# Schaum's Outline of Differential Equations, Fourth Edition

by: Richard Bronson, Ph.D., Gabriel B. Costa, Ph.D.

**Abstract:**Fortunately, there's Schaum's. This all-in-one package includes 563 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 20 detailed videos featuring math instructors who explain how to solve the most commonly tested problems—it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand.

Full details

## Table of Contents

**A.**DEDICATION**B.**PREFACE**1.**Basic Concepts**2.**An Introduction to Modeling and Qualitative Methods**3.**Classifications of First-Order Differential Equations**4.**Separable First-Order Differential Equations**5.**Exact First-Order Differential Equations**6.**Linear First-Order Differential Equations**7.**Applications of First-Order Differential Equations**8.**Linear Differential Equations: Theory of Solutions**9.**Second-Order Linear Homogeneous Differential Equations with Constant Coefficients**10.**nth-Order Linear Homogeneous Differential Equations with Constant Coefficients**11.**The Method of Undetermined Coefficients**12.**Variation of Parameters**13.**Initial-Value Problems for Linear Differential Equations**14.**Applications of Second-Order Linear Differential Equations**15.**Matrices**16.**eAt**17.**Reduction of Linear Differential Equations to a System of First-Order Equations**18.**Graphical and Numerical Methods for Solving First-Order Differential Equations**19.**Further Numerical Methods for Solving First-Order Differential Equations**20.**Numerical Methods for Solving Second-Order Differential Equations Via Systems**21.**The Laplace Transform**22.**Inverse Laplace Transforms**23.**Convolutions and the Unit Step Function**24.**Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms**25.**Solutions of Linear Systems by Laplace Transforms**26.**Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods**27.**Power Series Solutions of Linear Differential Equations with Variable Coefficients**28.**Series Solutions Near a Regular Singular Point**29.**Some Classical Differential Equations**30.**Gamma and Bessel Functions**31.**An Introduction to Partial Differential Equations**32.**Second-Order Boundary-Value Problems**33.**Eigenfunction Expansions**34.**An Introduction to Difference Equations**A.**APPENDIX A: Laplace Transforms**B.**APPENDIX B: Some Comments about Technology**C.**ANSWERS: Answers to Supplementary Problems

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## Expanded Table of Contents

**A.**DEDICATION**B.**PREFACE**1.**Basic Concepts**2.**An Introduction to Modeling and Qualitative Methods**3.**Classifications of First-Order Differential Equations**4.**Separable First-Order Differential Equations**5.**Exact First-Order Differential Equations**6.**Linear First-Order Differential Equations**7.**Applications of First-Order Differential Equations**8.**Linear Differential Equations: Theory of Solutions**9.**Second-Order Linear Homogeneous Differential Equations with Constant Coefficients**10.**nth-Order Linear Homogeneous Differential Equations with Constant Coefficients**11.**The Method of Undetermined Coefficients**12.**Variation of Parameters**13.**Initial-Value Problems for Linear Differential Equations**14.**Applications of Second-Order Linear Differential Equations**15.**Matrices**16.**eAt**17.**Reduction of Linear Differential Equations to a System of First-Order Equations**18.**Graphical and Numerical Methods for Solving First-Order Differential Equations**19.**Further Numerical Methods for Solving First-Order Differential Equations**20.**Numerical Methods for Solving Second-Order Differential Equations Via Systems**21.**The Laplace Transform**22.**Inverse Laplace Transforms**23.**Convolutions and the Unit Step Function**24.**Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms**25.**Solutions of Linear Systems by Laplace Transforms**26.**Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods**27.**Power Series Solutions of Linear Differential Equations with Variable Coefficients**28.**Series Solutions Near a Regular Singular Point**29.**Some Classical Differential Equations**30.**Gamma and Bessel Functions**31.**An Introduction to Partial Differential Equations**32.**Second-Order Boundary-Value Problems**33.**Eigenfunction Expansions**34.**An Introduction to Difference Equations**A.**APPENDIX A: Laplace Transforms**B.**APPENDIX B: Some Comments about Technology**C.**ANSWERS: Answers to Supplementary Problems- CHAPTER 1
- CHAPTER 2
- CHAPTER 3
- CHAPTER 4
- CHAPTER 5
- CHAPTER 6
- CHAPTER 7
- CHAPTER 8
- CHAPTER 9
- CHAPTER 10
- CHAPTER 11
- CHAPTER 12
- CHAPTER 13
- CHAPTER 14
- CHAPTER 15
- CHAPTER 16
- CHAPTER 17
- CHAPTER 18
- CHAPTER 19
- CHAPTER 20
- CHAPTER 21
- CHAPTER 22
- CHAPTER 23
- CHAPTER 24
- CHAPTER 25
- CHAPTER 26
- CHAPTER 27
- CHAPTER 28
- CHAPTER 29
- CHAPTER 30
- CHAPTER 31
- CHAPTER 32
- CHAPTER 33
- CHAPTER 34

**Book Details**

**Title: **Schaum's Outline of Differential Equations, Fourth Edition

**Publisher: **McGraw-Hill Education: New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi, Singapore, Sydney, Toronto

**Copyright / Pub. Date: **2014 McGraw-Hill Education

**ISBN: **9780071824859

**Authors:****Richard Bronson, Ph.D.**
is a professor of mathematics at Farleigh Dickinson University. Dr. Bronson has served as an associate editor of the journal Simulation, as a contributing editor to SIAM News, and as a consultant to Bell Laboratories. He has conducted joint research in mathematical modeling and computer simulation at Technion–Israel Institute of Technology and at the Wharton School of Business of the University of Pennsylvania. Dr. Bronson has published over 30 technical articles and books, the latter including Schaum's Outline of Matrix Operations and Schaum's Outline of Operations Research.
**Gabriel B. Costa, Ph.D.**
is a Catholic priest and a professor of mathematical sciences at the United States Military Academy at West Point, where he also functions as an associate chaplain. In addition to differential equations, Father Costa's academic interests include mathematics education and sabermetrics, the search for objective knowledge about baseball.

**Description: **
Fortunately, there's Schaum's. This all-in-one package includes 563 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 20 detailed videos featuring math instructors who explain how to solve the most commonly tested problems—it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.
More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. Helpful tables and illustrations increase your understanding of the subject at hand.