Differential equations : first and second order linear differential equations /
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, [New York] (222 East 46th Street, New York, NY 10017) :
Momentum Press,
2015.
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| Subjects: | |
| Online Access: | An electronic book accessible through the World Wide Web; click to view |
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Table of Contents:
- 1. Definition of terms and review of linear algebra
- 1.1 Basic definitions
- 1.1.1 What is a differential equation?
- 1.1.2 Solution to a differential equation
- 1.1.3 Family of solutions
- 1.1.4 Direction fields
- 1.2 Some linear algebra
- 1.2.1 Matrices
- 1.2.2 Systems of linear equations
- 1.2.3 Matrix addition and subtraction and scalar product
- 1.2.4 Transpose of a matrix
- 1.2.5 Dot product and matrix multiplication
- 1.2.6 Determinants
- 1.2.7 The inverse of a square matrix
- 1.2.8 Matrix form of a system of linear equations
- 1.2.9 Linear dependence
- 1.2.10 Eigenvalues and Eigenvectors
- 1.2.11 Diagonalization
- 2. Linear first order differential equations
- 2.1 Linear first order DE
- 2.1.1 Bernoulli differential equation
- 2.2 Separable differential equations
- 2.3 Exact differential equations
- 2.4 Homogeneous differential equations
- 2.5 Existence and uniqueness
- 3. Homogeneous second order differential equations
- 3.1 Linear homogeneous DE
- 3.2 Linear independence and the Wronskian
- 3.2.1 Linear independence
- 3.2.2 The Wronskian
- 3.3 Solving ay" + by' + cy = g(x)
- 3.3.1 The method of undetermined coefficients
- 3.3.2 Variation of parameters
- Bibliography
- Index.