MAT 2561 Differential Equations with Engineering Applications

Mathematics

Tác giả: Matthew Watts
Nhà xuất bản: Red Rocks Community College
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 183 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
2.1.01: Cooling and Mixing
2.1.1E: Cooling and Mixing (Exercises)
2.1.02: Cooling and Mixing (Exercises)
2.1E: Linear First Order Equations (Exercises)
2.02: Separable Equations
2.2E: Separable Equations (Exercises)
2.03: Substitution Methods - Transformation of Nonlinear Equations into Separable Equations
2.3.01: Autonomous Second Order Equations
2.3.02: Autonomous Second Order Equations (Exercises)
2.04: Existence and Uniqueness of Solutions of Nonlinear Equations
2.4.01: Elementary Mechanics
2.4.1.01: Elementary Mechanics (Exercises)
2.4E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
2.05: Transformation of Nonlinear Equations into Separable Equations
2.5.01: Autonomous Second Order Equations
2.5.1E: Autonomous Second Order Equations (Exercises)
2.5E: Transformation of Nonlinear Equations into Separable Equations (Exercises)
2.06: Exact Equations
2.6E: Exact Equations (Exercises)
2.07: Integrating Factors
2.7E: Integrating Factors (Exercises)
03: Numerical Methods
3.01: Euler's Method
3.1.01: Eulers Method (Exercises)
3.02: The Improved Euler Method and Related Methods
3.2.01: The Improved Euler Method and Related Methods (Exercises)
3.03: The Runge-Kutta Method
3.3.01: The Runge-Kutta Method (Exercises)
04: Applications of First Order Equations
4.01: Growth and Decay
4.1.01: Growth and Decay (Exercises)
4.02: Elementary Mechanics
4.2.01: Elementary Mechanics (Exercises)
4.03: Applications to Curves
4.3.01: Applications to Curves (Exercises)
05: Linear Second Order Equations
5.01: Homogeneous Linear Equations
5.1.01: Homogeneous Linear Equations (Exercises)
5.02: Constant Coefficient Homogeneous Equations
5.2.01: Constant Coefficient Homogeneous Equations (Exercises)
5.03: Nonhomgeneous Linear Equations
5.3.01: Nonhomgeneous Linear Equations (Exercises)
5.3.02: Spring Problems I
5.3.03: Spring Problems I (Exercises)
5.3.04: Spring Problems II
5.3.05: Spring Problems II (Exercises)
5.04: The Method of Undetermined Coefficients I
5.4.01: The Method of Undetermined Coefficients I (Exercises)
5.05: The Method of Undetermined Coefficients II
5.5.01: The Method of Undetermined Coefficients II (Exercises)
5.06: Reduction of Order
5.6.01: Reduction of Order (Exercises)
5.07: Variation of Parameters
5.7.01: Variation of Parameters (Exercises)
5.08: The RLC Circuit
5.8.01: The RLC Circuit (Exercises)
06: Applications of Linear Second Order Equations
6.01: Motion Under a Central Force
6.1.01: Motion Under a Central Force (Exercises)
07: Series Solutions of Linear Second Order Equations
7.01: Prelude to Series Solutions of Linear Second Order Equations
7.02: Review of Power Series
7.2.01: Review of Power Series (Exercises)
7.03: Series Solutions Near an Ordinary Point I
7.3E: Series Solutions Near an Ordinary Point I (Exercises)
7.04: Series Solutions Near an Ordinary Point II
7.4.01: Series Solutions Near an Ordinary Point II (Exercises)
7.05: Regular Singular Points Euler Equations
7.5.01: Regular Singular Points Euler Equations (Exercises)
7.06: The Method of Frobenius I
7.6.01: The Method of Frobenius I (Exercises)
7.07: The Method of Frobenius II
7.7.01: The Method of Frobenius II (Exercises)
7.08: The Method of Frobenius III
7.8.01: The Method of Frobenius III (Exercises)
08: Laplace Transforms
8.01: Introduction to the Laplace Transform
8.1.01: Introduction to the Laplace Transform (Exercises)
8.02: The Inverse Laplace Transform
8.2.01: The Inverse Laplace Transform (Exercises)
8.03: Solution of Initial Value Problems
8.3.01: Solution of Initial Value Problems (Exercises)
8.04: The Unit Step Function
8.4.01: The Unit Step Function (Exercises)
8.05: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
8.5.01: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
8.06: Convolution
8.6.01: Convolution (Exercises)
8.07: Constant Coefficient Equations with Impulses
8.7.01: Constant Coefficient Equations with Impulses (Exercises)
8.08: A Brief Table of Laplace Transforms (Trench's)
8.09: Professor Seeburger's Table of Laplace Transforms
8.10: Spring Problems I
8.10.01: Spring Problems I (Exercises)
8.11: Spring Problems II
8.11.01: Spring Problems II (Exercises)
09: Linear Systems of Differential Equations
9.01: Introduction to Systems of Differential Equations
9.1.01: Introduction to Systems of Differential Equations (Exercises)
9.02: Linear Systems of Differential Equations
9.2.01: Linear Systems of Differential Equations (Exercises)
9.03: Basic Theory of Homogeneous Linear Systems
9.3.01: Basic Theory of Homogeneous Linear Systems (Exercises)
9.04: Constant Coefficient Homogeneous Systems I
9.4.01: Constant Coefficient Homogeneous Systems I (Exercises)
9.05: Constant Coefficient Homogeneous Systems II
9.5.01: Constant Coefficient Homogeneous Systems II (Exercises)
9.06: Constant Coefficient Homogeneous Systems III
9.6.01: Constant Coefficient Homogeneous Systems III (Exercises)
9.07: Variation of Parameters for Nonhomogeneous Linear Systems
9.7.01: Variation of Parameters for Nonhomogeneous Linear Systems (Exercises)
10: Answers to Selected Exercises
10.01: A.1.2- Section 1.2 Answers
10.02: A.10.1- Section 10.1 Answers
10.03: A.10.2 Section 10.2 Answers
10.04: A.10.3- Section 10.3 Answers
10.05: A.10.4 Section 10.4 Answers
10.06: A.10.5- Section 10.5 Answers
10.07: A.10.6 Section 10.6 Answers
10.08: A.10.7- Section 10.7 Answers
10.09: A.11.1- Section 11.1 Answers
10.10: A.11.2- Section 11.2 Answers
10.11: A.11.3- Section 11.3 Answers
10.12: A.12.1- Section 12.1 Answers
10.13: A.12.2- Section 12.2 Answers
10.14: A.12.3- Section 12.3 Answers
10.15: A.12.4- Section 12.4 Answers
10.16: A.13.1- Section 13.1 Answers
10.17: A.13.2- Section 13.2 Answers
10.18: A.2.1- Section 2.1 Answers
10.19: A.2.2- Section 2.2 Answers
10.20: A.2.3- Section 2.3 Answers
10.21: A.2.4- Section 2.4 Answers
10.22: A.2.5- Section 2.5 Answers
10.23: A.2.6- Section 2.6 Answers
10.24: A.3.1- Section 3.1 Answers
10.25: A.3.2- Section 3.2 Answers
10.26: A.3.3- Section 3.3 Answers
10.27: A.4.1- Section 4.1 Answers
10.28: A.4.2- Section 4.2 Answers
10.29: A.4.3- Section 4.3 Answers
10.30: A.4.4- Section 4.4 Answers
10.31: A.4.5- Section 4.5 Answers
10.32: A.5.1- Section 5.1 Answers
10.33: A.5.2- Section 5.2 Answers
10.34: A.5.3- Section 5.3 Answers
10.35: A.5.4- Section 5.4 Answers
10.36: A.5.5- Section 5.5 Answers
10.37: A.5.6- Section 5.6 Answers
10.38: A.5.7- Section 5.7 Answers
10.39: A.6.1- Section 6.1 Answers
10.40: A.6.2- Section 6.2 Answers
10.41: A.6.3- Section 6.3 Answers
10.42: A.6.4- Section 6.4 Answers
10.43: A.7.1- Section 7.1 Answers
10.44: A.7.2- Section 7.2 Answers
10.45: A.7.3- Section 7.3 Answers
10.46: A.7.4- Section 7.4 Answers
10.47: A.7.5- Section 7.5 Answers
10.48: A.7.6- Section 7.6 Answers
10.49: A.7.7- Section 7.7 Answers
10.50: A.8.1- Section 8.1 Answers
10.51: A.8.2- Section 8.2 Answers
10.52: A.8.3- Section 8.3 Answers
10.53: A.8.4- Section 8.4 Answers
10.54: A.8.5- Section 8.5 Answers
10.55: A.8.6- Section 8.6 Answers
10.56: A.8.7- Section 8.7 Answers
10.57: A.9.1- Section 9.1 Answers
10.58: A.9.2- Section 9.2 Answers
10.59: A.9.3 Section 9.3 Answers
10.60: A.9.4- Section 9.4 Answers
10.61: A Brief Table of Integrals (by Trench)
10.62: A Brief Table of Integrals (edited by Prof. Seeburger)
10.63: Index