Introduction to Differential Equations (IVC Math 24)

This textbook covers a first course in ordinary differential equations, including first order (linear and non-linear), higher order linear differential equations, Laplace Transformations, power series solutions, and a wide array of real-world applications.

Mathematics

Tác giả: Kenn Huber
Nhà xuất bản: Irvine Valley 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· 101 mục

01: First Order Differential Equations
1.01: Integration Review
1.1.01: Integration Review
1.1.02: Practice Set
1.02: Basic Terminology
1.2.01: Linear Algebra Review
1.2.02: Differential Equation Terminology
1.2.03: Practice Set
1.03: Partial Derivatives and Exact Equations
1.3.01: Partial Differentiation and Integration
1.3.02: Exact Equations
1.3.03: Practice Set
1.04: Separable Equations and Existence Theorem
1.4.01: Picard's Existence Theorem
1.4.02: Separable Differential Equations
1.4.03: Practice Set
1.05: First Order Linear Differential Equations
1.5.01: Solving Linear Differential Equations
1.5.02: Practice Set
1.06: Substitutions
1.6.01: Substitution In Differential Equations
1.6.02: Famous DEs and Their Substitutions
1.6.03: Practice Set
02: Higher Order Linear Differential Equations
2.01: Independent Solutions
2.1.01: Higher Order LDE Solution Sets
2.1.02: Practice Set
2.02: Constant Coeffecient and Cauchy Euler LDEs
2.2.01: Constant Coeffecient LDEs
2.2.02: Cauchy Euler LDEs
2.2.03: Practice Set
2.03: Reduction of Order
2.3.01: Reduction of Order in 2nd Order LDEs
2.3.02: Practice Set
2.04: Undetermined Coefficients
2.4.01: Guessing Solutions
2.4.02: Practice Set
2.05: Variation of Parameters
2.5.01: Varation of Parameters for 2nd order LDEs
2.5.02: Practice Set
2.06: Systems of LDEs
2.6.01: Solving Linear Systems of LDEs
2.6.02: Practice Set
03: Laplace Transformations
3.01: The Laplace Transformation
3.1.01: Laplace Transformation Basics
3.1.02: The Inverse Laplace Transformation
3.1.03: Practice Set
3.02: Laplace Derivative Properties
3.2.01: Differentiation of Outputs of Laplace
3.2.02: Differentiation of Inputs of Laplace
3.2.03: Practice Set
3.03: Piecewise Differential Equations
3.3.01: Piecewise Functions and the Unit Step Function
3.3.02: Laplace Transformations of Piecewise Functions
3.3.03: Practice Set
3.04: Integro-Differential Equations
3.4.01: Convolutions and Laplace
3.4.02: Practice Set
3.05: Dirac Delta
3.5.01: The Dirac Delta Function
3.5.02: Practice Set
3.06: Systems of Differential Equations Revisited
3.6.01: Solving Systems using Laplace
3.6.02: Practice Set
04: Power Series Methods and Approximations
4.01: Power Series
4.1.01: Power Series Review
4.1.02: Practice Set
4.02: First order LDE Power Series solutions
4.2.01: Power Series Solutions
4.2.02: Practice Set
4.03: Second Order Power Series Solutions
4.3.01: Second Order Power Series Solutions
4.3.02: Practice Set
4.04: Power Series Solutions at Singular Points
4.4.01: The Method of Frobenius and Indicial Equation
4.4.02: Distinct Power Series Solutions using Frobenius Method
4.4.03: Frobenius Method (bad cases)
4.4.04: Practice Set
4.05: Approximating Solutions
4.5.01: Euler's Method
4.5.02: Runge-Kutta Approximation
4.5.03: Power Series Approximation
4.5.04: Practice Set
05: Applications
5.01: Applications of First Order Differential Equations
5.1.01: Separable Models
5.1.02: Practice Set
5.02: Orthogonal Curves
5.2.01: Orthogonal Trajectories
5.2.02: Practice Set
5.03: Mixtures
5.3.01: Mixture Problems
5.3.02: Practice Set
5.04: Hooke's Law
5.4.01: Springs
5.4.02: Practice Set
5.05: Circuits
5.5.01: RLC Circuits and External Forces
5.5.02: Practice Set