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Content
Model with first-order differential equations (DE) and identify initial value problems. Solve scalar differential equations, homogeneous and non-homogeneous, using methods including separation of variables, integrating factors, eigenvalues, LaPlace transformations. Model with systems of first-order DEs and higher-order DEs. Solve systems of linear differential equations using matrices and eigenvalues.
Chapter 1. Introduction
Terminology
Classification of Differential Equations
Initial Value Problem. Cauchy's Theorem of y' = f(x, y)
Mathematical Models and Direction of Fields
Integrating Factors
Separation of Variables
Exact Equations
First Order Linear Equations
Equations with Homogeneous Coefficients
Solution by Substitutions
Bernoulli's DE
Computer Solutions
Chapter 2. First Order Ordinary Differential Equations (ODE)
Chapter 3. Second Order Ordinary Differential Equations
The General Second Order Linear Homogeneous Equation
Linear Independence
Existence and Uniqness Theorem
The Wronskian
General Solution of a Homogeneous Equation
General Solution of a Nonhomogeneous Equation
Differential Operators
Chapter 4. Higher Order Constant Coefficients Linear Equations
Power Series
Series Solutions Near an Ordinary Point
Euler Equations, Regular Singular Points
Series Solutions Near an Regular Singular Point
Bessel's Equation
Chapter 5. Series Solutions of 2d Order LDE
Power Series
Series Solutions Near an Ordinary Point
Euler Equations, Regular Singular Points
Series Solutions Near an Regular Singular Point
Bessel's Equation
Chapter 6. Laplace Transform
Definition
Solution of Initial Value Probems
Step Fucntions
Impulse Functions
The Convolution Integral
Chapter 7. Systems of First Order Differential Equations
Review of Matrices
Systems of Linear Equations. Linear Independence
Eigenvectors, Eigenvalues
Basic Theory
Homogeneous Linear Systems with Constant Coefficients
Nonhomogeneous Linear Systems
Chapter 8. Numerical Methods
The Euler's Method
Runge-Kutta Method
Multi Step Methods
Systems of First order Equations
Bibliography
Boyce, W. E., DiPrima, R. Elementary Differential Equations and Boundary Problems. 8th ed., Wiley & Sons Inc., New York.
Zill, D. A First Course in Differential Equations with Modeling Applications. 10th ed., Brooks/Cole, London, 1997.
