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More copies of this ISBNThis title in other editionsOther titles in the Featured Titles for Differential Equations series:Fundamentals of Differential Equationsby R. Kent Nagle
Synopses & ReviewsPublisher Comments:Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software.
Fundamentals of Differential Equations, Eighth Edition is suitable for a onesemester sophomore or juniorlevel course. Fundamentals of Differential Equations with Boundary Value Problems, Sixth Edition, contains enough material for a twosemester course that covers and builds on boundary value problems. The Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and SturmLiouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory). Table of Contents1. Introduction 1.1 Background 1.2 Solutions and Initial Value Problems 1.3 Direction Fields 1.4 The Approximation Method of Euler Chapter Summary Technical Writing Exercises Group Projects for Chapter 1 A. Taylor Series Method B. Picard's Method C. The Phase Line
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 Chapter Summary Review Problems Technical Writing Exercises Group Projects for Chapter 2 A. Oil Spill in a Canal B. Differential Equations in Clinical Medicine C. Torricelli's Law of Fluid Flow D. The Snowplow Problem E. Two Snowplows F. Clairaut Equations and Singular Solutions G. Multiple Solutions of a FirstOrder Initial Value Problem H. Utility Functions and Risk Aversion I. Designing a Solar Collector J. Asymptotic Behavior of Solutions to Linear Equations
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 Group Projects for Chapter 3 A. Dynamics of HIV Infection B. Aquaculture C. Curve of Pursuit D. Aircraft Guidance in a Crosswind E. Feedback and the Op Amp F. BangBang Controls G. Market Equilibrium: Stability and Time Paths H. Stability of Numerical Methods I. Period Doubling and Chaos
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 Chapter Summary Review Problems Technical Writing Exercises Group Projects for Chapter 4 A. Nonlinear Equations Solvable by FirstOrder Techniques B. Apollo Reentry C. Simple Pendulum D. Linearization of Nonlinear Problems E. Convolution Method F. Undetermined Coefficients Using Complex Arithmetic G. Asymptotic Behavior of Solutions
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, Poincaré Maps, and Chaos Chapter Summary Review Problems Group Projects for Chapter 5 A. Designing a Landing System for Interplanetary Travel B. Spread of Staph Infections in HospitalsPart 1 C. Things That Bob D. Hamiltonian Systems E. Cleaning Up the Great Lakes
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 Chapter Summary Review Problems Technical Writing Exercises Group Projects for Chapter 6 A. Computer Algebra Systems and Exponential Shift B. Justifying the Method of Undetermined Coefficients C. Transverse Vibrations of a Beam
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 and Periodic Functions 7.7 Convolution 7.8 Impulses and the Dirac Delta Function 7.9 Solving Linear Systems with Laplace Transforms Chapter Summary Review Problems Technical Writing Exercises Group Projects for Chapter 7 A. Duhamel's Formulas B. Frequency Response Modeling C. Determining System Parameters
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 Chapter Summary Review Problems Technical Writing Exercises Group Projects for Chapter 8 A. Alphabetization Algorithms B. Spherically Symmetric Solutions to Shrödinger's Equation for the Hydrogen Atom C. Airy's Equation D. Buckling of a Tower E. Aging Spring and Bessel 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 Chapter Summary Review Problems Technical Writing Exercises Group Projects for Chapter 9 A. Uncoupling Normal Systems B. Matrix Laplace Transform Method C. Undamped SecondOrder Systems D. Undetermined Coefficients for System Forced by Homogeneous
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 Chapter Summary Technical Writing Exercises Group Projects for Chapter 10 A. SteadyState Temperature Distribution in a Circular Cylinder B. A Laplace Transform Solution of the Wave Equation C. Green's Function D. Numerical Method for u=f on a Rectangle
Appendices A. Newton's Method B. Simpson's Rule C. Cramer's Rule D. Method of Least Squares E. RungeKutta Procedure for n Equations
Answers to OddNumbered Problems
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