Elementary Differential Equations with Boundary Values Problems

This text is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. This book is intended to serve as the book for students in MAT 266 Differential Equations with Linear Algebra at Community College of Denver.

Mathematics

Tác giả: William F. Trench
Nhà xuất bản: Trinity University
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· 174 mục

01: Introduction
1.01: Applications Leading to Differential Equations
1.02: Basic Concepts
1.2E: Basic Concepts (Exercises)
1.03: Direction Fields for First Order Equations
1.3E: Direction Fields for First Order Equations (Exercises)
02: First Order Equations
2.01: Linear First Order Equations
2.1E: Linear First Order Equations (Exercises)
2.02: Separable Equations
2.2E: Separable Equations (Exercises)
2.03: Existence and Uniqueness of Solutions of Nonlinear Equations
2.3E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
2.04: Transformation of Nonlinear Equations into Separable Equations
2.4E: Transformation of Nonlinear Equations into Separable Equations (Exercises)
2.05: Exact Equations
2.5E: Exact Equations (Exercises)
2.06: Integrating Factors
2.6E: Integrating Factors (Exercises)
03: Numerical Methods
3.01: Euler's Method
3.1E: Eulers Method (Exercises)
3.02: The Improved Euler Method and Related Methods
3.2E: The Improved Euler Method and Related Methods (Exercises)
3.03: The Runge-Kutta Method
3.3E: The Runge-Kutta Method (Exercises)
04: Applications of First Order Equations
4.01: Growth and Decay
4.1E: Growth and Decay (Exercises)
4.02: Cooling and Mixing
4.2E: Cooling and Mixing (Exercises)
4.03: Elementary Mechanics
4.3E: Elementary Mechanics (Exercises)
4.04: Autonomous Second Order Equations
4.4E: Autonomous Second Order Equations (Exercises)
4.05: Applications to Curves
4.5E: Applications to Curves (Exercises)
05: Linear Second Order Equations
5.01: Homogeneous Linear Equations
5.1E: Homogeneous Linear Equations (Exercises)
5.02: Constant Coefficient Homogeneous Equations
5.2E: Constant Coefficient Homogeneous Equations (Exercises)
5.03: Nonhomogeneous Linear Equations
5.3E: Nonhomgeneous Linear Equations (Exercises)
5.04: The Method of Undetermined Coefficients I
5.4E: The Method of Undetermined Coefficients I (Exercises)
5.05: The Method of Undetermined Coefficients II
5.5E: The Method of Undetermined Coefficients II (Exercises)
5.06: Reduction of Order
5.6E: Reduction of Order (Exercises)
5.07: Variation of Parameters
5.7E: Variation of Parameters (Exercises)
06: Applications of Linear Second Order Equations
6.01: Spring Problems I
6.1E: Spring Problems I (Exercises)
6.02: Spring Problems II
6.2E: Spring Problems II (Exercises)
07: Series Solutions of Linear Second Order Equations
7.01: Review of Power Series
7.1E: Review of Power Series (Exercises)
7.02: Series Solutions Near an Ordinary Point I
7.2E: Series Solutions Near an Ordinary Point I (Exercises)
7.03: Series Solutions Near an Ordinary Point II
7.3E: Series Solutions Near an Ordinary Point II (Exercises)
Prelude to Series Solutions of Linear Second Order Equations
08: Laplace Transforms
8.01: Introduction to the Laplace Transform
8.1E: Introduction to the Laplace Transform (Exercises)
8.02: The Inverse Laplace Transform
8.2E: The Inverse Laplace Transform (Exercises)
8.03: Solution of Initial Value Problems
8.3E: Solution of Initial Value Problems (Exercises)
8.04: A Brief Table of Laplace Transforms
09: Linear Higher Order Differential Equations
9.01: Introduction to Linear Higher Order Equations
9.1E: Introduction to Linear Higher Order Equations (Exercises)
9.02: Higher Order Constant Coefficient Homogeneous Equations
9.2E: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
9.03: Undetermined Coefficients for Higher Order Equations
9.3E: Undetermined Coefficients for Higher Order Equations (Exercises)
9.04: Variation of Parameters for Higher Order Equations
9.4E: Variation of Parameters for Higher Order Equations (Exercises)
10: Linear Systems of Differential Equations
10.01: Introduction to Systems of Differential Equations
10.1E: Introduction to Systems of Differential Equations (Exercises)
10.02: Linear Systems of Differential Equations
10.2E: Linear Systems of Differential Equations (Exercises)
10.03: Basic Theory of Homogeneous Linear Systems
10.3E: Basic Theory of Homogeneous Linear Systems (Exercises)
10.04: Constant Coefficient Homogeneous Systems I
10.4E: Constant Coefficient Homogeneous Systems I (Exercises)
10.05: Constant Coefficient Homogeneous Systems II
10.5E: Constant Coefficient Homogeneous Systems II (Exercises)
10.06: Constant Coefficient Homogeneous Systems III
10.6E: Constant Coefficient Homogeneous Systems III (Exercises)
11: Systems of Equations
11.01: Geometry
11.02: Elementary Operations
11.03: Gaussian Elimination
11.E: Exercises
12: Matrices and Determinants
12.01: Matrix Arithmetic
12.02: Multiplication of Matrices
12.03: The ijth Entry of a Product
12.04: Properties of Matrix Multiplication
12.05: The Transpose
12.06: The Identity and Inverses
12.07: Finding the Inverse of a Matrix
12.08: Basic Techniques of Determinants
12.09: Properties of Determinants
12.10: Finding Determinants using Row Operations
12.E: Exercises
13: Vector Spaces
13.01: Algebraic Considerations
13.02: Spanning Sets
13.03: Linear Independence
13.04: Subspaces and Basis
13.05: Sums and Intersections
13.06: Linear Transformations
13.E Exercises
14: Appendices and Answers to Exercises
14.01: A Brief Table of Integrals
14.02: Index
14.03: Section 1.2 Answers
14.04: Section 2.1 Answers
14.05: Section 2.2 Answers
14.06: Section 2.3 Answers
14.07: Section 2.4 Answers
14.08: Section 2.5 Answers
14.09: Section 2.6 Answers
14.10: Section 3.1 Answers
14.11: Section 3.2 Answers
14.12: Section 3.3 Answers
14.13: Section 4.1 Answers
14.14: Section 4.2 Answers
14.15: Section 4.3 Answers
14.16: Section 4.4 Answers
14.17: Section 4.5 Answers
14.18: Section 5.1 Answers
14.19: Section 5.2 Answers
14.20: Section 5.3 Answers
14.21: Section 5.4 Answers
14.22: Section 5.5 Answers
14.23: Section 5.6 Answers
14.24: Section 5.7 Answers
14.25: Section 6.1 Answers
14.26: Section 6.2 Answers
14.27: Section 6.3 Answers
14.28: Section 6.4 Answers
14.29: Section 7.1 Answers
14.30: Section 7.2 Answers
14.31: Section 7.3 Answers
14.32: Section 7.4 Answers
14.33: Section 7.5 Answers
14.34: Section 7.6 Answers
14.35: Section 7.7 Answers
14.36: Section 8.1 Answers
14.37: Section 8.2 Answers
14.38: Section 8.3 Answers
14.39: Section 8.4 Answers
14.40: Section 8.5 Answers
14.41: Section 8.6 Answers
14.42: Section 8.7 Answers
14.43: Section 9.1 Answers
14.44: Section 9.2 Answers
14.45: Section 9.3 Answers
14.46: Section 9.4 Answers
14.47: Section 10.1 Answers
14.48: Section 10.2 Answers
14.49: Section 10.3 Answers
14.50: Section 10.4 Answers
14.51: Section 10.5 Answers
14.52: Section 10.6 Answers
14.53: Section 10.7 Answers