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Interactive Differential Equations:
A Step-by-Step Approach to Methods & Modeling
Geoffrey W. Cox, Ph.D., ?
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Front Matter
Colophon
Preface
I
Fundamentals
1
What’s a Differential Equation?
1.1
An Analogy
1.1
Check your Understanding
1.2
Definition
1.2
Check your Understanding
1.3
Variables
1.3
Check your Understanding
1.4
Terms & Coefficients
1.4
Check your Understanding
1.5
Order
1.5
Check your Understanding
1.6
Linear Terms
1.6
Check your Understanding
1.7
Linearity
1.7
Check your Understanding
1.8
Summary & Exercises
1.8
Exercises
1.8
Exercises
2
Solutions
2.1
What is a Solution?
2.1
Check your Understanding
2.2
Verifying Solutions
2.2
Check your Understanding
2.3
Types of Solutions
2.3
Check your Understanding
2.4
Visualizing Solutions
2.4
Check your Understanding
2.5
Initial Conditions & Particular Solutions
2.5
Check your Understanding
2.6
Summary & Exercises
2.6
Exercises
II
First-Order Methods
3
Direct Integration
3.1
Antiderivatives
3.1
Check your Understanding
3.2
Solutions by Direct Integration
3.2
Check your Understanding
3.3
Summary & Exercises
3.3
Exercises
4
Separation of Variables
4.1
Separable Form
4.1
Check your Understanding
4.2
Verifying Separable
4.2
Check your Understanding
4.3
Separation of Variables Method (SOV)
4.3
Check your Understanding
4.4
Additional Examples
4.4
Check your Understanding
4.5
Summary & Exercises
4.5
Exercises
5
Integrating Factor
5.1
Product Rule
5.1
Check your Understanding
5.2
The Integrating Factor
5.2
Check your Understanding
5.3
Integrating Factor Method
5.3
Check your Understanding
5.4
Additional Examples
5.4
Check your Understanding
5.5
Summary & Exercises
5.5
Exercises
III
Linear Constant Coefficient Methods
6
Homogeneous
6.1
Classification
6.1
Check your Understanding
6.2
Solutions
6.2
Check your Understanding
6.3
1st-Order Equations
6.3
Check your Understanding
6.4
2nd-Order Equations
6.4
Check your Understanding
6.5
Higher-Order Equations
6.5
Check your Understanding
6.6
Summary & Exercises
6.6
Exercises
7
Nonhomogeneous
8
Variation of Parameters
IV
Laplace Transform Method
9
Forward Transforms
10
Backward Transforms
11
Solving Equations
12
Piecewise Forcing Functions
V
Systems of Equations
13
Linear Systems
14
Nonlinear Systems
15
Applications
VI
Numerical Methods
16
Euler’s Method
17
Runge-Kutta Methods
18
Error Analysis
VII
Orphaned Exercises
19
Miscellaneous Exercises
VIII
Modeling Stuff
20
Intro Modeling
21
SOV Modeling
22
IF Modeling
23
UC Modeling
A
Algebra Review
A.1
Exponential and Logarithmic Functions
A.2
Rational Functions
A.3
Quadratic equations
A.4
Trigonometric Identities
A.5
Solving Polynomial Equations
B
Calculus Review
B.1
Product Rule
B.2
Integration by parts
C
Details
C.1
Direct Integration
C.2
Visualizing Solutions
C.3
Integrating Factor
C.4
Linear Homogeneous Constant Coefficients
D
Orphaned Content (Reader Ignore)
Colophon
Colophon
Edition
1st Edition
Website
https://math-blox.com
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