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.