Nguồn ngoài
A First Course in Differential Equations for Scientists and Engineers
This book is written for an undergraduate course on the introduction to differential equations typically taken by majors in mathematics, the physical sciences, and engineering. In this course we will investigate analytical, graphical, and approximate solutions of differential equations. We will study the theory, methods of solution and applications of ordinary differential equations. This will include common methods of finding solutions, such as using Laplace transform and power series methods.
- Tác giả
- Russell Herman
- Nhà xuất bản
- University of North Carolina Wilmington
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC-SA
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 86 mục
- 01: First Order ODEs
- 1.01: Free Fall
- 1.02: First Order Differential Equations
- 1.03: Applications
- 1.04: Other First Order Equations
- 1.05: Problems
- 02: Second Order ODEs
- 2.01: Introduction
- 2.02: Constant Coefficient Equations
- 2.03: Simple Harmonic Oscillators
- 2.04: Forced Systems
- 2.05: Cauchy-Euler Equations
- 2.06: Problems
- 03: Numerical Solutions
- 3.01: Eulers Method
- 3.02: Implementation of Numerical Packages
- 3.03: Higher Order Taylor Methods
- 3.04: Runge-Kutta Methods
- 3.05: Numerical Applications
- 3.5.01: The Nonlinear Pendulum
- 3.5.02: Extreme Sky Diving
- 3.5.03: The Flight of Sports Balls
- 3.5.04: Falling Raindrops
- 3.5.05: The Two-body Problem
- 3.5.06: The Expanding Universe
- 3.5.07: The Coefficient of Drag
- 3.06: Problems
- 04: Series Solutions
- 4.01: Introduction to Power Series
- 4.02: Power Series Method
- 4.03: Singular Points
- 4.04: The Frobenius Method
- 4.4.01: Introduction
- 4.4.02: Roots of Indicial Equation
- 4.05: Legendre Polynomials
- 4.06: Bessel Functions
- 4.07: Gamma Function
- 4.08: Hypergeometric Functions
- 4.09: Problems
- 05: Laplace Transforms
- 5.01: The Laplace Transform
- 5.02: Properties and Examples of Laplace Transforms
- 5.03: Solution of ODEs Using Laplace Transforms
- 5.04: Step and Impulse Functions
- 5.05: The Convolution Theorem
- 5.06: Systems of ODEs
- 5.07: Problems
- 06: Linear Systems
- 6.01: Linear Systems
- 6.02: Applications
- 6.2.01: Mass-Spring Systems
- 6.2.02: Circuits
- 6.2.03: Mixture Problems
- 6.2.04: Chemical Kinetics
- 6.2.05: Predator Prey Models
- 6.2.06: Love Affairs
- 6.2.07: Epidemics
- 6.03: Matrix Formulation
- 6.04: Eigenvalue Problems
- 6.05: Solving Constant Coefficient Systems in 2D
- 6.06: Examples of the Matrix Method
- 6.07: Theory of Homogeneous Constant Coefficient Systems
- 6.08: Nonhomogeneous Systems
- 6.09: Problems
- 07: Nonlinear Systems
- 7.01: Introduction
- 7.02: The Logistic Equation
- 7.03: Autonomous First Order Equations
- 7.04: Bifurcations for First Order Equations
- 7.05: The Stability of Fixed Points in Nonlinear Systems
- 7.06: Nonlinear Population Models
- 7.07: Limit Cycles
- 7.08: Nonautonomous Nonlinear Systems
- 7.09: The Period of the Nonlinear Pendulum
- 7.10: Exact Solutions Using Elliptic Functions
- 7.11: Problems
- 08: Appendix Calculus Review
- 8.01: Introduction
- 8.02: Trigonometric Functions
- 8.03: Hyperbolic Functions
- 8.04: Derivatives
- 8.05: Integrals
- 8.06: Geometric Series
- 8.07: Power Series
- 8.08: The Binomial Expansion
- 8.09: Problems