Topics for Math 2090: “Elementary Differential Equations and Linear Algebra”

Textbook

Title
Differential Equations and Linear Algebra, Fourth Edition, 2021.
Mymathlab with Pearson E-text access codes.
Authors
Edwards, Penney, and Calvis

Topics

Chapter 1: First-Order Differential Equations

Section 1.1
Differential Equations and Mathematical Models
Section 1.2
Integrals as General and Particular Solutions
Section 1.4
Separable Equations and Applications
Section 1.5
Linear First-Order Equations
Section 1.6
Exact Equations

Chapter 2: Mathematical Models and Numerical Methods

Section 2.1
Population Models
Section 2.3
Acceleration-Velocity Models

Chapter 3: Linear Systems and Matrices

Section 3.1
Introduction to Linear Systems
Section 3.2
Matrices and Gaussian Elimination
Section 3.3
Reduced Row-Echelon Matrices
Section 3.4
Matrix Operations
Section 3.5
Inverses of Matrices
Section 3.6
Determinants

Chapter 4: Vector Spaces

Section 4.1
The Vector Space $\mathbf{R}^3$
Section 4.2
The Vector Space $\mathbf{R}^3$ and Subspaces
Section 4.3
Linear Combinations and Independence of Vectors
Section 4.4
Bases and Dimension for Vector Spaces
Section 4.5
Row and Column Spaces
Section 4.7
General Vector Spaces

Chapter 5: Higher-Order Linear Differential Equations

Section 5.1
Introduction: Second-Order Linear Equations
Section 5.2
General Solutions of Linear Equations
Section 5.3
Homogeneous Equations with Constant Coefficients
Section 5.4
Mechanical Vibrations
Section 5.5
Nonhomogeneous Equations and Undetermined Coefficients
Section 5.6
Forced Oscillations and Resonance

Chapter 6: Eigenvalues and Eigenvectors

Section 6.1
Introduction to Eigenvalues
Section 6.2
Diagonalization of Matrices (optional)

Chapter 7: Linear Systems of Differential Equations

Section 7.1
First-Order Systems and Applications
Section 7.2
Matrices and Linear Systems
Section 7.3
The Eigenvalue Method for Linear Systems

Chapter 8: Matrix Exponential Methods

Section 8.1
Matrix Exponentials and Linear Systems (optional)
Section 8.2
Nonhomogeneous Linear Systems

Chapter 10: Laplace Transform Methods

Section 10.1
Laplace Transforms and Inverse Transforms
Section 10.2
Transformation of Initial Value Problems
Section 10.3
Translation and Partial Fractions
Section 10.4
Derivatives, Integrals, and Products of Transforms

Updated by Ameziane Harhad in December 2024.