibrium Solutions and Stability Exercises 2.2 Solutions 2.2
2.3 Acceleration Velocity Models — —
2.4 Euler Method Exercises 2.4 Solutions 2.4
2.5 Advanced Euler Method — —
3.1 & 3.2 Linear Systems Exercises 3.1
Exercises 3.2		 Solutions 3.1
Solutions 3.2
3.3 Reduced Echelon Matrices Exercises 3.3 Solutions 3.3
3.4 Matrix Operations Exercises 3.4 Solutions 3.4
3.5 Inverses of Matrices Exercises 3.5 Solutions 3.5
3.6 Determinants Exercises 3.6 Solutions 3.6
3.7 Linear Equations and Curve Fitting — —
4.1 Vector Space Exercises 4.1 Solutions 4.1
4.2 Subspaces Exercises 4.2 Solutions 4.2
4.3 Linear Combinations and Independence of Vectors Exercises 4.3 Solutions 4.3
4.4 Bases and Dimension for Vector Spaces Exercises 4.4 Solutions 4.4
4.5 Row and Column Spaces — —
4.7 General Vector Spaces — —
5.1 Second-Order Linear Equations Exercises 5.1 Solutions 5.1
5.2 General Solutions of Linear Equations Exercises 5.2 Solutions 5.2
5.3 Homogeneous Equations with Constant Coefficients Exercises 5.3 Solutions 5.3
5.4 Mechanical Vibrations — —
5.5 Nonhomogeneous Equations, Undetermined Coefficients Exercises 5.5 Solutions 5.5
5.6 Forced Oscillations and Resonance — —
6.1 Eigenvalues Exercises 6.1 Solutions 6.1
6.2 Diagonals of Matrices Exercises 6.2 Solutions 6.2
6.3 Powers of Matrices Exercises 6.3 Solutions 6.3
7.1 First-Order Systems Exercises 7.1 Solutions 7.1
7.2 Matrices and Linear Systems Exercises 7.2 Solutions 7.2
7.3 Eigenvalue Method for Linear Systems Exercises 7.3 Solutions 7.3
7.4 Solution Curves of Linear Systems Exercises 7.4 Solutions 7.4
7.5 Second Order Systems and Mechanical Applications — —
7.6 Multiple Eigenvalue — —
7.7 Numerical Methods for Systems — —
8.2 Nonhomogeneous Linear Differential Equations Exercises 8.2 Solutions 8.2
9.1 Stability and the Phase Plane Exercises 9.1 Solutions 9.1
9.2 Linear and Almost Linear Systems Exercises 9.2 Solutions 9.2
9.3 Ecological Models — —
10.1 Laplace Transform Exercises 10.1 Solutions 10.1
10.2 Laplace Transformation of Initial Value Problems Exercises 10.2 Solutions 10.2
10.3 Translation and Partial Fractions — —
11.1 Power Series Method Exercises 11.1 Solutions 11.1