DIFFERENTIAL EQUATIONS : An Introduction to Modern Methods and Applications / James R. Brannan; William E. Boyce
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| | | | | | DIFFERENTIAL EQUATIONS : An Introduction to Modern Methods and Applications. | | xii, 673 pages : color illustrations ; 26 cm. | | Includes index. | | Cover -- Title Page -- Copyright -- Preface -- Acknowledgments -- Contents -- CHAPTER 1 Introduction -- 1.1 Mathematical Models and Solutions -- 1.2 Qualitative Methods: Phase Lines and Direction Fields -- 1.3 Definitions, Classification, and Terminology -- CHAPTER 2 First Order Differential Equations -- 2.1 Separable Equations -- 2.2 Linear Equations: Method of Integrating Factors -- 2.3 Modeling with First Order Equations -- 2.4 Differences Between Linear and Nonlinear Equations -- 2.5 Autonomous Equations and Population Dynamics -- 2.6 Exact Equations and Integrating Factors -- 2.7 Substitution Methods -- Projects -- 2.P.1 Harvesting a Renewable Resource -- 2.P.2 A Mathematical Model of a Groundwater Contaminant Source -- 2.P.3 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin -- CHAPTER 3 Systems of Two First Order Equations -- 3.1 Systems of Two Linear Algebraic Equations -- 3.2 Systems of Two First Order Linear Differential Equations -- 3.3 Homogeneous Linear Systems with Constant Coefficients -- 3.4 Complex Eigenvalues -- 3.5 Repeated Eigenvalues -- 3.6 A Brief Introduction to Nonlinear Systems -- Projects -- 3.P.1 Estimating Rate Constants for an Open Two-Compartment Model -- 3.P.2 A Blood-Brain Pharmacokinetic Model -- CHAPTER 4 Second Order Linear Equations -- 4.1 Definitions and Examples -- 4.2 Theory of Second Order Linear Homogeneous Equations -- 4.3 Linear Homogeneous Equations with Constant Coefficients -- 4.4 Mechanical and Electrical Vibrations -- 4.5 Nonhomogeneous Equations -- Method of Undetermined Coefficients -- 4.6 Forced Vibrations, Frequency Response, and Resonance -- 4.7 Variation of Parameters -- Projects -- 4.P.1 A Vibration Insulation Problem -- 4.P.2 Linearization of a Nonlinear Mechanical System -- 4.P.3 A Spring-Mass Event Problem -- 4.P.4 Euler-Lagrange Equations. CHAPTER 5 The Laplace Transform -- 5.1 Definition of the Laplace Transform -- 5.2 Properties of the Laplace Transform -- 5.3 The Inverse Laplace Transform -- 5.4 Solving Differential Equations with Laplace Transforms -- 5.5 Discontinuous Functions and Periodic Functions -- 5.6 Differential Equations with Discontinuous Forcing Functions -- 5.7 Impulse Functions -- 5.8 Convolution Integrals and Their Applications -- 5.9 Linear Systems and Feedback Control -- Projects -- 5.P.1 An Electric Circuit Problem -- 5.P.2 The Watt Governor, Feedback Control, and Stability -- CHAPTER 6 Systems of First Order Linear Equations -- 6.1 Definitions and Examples -- 6.2 Basic Theory of First Order Linear Systems -- 6.3 Homogeneous Linear Systems with Constant Coefficients -- 6.4 Nondefective Matrices with Complex Eigenvalues -- 6.5 Fundamental Matrices and the Exponential of a Matrix -- 6.6 Nonhomogeneous Linear Systems -- 6.7 Defective Matrices -- Projects -- 6.P.1 Earthquakes and Tall Buildings -- 6.P.2 Controlling a Spring-Mass System to Equilibrium -- CHAPTER 7 Nonlinear Differential Equations and Stability -- 7.1 Autonomous Systems and Stability -- 7.2 Almost Linear Systems -- 7.3 Competing Species -- 7.4 Predator-Prey Equations -- 7.5 Periodic Solutions and Limit Cycles -- 7.6 Chaos and Strange Attractors: The Lorenz Equations -- Projects -- 7.P.1 Modeling of Epidemics -- 7.P.2 Harvesting in a Competitive Environment -- 7.P.3 The Rossler System -- CHAPTER 8 Numerical Methods -- 8.1 Numerical Approximations: Euler's Method -- 8.2 Accuracy of Numerical Methods -- 8.3 Improved Euler and Runge-Kutta Methods -- 8.4 Numerical Methods for Systems of First Order Equations -- Projects -- 8.P.1 Designing a Drip Dispenser for a Hydrology Experiment -- 8.P.2 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin -- APPENDIX A Matrices and Linear Algebra. A.1 Matrices -- A.2 Systems of Linear Algebraic Equations, Linear Independence, and Rank -- A.3 Determinants and Inverses -- A.4 The Eigenvalue Problem -- Answers -- References -- Index --. | | ISBN 9781118531778. | | | | 1. Differential equations 2. MATHEMATICS - Calculus 3. MATHEMATICS - Mathematical Analysis.I. Boyce, William E. II. Title | | Control No. : 28505 | | | Library : UiTM Shah Alam |
| | Accn No. | Item Status | Add Id | Location | SMD | Item Category | | 1028591 | Shelf | | PERPUSTAKAAN TUN ABDUL RAZAK(P1) | BOOK | slr | | 1028592 | Shelf | | PERPUSTAKAAN TUN ABDUL RAZAK(P1) | BOOK | OSs |
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