Differential Equations (No Linear Algebra Required)

Mathematics

Tác giả: Marilena Beckstrand, Adam Manriquez & Emad Shonoda
Nhà xuất bản: Mt. San Jacinto College
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 88 mục

01: Introduction to Differential Equations
1.01: Introduction to Differential Equations
1.1E: Introduction to Differential Equations (Exercises)
1.02: Classification of Differential Equations
1.2E: Classification of Differential Equations (Exercises)
1.03: Existence and Uniqueness of Solutions
1.3E: Existence and Uniqueness of Solutions (Exercises)
02: First Order Equations
2.01: Integrals as Solutions
2.1E: Integrals as Solutions (Exercises)
2.02: Slope Fields
2.2E: Slope Fields (Exercises)
2.03: Separable Equations
2.3E: Separable Equations (Exercises)
2.04: First Order Linear Differential Equations
2.4E: First Order Linear Differential Equations (Exercises)
2.05: Exact Equations
2.5E: Exact Equations (Exercises)
2.06: Substitution
2.6E: Substitution (Exercises)
2.07: Numerical Methods- Eulers Method
2.7E: Numerical Methods- Eulers Method (Exercises)
03: Applications of First Order Equations
3.01: Growth and Decay
3.1E: Growth and Decay (Exercises)
3.02: Cooling and Mixing
3.2E: Cooling and Mixing (Exercises)
3.03: Newton's Second Law of Motion
3.3E: Elementary Mechanics (Exercises)
04: Higher Order Linear ODEs
4.01: Homogeneous Linear Second Order Equations
4.1E: Homogeneous Linear Second Order Equations (Exercises)
4.02: Nonhomogeneous Linear Second Order Equations
4.2E: Nonhomogeneous Linear Second Order Equations (Exercises)
4.03: Reduction of Order
4.3E: Reduction of Order (Exercises)
4.04: Homogeneous Linear Second Order Equations with Constant Coefficients
4.4E: Homogeneous Linear Second Order Equations with Constant Coefficients (Exercises)
4.05: Homogeneous Linear Higher-Order Differential Equations
4.5E: Homogeneous Linear Higher-Order Differential Equations (Exercises)
4.06: Undetermined Coefficients - Annihilator Approach
4.6E: Undetermined Coefficients - Annihilator Approach (Exercises)
4.07: Variation of Parameters
4.7E: Variation of Parameters (Exercises)
4.08: Cauchy-Euler Equations
4.8E: Cauchy-Euler Equations (Exercises)
4.09: Systems of Linear Equations by Systemic Elimination
4.9E: Systems of Linear Equations by Systemic Elimination (Exercises)
05: Applications of Second Order Linear Equations
5.01: Applications of Second-Order Differential Equations
5.1E: Spring-Mass Problems (Exercises)
06: Series Solutions of Linear Equations
6.01: Review of Power Series
6.1E: Review of Power Series (Exercises)
6.02: Series Solutions About Ordinary Points
6.2E: Series Solutions About Ordinary Points (Exercises)
6.03: Singular Points and the Method of Frobenius
6.3E: Singular Points and the Method of Frobenius (Exercises)
07: Laplace Transform
7.01: Introduction to the Laplace Transform
7.1E: Introduction to the Laplace Transform (Exercises)
7.02: The Inverse Laplace Transform
7.2E: The Inverse Laplace Transform (Exercises)
7.03: Solution of Initial Value Problems
7.3E: Solution of Initial Value Problems (Exercises)
7.04: Derivatives of Laplace Transforms and Linear Models
7.4E: Derivatives of Laplace Transforms and Linear Models (Exercises)
7.05: Convolution
7.5E: Convolution (Exercises)
08: Appendices
8.01: Functions of Several Variables
8.1E: Functions of Several Variables (Exercises)
8.02: Partial Derivatives
8.2E: Partial Derivatives (Exercises)
8.03: Determinants and Cramer's Rule for 2 X 2 Matrices
8.3E: Determinants and Cramer's Rule for 2 X 2 Matrices (Exercises)
8.04: A Brief Table of Integrals
8.05: A Brief Table of Trigonometric Identities and Logarithmic Laws
8.06: A Brief Table of Laplace Transforms
09: Answers to Exercises
9.01: Chapter 1 Answers
9.02: Chapter 2 Answers
9.03: Chapter 3 Answers
9.04: Chapter 4 Answers
9.05: Chapter 5 Answers
9.06: Chapter 6 Answers
9.07: Chapter 7 Answers
9.08: Table of Contents