Chapter 1
Introduction To Differential Equations
1.1 
Definitions and Terminology 
Exercises 
p.10 
1.2 
InitialValue Problems 
Exercises 
p.17 
1.3 
Differential Equations as Mathematical Models 
Exercises 
p.27 


Chapter 1 in Review 
p.32 
Chapter 2
FirstOrder Differential Equations
2.1 
Solution Curves Without a Solution 
Exercises 
p.41 
2.2 
Separable Equations 
Exercises 
p.50 
2.3 
Linear Equations 
Exercises 
p.60 
2.4 
Exact Equations 
Exercises 
p.68 
2.5 
Solutions By Substitutions 
Exercises 
p.74 
2.6 
A Numerical Method 
Exercises 
p.79 


Chapter 2 in Review 
p.80 
Chapter 3
Modeling With FirstOrder Differential Equations
3.1 
Linear Models 
Exercises 
p.89 
3.2 
Nonlinear Models 
Exercises 
p.99 
3.3 
Modeling with Systems of FirstOrder DEs 
Exercises 
p.110 


Chapter 3 in Review 
p.113 
Chapter 4
HigherOrder Differential Equations
4.1 
Preliminary Theory  Linear Equations 
Exercises 
p.128 
4.2 
Reduction of Order 
Exercises 
p.132 
4.3 
Homogeneous Linear Equations with Constant Coefficients 
Exercises 
p.138 
4.4 
Undetermined Coefficients  Superposition Approach 
Exercises 
p.148 
4.5 
Undetermined Coefficients  Annihilator Approach 
Exercises 
p.156 
4.6 
Variation of Parameters 
Exercises 
p.161 
4.7 
CauchyEuler Equation 
Exercises 
p.168 
4.8 
Solving Systems of Linear Des by Elemination 
Exercises 
p.172 
4.9 
Nonlinear Differential Equations 
Exercises 
p.177 


Chapter 4 in Review 
p.178 
Chapter 5
Modeling With HigherOrder Differential Equations
5.1 
Linear Models: InitialValue Problems 
Exercises 
p.194 
5.2 
Linear Models: BoundaryValue Problems 
Exercises 
p.204 
5.3 
Nonlinear Models 
Exercises 
p.213 


Chapter 5 in Review 
p.216 
Chapter 6
Series Solutions Of Linear Equations
6.1 
Solutions About Ordinary Points 
Exercises 
p.230 
6.2 
Solutions about Singular Points 
Exercises 
p.239 
6.3 
Special Functions 
Exercises 
p.250 


Chapter 6 in Review 
p.253 
Chapter 7
The Laplace Transform
7.1 
Definition of the Laplace Transform 
Exercises 
p.261 
7.2 
Inverse Transforms and Transforms of Derivatives 
Exercises 
p.269 
7.3 
Operation Properties I 
Exercises 
p.278 
7.4 
Operational Properties II 
Exercises 
p.289 
7.5 
The Dirac Delta Function 
Exercises 
p.295 
7.6 
Systems of Linear Differential Equations 
Exercises 
p.299 


Chapter 7 in Review 
p.300 
Chapter 8
Systems Of Linear FirstOrder Differential Equations
8.1 
Preliminary Theory  Linear Systems 
Exercises 
p.310 
8.2 
Homogeneous Linear Systems 
Exercises 
p.324 
8.3 
Nonhomogeneous Linear Systems 
Exercises 
p.332 
8.4 
Matrix Exponential 
Exercises 
p.336 


Chapter 8 in Review 
p.337 
Chapter 9
Numerical Solutions Of Ordinary Differential Equations
9.1 
Euler Methods and Error Analysis 
Exercises 
p.344 
9.2 
RungeKutta Methods 
Exercises 
p.348 
9.3 
Multistep Methods 
Exercises 
p.353 
9.4 
HigherOrder Equations and Systems 
Exercises 
p.357 
9.5 
SecondOrder BoundaryValue Problems 
Exercises 
p.361 


Chapter 9 in Review 
p.362 
Chapter 10
Plane Autonomous Systems
10.1 
Autonomous Systems 
Exercises 
p.369 
10.2 
Stability of Linear Systems 
Exercises 
p.377 
10.3 
Linearization and Local Stability 
Exercises 
p.386 
10.4 
Autonomous Systems as Mathematical Models 
Exercises 
p.393 


Chapter 10 in Review 
p.395 
Chapter 11
Fourier Series
11.1 
Orthogonal Functions 
Exercises 
p.402 
11.2 
Fourier Series 
Exercises 
p.407 
11.3 
Fourier Cosine and Sine Series 
Exercises 
p.414 
11.4 
SturmLiouville Problem 
Exercises 
p.422 
11.5 
Bessel and Legendre Series 
Exercises 
p.429 


Chapter 11 in Review 
p.430 
Chapter 12
BoundaryValue Problems In Rectangular Coordinates
12.1 
Separable Partial Differential Equations 
Exercises 
p.436 
12.2 
Classical PDEs and BoundaryValue Problems 
Exercises 
p.442 
12.3 
Heat Equation 
Exercises 
p.445 
12.4 
Wave Equation 
Exercises 
p.448 
12.5 
Laplace's Equation 
Exercises 
p.454 
12.6 
Nonhomogeneous BoundaryValue Problems 
Exercises 
p.459 
12.7 
Orthogonal Series Expansions 
Exercises 
p.465 
12.8 
HigherDimensional Problems 
Exercises 
p.469 


Chapter 12 in Review 
p.469 
Chapter 13
BoundaryValue Problems In Other Coordinate Systems
13.1 
Polar Coordinates 
Exercises 
p.475 
13.2 
Polar and Cylindrical Coordinates 
Exercises 
p.481 
13.3 
Spherical Coordinates 
Exercises 
p.485 


Chapter 13 in Review 
p.486 
Chapter 14
Integral Transforms
14.1 
Error Function 
Exercises 
p.490 
14.2 
Laplace Transform 
Exercises 
p.495 
14.3 
Fourier Integral 
Exercises 
p.503 
14.4 
Fourier Transforms 
Exercises 
p.508 


Chapter 14 in Review 
p.510 
Chapter 15
Numerical Solutions Of Partial Differential Equations
15.1 
Laplace's Equation 
Exercises 
p.517 
15.2 
Heat Equation 
Exercises 
p.521 
15.3 
Wave Equation 
Exercises 
p.525 


Chapter 15 in Review 
p.526 
Differential Equations with BoundaryValue Problems, 8th Edition
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