Fundamentals of differential equations
 Responsibility
 R. Kent Nagle, Edward B. Saff, Vanderbilt University, Arthur David Snider, University of South Florida.
 Edition
 Ninth edition.
 Publication
 Boston : Pearson, [2018]
 Physical description
 1 volume (various pagings) ; 26 cm
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA371 .N24 2018  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Nagle, R. Kent.
 Contributor
 Saff, E. B., 1944
 Snider, Arthur David, 1940
Contents/Summary
 Contents

 1. Introduction 1.1 Background 1.2 Solutions and Initial Value Problems 1.3 Direction Fields 1.4 The Approximation Method of Euler
 2. FirstOrder Differential Equations 2.1 Introduction: Motion of a Falling Body 2.2 Separable Equations 2.3 Linear Equations 2.4 Exact Equations 2.5 Special Integrating Factors 2.6 Substitutions and Transformations
 3. Mathematical Models and Numerical Methods Involving First Order Equations 3.1 Mathematical Modeling 3.2 Compartmental Analysis 3.3 Heating and Cooling of Buildings 3.4 Newtonian Mechanics 3.5 Electrical Circuits 3.6 Improved Euler's Method 3.7 HigherOrder Numerical Methods: Taylor and RungeKutta
 4. Linear SecondOrder Equations 4.1 Introduction: The MassSpring Oscillator 4.2 Homogeneous Linear Equations: The General Solution 4.3 Auxiliary Equations with Complex Roots 4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients 4.5 The Superposition Principle and Undetermined Coefficients Revisited 4.6 Variation of Parameters 4.7 VariableCoefficient Equations 4.8 Qualitative Considerations for VariableCoefficient and Nonlinear Equations 4.9 A Closer Look at Free Mechanical Vibrations 4.10 A Closer Look at Forced Mechanical Vibrations
 5. Introduction to Systems and Phase Plane Analysis 5.1 Interconnected Fluid Tanks 5.2 Elimination Method for Systems with Constant Coefficients 5.3 Solving Systems and HigherOrder Equations Numerically 5.4 Introduction to the Phase Plane 5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models 5.6 Coupled MassSpring Systems 5.7 Electrical Systems 5.8 Dynamical Systems, Poincare Maps, and Chaos
 6. Theory of HigherOrder Linear Differential Equations 6.1 Basic Theory of Linear Differential Equations 6.2 Homogeneous Linear Equations with Constant Coefficients 6.3 Undetermined Coefficients and the Annihilator Method 6.4 Method of Variation of Parameters
 7. Laplace Transforms 7.1 Introduction: A Mixing Problem 7.2 Definition of the Laplace Transform 7.3 Properties of the Laplace Transform 7.4 Inverse Laplace Transform 7.5 Solving Initial Value Problems 7.6 Transforms of Discontinuous Functions 7.7 Transforms of Periodic and Power Functions 7.8 Convolution 7.9 Impulses and the Dirac Delta Function 7.10 Solving Linear Systems with Laplace Transforms
 8. Series Solutions of Differential Equations 8.1 Introduction: The Taylor Polynomial Approximation 8.2 Power Series and Analytic Functions 8.3 Power Series Solutions to Linear Differential Equations 8.4 Equations with Analytic Coefficients 8.5 CauchyEuler (Equidimensional) Equations 8.6 Method of Frobenius 8.7 Finding a Second Linearly Independent Solution 8.8 Special Functions
 9. Matrix Methods for Linear Systems 9.1 Introduction 9.2 Review
 1: Linear Algebraic Equations 9.3 Review
 2: Matrices and Vectors 9.4 Linear Systems in Normal Form 9.5 Homogeneous Linear Systems with Constant Coefficients 9.6 Complex Eigenvalues 9.7 Nonhomogeneous Linear Systems 9.8 The Matrix Exponential Function
 10. Partial Differential Equations 10.1 Introduction: A Model for Heat Flow 10.2 Method of Separation of Variables 10.3 Fourier Series 10.4 Fourier Cosine and Sine Series 10.5 The Heat Equation 10.6 The Wave Equation 10.7 Laplace's Equation
 Appendix A Newton's Method Appendix B Simpson's Rule Appendix C Cramer's Rule Appendix D Method of Least Squares Appendix E RungeKutta Procedure for n Equations.
 (source: Nielsen Book Data)
 Publisher's Summary
 ["For onesemester sophomore or juniorlevel courses in Differential Equations. An introduction to the basic theory and applications of differential equations Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. This flexible text allows instructors to adapt to various course emphases (theory, methodology, applications, and numerical methods) and to use commercially available computer software. For the first time, MyLab(TM) Math is available for this text, providing online homework with immediate feedback, the complete eText, and more. Note that a longer version of this text, entitled Fundamentals of Differential Equations and Boundary Value Problems, 7th Edition, contains enough material for a twosemester course. This longer text consists of the main text plus three additional chapters (Eigenvalue Problems and SturmLiouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory). Also available with MyLab Math MyLab(TM) Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. Note: You are purchasing a standalone product; MyLab does not come packaged with this content. Students, if interested in purchasing this title with MyLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab, search for: 0134665686 / 9780134665689 Fundamentals of Differential Equations Plus MyLab Math with Pearson eText  Access Card Package Package consists of: *0321431308 / 9780321431301 MyLab Math  Gluein Access Card*0321654064 / 9780321654069 MyLab Math Inside Star Sticker*0321977068 / 9780321977069 Fundamentals of Differential Equations.", {"source"=>"(source: Nielsen Book Data)"}, "9780321977069", "20170717"]
Subjects
Bibliographic information
 Publication date
 2018
 Note
 Includes index.
 ISBN
 9780321977069 (hardcover)
 0321977068 (hardcover)