# Schaum’s Outline of Differential Equations, 5th Edition

- Length: 432 pages
- Edition: 5
- Language: English
- Publisher: McGraw-Hill Education
- Publication Date: 2021-11-10
- ISBN-10: 1264258828
- ISBN-13: 9781264258826
- Sales Rank: #337597 (See Top 100 Books)

**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

Cover Title Page Copyright Page Dedication Preface to the Fifth Edition Contents Chapter 1 Basic Concepts Differential Equations Notation Solutions Initial-Value and Boundary-Value Problems Chapter 2 An Introduction to Modeling and Qualitative Methods Mathematical Models The “Modeling Cycle” Qualitative Methods Chapter 3 Classifications of First-Order Differential Equations Standard Form and Differential Form Linear Equations Bernoulli Equations Homogeneous Equations Separable Equations Exact Equations Chapter 4 Separable First-Order Differential Equations General Solution Solutions to the Initial-Value Problem Reduction of Homogeneous Equations Chapter 5 Exact First-Order Differential Equations Defining Properties Method of Solution Integrating Factors Chapter 6 Linear First-Order Differential Equations Method of Solution Reduction of Bernoulli Equations Chapter 7 Applications of First-Order Differential Equations Growth and Decay Problems Temperature Problems Falling Body Problems Dilution Problems Electrical Circuits Orthogonal Trajectories Chapter 8 Linear Differential Equations: Theory of Solutions Linear Differential Equations Linearly Independent Solutions The Wronskian Nonhomogeneous Equations Chapter 9 Second-Order Linear Homogeneous Differential Equations with Constant Coefficients Introductory Remark The Characteristic Equation The General Solution Chapter 10 nth-Order Linear Homogeneous Differential Equations with Constant Coefficients The Characteristic Equation The General Solution Chapter 11 The Method of Undetermined Coefficients Simple Form of the Method Generalizations Modifications Limitations of the Method Chapter 12 Variation of Parameters The Method Scope of the Method Chapter 13 Initial-Value Problems for Linear Differential Equations Chapter 14 Applications of Second-Order Linear Differential Equations Spring Problems Electrical Circuit Problems Buoyancy Problems Classifying Solutions Chapter 15 Matrices Matrices and Vectors Matrix Addition Scalar and Matrix Multiplication Powers of a Square Matrix Differentiation and Integration of Matrices The Characteristic Equation Chapter 16 eAt Definition Computation of eAt Chapter 17 Reduction of Linear Differential Equations to a System of First-Order Equations An Example Reduction of an nth Order Equation Reduction of a System Chapter 18 Graphical and Numerical Methods for Solving First-Order Differential Equations Qualitative Methods Direction Fields Euler’s Method Stability Chapter 19 Further Numerical Methods for Solving First-Order Differential Equations General Remarks Modified Euler’s Method Runge–Kutta Method Adams–Bashford–Moulton Method Milne’s Method Starting Values Order of a Numerical Method Chapter 20 Numerical Methods for Solving Second-Order Differential Equations Via Systems Second-Order Differential Equations Euler’s Method Runge–Kutta Method Adams–Bashford–Moulton Method Chapter 21 The Laplace Transform Definition Properties of Laplace Transforms Functions of Other Independent Variables Chapter 22 Inverse Laplace Transforms Definition Manipulating Denominators Manipulating Numerators Chapter 23 Convolutions and the Unit Step Function Convolutions Unit Step Function Translations Chapter 24 Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms Laplace Transforms of Derivatives Solutions of Differential Equations Chapter 25 Solutions of Linear Systems by Laplace Transforms The Method Chapter 26 Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods Solution of the Initial-Value Problem Solution with No Initial Conditions Chapter 27 Power Series Solutions of Linear Differential Equations with Variable Coefficients Second-Order Equations Analytic Functions and Ordinary Points Solutions Around the Origin of Homogeneous Equations Solutions Around the Origin of Nonhomogeneous Equations Initial-Value Problems Solutions Around Other Points Chapter 28 Series Solutions Near a Regular Singular Point Regular Singular Points Method of Frobenius General Solution Chapter 29 Some Classical Differential Equations Classical Differential Equations Polynomial Solutions and Associated Concepts Chapter 30 Gamma and Bessel Functions Gamma Function Bessel Functions Algebraic Operations on Infinite Series Chapter 31 An Introduction to Partial Differential Equations Introductory Concepts Solutions and Solution Techniques Chapter 32 Second-Order Boundary-Value Problems Standard Form Solutions Eigenvalue Problems Sturm–Liouville Problems Properties of Sturm–Liouville Problems Chapter 33 Eigenfunction Expansions Piecewise Smooth Functions Fourier Sine Series Fourier Cosine Series Chapter 34 An Introduction to Difference Equations Introduction Classifications Solutions Chapter 35 Solving Differential Equations Using Mathematica Introduction Chapter 36 Solving Systems of Differential Equations via Eigenvalues Using Mathematica Introduction Terminology Chapter 37 Qualitative Methods Introduction Terminology Chapter 38 Euler’s Method Using Microsoft Excel® The Method Chapter 39 Some Interesting Modeling Problems Examples APPENDIX Laplace Transforms ANSWERS TO SUPPLEMENTARY PROBLEMS INDEX

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