# Differential Equations

ISBN-10: 1133110592

ISBN-13: 9781133110590

Pub. Date: 12/28/2011

Publisher: Cengage Learning

Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems

## Overview

Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems focus emphasizes predicting the long-term behavior of these recurring models. Users will discover how to identify and harness the mathematics they will use in their careers, and apply it effectively outside the classroom.

## Product Details

ISBN-13:
9781133110590
Publisher:
Cengage Learning
Publication date:
12/28/2011

 1 First-Order Differential Equations 1 1.1 Modeling via Differential Equations 2 1.2 Analytic Technique: Separation of Variables 20 1.3 Qualitative Technique: Slope Fields 36 1.4 Numerical Technique: Euler's Method 53 1.5 Existence and Uniqueness of Solutions 65 1.6 Equilibria and the Phase Line 76 1.7 Bifurcations 96 1.8 Linear Differential Equations 113 1.9 Changing Variables 123 Labs for Chapter 1 138 2 First-Order Systems 147 2.1 Modeling via Systems 148 2.2 The Geometry of Systems 165 2.3 Analytic Methods for Special Systems 183 2.4 Euler's Method for Systems 194 2.5 The Lorenz Equations 209 Labs for Chapter 2 216 3 Linear Systems 225 3.1 Properties of Linear Systems and the Linearity Principle 226 3.2 Straight-Line Solutions 250 3.3 Phase Planes for Linear Systems with Real Eigenvalues 266 3.4 Complex Eigenvalues 282 3.5 Special Cases: Repeated and Zero Eigenvalues 301 3.6 Second-Order Linear Equations 316 3.7 The Trace-Determinant Plane 333 3.8 Linear Systems in Three Dimensions 346 Labs for Chapter 3 362 4 Forcing and Resonance 369 4.1 Forced Harmonic Oscillators 370 4.2 Sinusoidal Forcing 385 4.3 Undamped Forcing and Resonance 397 4.4 Amplitude and Phase of the Steady State 409 4.5 The Tacoma Narrows Bridge 421 Labs for Chapter 4 431 5 Nonlinear Systems 437 5.1 Equilibrium Point Analysis 438 5.2 Qualitative Analysis 457 5.3 Hamiltonian Systems 470 5.4 Dissipative Systems 488 5.5 Nonlinear Systems in Three Dimensions 510 5.6 Periodic Forcing of Nonlinear Systems and Chaos 518 Labs for Chapter 5 535 6 Laplace Transforms 541 6.1 Laplace Transforms 542 6.2 Discontinuous Functions 554 6.3 Second-Order Equations 563 6.4 Delta Functions and Impulse Forcing 577 6.5 Convolutions 585 6.6 The Qualitative Theory of Laplace Transforms 594 Labs for Chapter 6 603 7 Numerical Methods 607 7.1 Numerical Error in Euler's Method 608 7.2 Improving Euler's Method 621 7.3 The Runge-Kutta Method 629 7.4 The Effects of Finite Arithmetic 640 Labs for Chapter 7 644 8 Discrete Dynamical Systems 647 8.1 The Discrete Logistic Equation 648 8.2 Fixed Points and Periodic Points 661 8.3 Bifurcations 670 8.4 Chaos 679 8.5 Chaos in the Lorenz System 687 Labs for Chapter 8 693 Appendices 699 A First-Order Linear Equations Revisited 700 B Complex Numbers and Euler's Formula 711 Hints and Answers 717 Index 777

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### Most Helpful Customer Reviews

Differential Equations 2.5 out of 5 based on 0 ratings. 2 reviews.
 Anonymous More than 1 year ago
I hate this math book. Don't get me wrong! It taught the material, but it wanted to be read like a book which made it rather confusing and hard to understand/find examples of what you were suppose to be doing.
 Anonymous 4 months ago
It's one of the hardest differential equations books i've used. The format that's written is just like a normal book. Words everywhere and very few examples. Good luck if you need it for a class.