Fundamentals of Differential Equations by Edward Saff, R. Nagle and Arthur Snider (2017, Hardcover)

Pearson Education

0321977068

9780321977069

234451120

720 Pages

English

Fundamentals of Differential Equations

Differential Equations / General, General

2017

Textbook

Mathematics

Edward Saff, R. Nagle, Arthur Snider

Hardcover

1.3 in

52.8 Oz

9.7 in

8 in

9

College Audience

2016-030706

23

{"IsNonfiction":["No"],"IsOther":["No"],"IsAdult":["No"],"MuzeFormatDesc":["Hardcover"],"IsChildren":["No"],"Genre":["MATHEMATICS"],"Topic":["General","Differential Equations / General"],"IsTextBook":["Yes"],"IsFiction":["No"]}

Yes

515/.35

1. Introduction 1.1 Background 1.2 Solutions and Initial Value Problems 1.3 Direction Fields 1.4 The Approximation Method of Euler 2. First-Order 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 Higher-Order Numerical Methods: Taylor and Runge-Kutta 4. Linear Second-Order Equations 4.1 Introduction: The Mass-Spring 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 Variable-Coefficient Equations 4.8 Qualitative Considerations for Variable-Coefficient 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 Higher-Order Equations Numerically 5.4 Introduction to the Phase Plane 5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models 5.6 Coupled Mass-Spring Systems 5.7 Electrical Systems 5.8 Dynamical Systems, Poincaré Maps, and Chaos 6. Theory of Higher-Order 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 Cauchy-Euler (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 Appendices Newton''s Method Simpson''s Rule Cramer''s Rule Method of Least Squares Runge-Kutta Procedure for n Equations

For one-semester sophomore- or junior-level 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 two-semester course. This longer text consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm--Liouville 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. Students, if interested in purchasing this title with MyLab Math, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information., For one-semester sophomore- or junior-level 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 two-semester course. This longer text consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm--Liouville 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: 0134768744 / 9780134768748 Fundamentals of Differential Equations plus MyLab Math with Pearson eText -- Title-Specific Access Card Package, 9/e Package consists of: 0134764838 / 9780134764832 MyLab Math with Pearson eText -- Standalone Access Card -- for Fundamentals of Differential Equations 0321977068 / 9780321977069 Fundamentals of Differential Equations, For one-semester sophomore- or junior-level 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 two-semester course. This longer text consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville 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 -- Glue-in Access Card 0321654064 / 9780321654069 MyLab Math Inside Star Sticker 0321977068 / 9780321977069 Fundamentals of Differential Equations

QA371.N24 2018

2018

4