9781292240992

Fundamentals of Differential Equations, Global Edition

3-2

Compartmental Analysis

Exercises

p.100

3-3

Heating and Cooling of Building

Exercises

p.107

3-4

Newtonian Mechanics

Exercises

p.115

3-5

Electrical Circuits

Exercises

p.121

3-6

Numerical Methods: A Closer Look at Euler's Algorithm

Exercises

p.129

3-7

Higher-Order Numerical Methods: Taylor and Runge-Kutta

Exercises

p.139

4-1

Introduction: The Mass-Spring Oscillator

Exercises

p.156

4-2

Homogeneous Linear Equations: The General Solution

Exercises

p.164

4-3

Auxiliary Equations with Complex Roots

Exercises

p.172

4-4

Nonhomogeneous Equations: the Method of Undetermined Coefficients

Exercises

p.180

4-5

The Superposition Principle and Undetermined Coefficients Revisited

Exercises

p.185

4-6

Variation of Parameters

Exercises

p.191

4-7

Variable-Coefficient Equations

Exercises

p.199

4-8

Qualitative Considerations for Variable-Coefficient and Nonlinear Equations

Exercises

p.210

4-9

A Closer Look at Free Mechanical Vibrations

Exercises

p.220

4-10

A Closer Look at Force Mechanical Vibrations

Exercises

p.227

Review Problems

p.231

Technical Writing Exercises

p.232

5-2

Differential Operators and the Elimination Method* for Systems

Exercises

p.249

5-3

Solving Systems and Higher-Order Equations Numerically

Exercises

p.259

5-4

Introduction to the Phase Plane

Exercises

p.271

5-5

Applications to Biomathematics: Epidemic and Tumor Growth Models

Exercises

p.281

5-6

Coupled Mass-Spring Systems

Exercises

p.287

5-7

Electrical Systems

Exercises

p.294

5-8

Dynamical Systems, PoincarĂ© Maps, and Chaos

Exercises

p.303

Review Problems

p.306

6-1

Basic Theory of Linear Differential Equations

Exercises

p.326

6-2

Homogenous Linear Equations with Constant Coefficients

Exercises

p.332

6-3

Undetermined Coefficients and the Annihilator Method

Exercises

p.337

6-4

Method of Variation of Parameters

Exercises

p.341

Review Problems

p.343

Technical Writing Exercises

p.344

7-2

Definition of the Laplace Transform

Exercises

p.360

7-3

Properties of the Laplace Transform

Exercises

p.365

7-4

Inverse Laplace Transform

Exercises

p.374

7-5

Solving Initial Value Problems

Exercises

p.382

7-6

Transforms of Discontinuous Functions

Exercises

p.390

7-7

Transforms of Periodic and Power Functions

Exercises

p.396

7-8

Convolution

Exercises

p.404

7-9

Impulses and the Dirac Delta Function

Exercises

p.410

7-10

Solving Linear Systems with Laplace Transforms

Exercises

p.414

Review Problems

p.415

Technical Writing Exercises

p.416

8-1

Introduction: The Taylor Polynomial Approximation

Exercises

p.425

8-2

Power Series and Analytic Functions

Exercises

p.433

8-3

Power Series Solutions to Linear Differential Equations

Exercises

p.443

8-4

Equations with Analytic Coefficients

Exercises

p.449

8-5

Cauchy-Euler (Equidimensional) Equations

Exercises

p.453

8-6

Method of Frobenius

Exercises

p.464

8-7

Finding a Second Linearly Independent Solution

Exercises

p.473

8-8

Special Functions

Exercises

p.485

Review Problems

p.489

Technical Writing Exercises

p.490

9-1

Introduction

Exercises

p.500

9-2

Review 1: Linear Algebraic Equations

Exercises

p.504

9-3

Review 2: Matrices and Vectors

Exercises

p.513

9-4

Linear Systems in Normal Form

Exercises

p.521

9-5

Homogeneous Linear Systems with Constant Coefficients

Exercises

p.531

9-6

Complex Eigenvalues

Exercises

p.537

9-7

Nonhomogeneous Linear Systems

Exercises

p.542

9-8

The Matrix Exponential Function

Exercises

p.551

Review Problems

p.555

Technical Writing Exercises

p.556