Study smarter and stay on top of your differential equations course with the bestselling Schaum’s Outline―now with the NEW Schaum’s app and website!

Schaum’s Outline of Differential Equations, Fifth Edition is the go-to study guide for all students of science who need to learn or refresh their knowledge of differential equations. With an outline format that facilitates quick and easy review and mirrors the course in scope and sequence, this book helps you understand basic concepts and get the extra practice you need to excel in the course. It supports the all major differential equations textbooks and is useful for study in Calculus (I, II, and III), Mathematical Modeling, Introductory Differential Equations and Differential Equations.

Chapters include an Introduction to Modeling and Qualitative Methods, Classifications of First-Order Differential Equations, Linear Differential Equations, Variation of Parameters, Initial-Value Problems for Linear Differential Equations, Graphical and Numerical Methods for Solving First-Order Differential Equations, Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms, and more.

Features:

• NEW to this edition: the new Schaum’s app and website!
• NEW CHAPTERS include Autonomous Differential Equations and Qualitative Methods; Eigenvalues and Eigenvectors; three chapters dealing with Solutions of Systems of Autonomous Equations via Eigenvalues and Eigenvectors (real and distinct, real and equal, and complex conjugate Eigenvalues)
• 20 problem-solving videos online
• 563 solved problems
• Outline format provides a quick and easy review of differential equations
• Clear, concise explanations of differential equations concepts
• Hundreds of examples with explanations of key concepts
• Supports all major textbooks for differential equations courses
• Appropriate for the following courses: Calculus (I, II, and III), Mathematical Modeling, Introductory Differential Equations, and Differential Equations

Chapter 1 Basic Concepts

Chapter 2 An Introduction to Modeling and Qualitative Methods

Chapter 3 Classifications of First-Order Differential Equations

Chapter 4 Separable First-Order Differential Equations

Chapter 5 Exact First-Order Differential Equations

Chapter 6 Linear First-Order Differential Equations

Chapter 7 Applications of First-Order Differential Equations

Chapter 8 Linear Differential Equations: Theory of Solutions

Chapter 9 Second-Order Linear Homogeneous Differential Equations with Constant Coefficients

Chapter 10 nth-Order Linear Homogeneous Differential Equations with Constant Coefficients

Chapter 11 The Method of Undetermined Coefficients

Chapter 12 Variation of Parameters

Chapter 13 Initial-Value Problems for Linear Differential Equations

Chapter 14 Applications of Second-Order Linear Differential Equations

Chapter 15 Matrices

Chapter 16 eAt

Chapter 17 Reduction of Linear Differential Equations to a System of First-Order Equations

Chapter 18 Graphical and Numerical Methods for Solving First-Order Differential Equations

Chapter 19 Further Numerical Methods for Solving First-Order Differential Equations

Chapter 20 Numerical Methods for Solving Second-Order Differential Equations Via Systems

Chapter 21 The Laplace Transform

Chapter 22 Inverse Laplace Transforms

Chapter 23 Convolutions and the Unit Step Function

Chapter 24 Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms

Chapter 25 Solutions of Linear Systems by Laplace Transforms

Chapter 26 Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods

Chapter 27 Power Series Solutions of Linear Differential Equations with Variable Coefficients

Chapter 28 Series Solutions Near a Regular Singular Point

Chapter 29 Some Classical Differential Equations

Chapter 30 Gamma and Bessel Functions

Chapter 31 An Introduct ion to Partial Differential Equations

Chapter 32 Second-Order Boundary-Value Problems

Chapter 33 Eigenfunction Expansions

Chapter 34 An Introduction to Difference Equations

Chapter 35 Solving Differential Equations Using Mathematica

Chapter 36 Solving Systems of Differential Equations via Eigenvalues Using Mathematica

Chapter 37 Qualitative Methods

Chapter 38 Euler's Method Using Microsoft Excel®

Chapter 39 Some Interesting Modeling Problems

APPENDIX Laplace Transforms

ANSWERS TO SUPPLEMENTARY PROBLEMS

About the Author

Richard Bronson, Ph.D., is a professor of mathematics at Farleigh Dickenson University. 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 the Wharton School of Business at the University of Pennsylvania. Bronson has published over 30 technical articles and books, including Schaum’s Outline of Matrix Operations and Shaum’s Outline of Operations Research.

Gabriel B. Costa, Ph.D., is an associate 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, his academic interests include mathematics equation and sabermetrics, the search for objective knowledge about baseball.

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