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Full Description
For one-semester sophomore- or junior-level courses in Differential Equations.
Fosters the conceptual development and geometric visualization students need - now available with MyLab Math
Differential Equations and Boundary Value Problems: Computing and Modeling blends traditional algebra problem-solving skills with the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena—a comprehensive approach that makes accessible a wider range of more realistic applications.
The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout. For the first time, MyLab™ Math is available for the 5th Edition, providing online homework with immediate feedback, the complete eText, and more. Additionally, new presentation slides created by author David Calvis are now live in MyLab Math, available in Beamer (LaTeX) and PDF formats. The slides are ideal for both classroom lectures and student review, and combined with Calvis' superlative videos offer a level of support not found in any other Differential Equations course.
Also available with MyLab Math
MyLab™ Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student.
Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm 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 Math, search for:
0134995988 / 9780134995984 Differential Equations and Boundary Value Problems: Computing and Modeling (Tech Update) and MyLab Math with Pearson eText - Title-Specific Access Card Package Package consists of:
0134837398 / 9780134837390 Differential Equations and Boundary Value Problems: Computing and Modeling (Tech Update)
0134872975 / 9780134872971 MyLab Math with Pearson eText - Standalone Access Card - for Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update
Contents
Table of Contents
First-Order Differential Equations
1.1 Differential Equations and Mathematical Models
1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations and Applications
1.5 Linear First-Order Equations
1.6 Substitution Methods and Exact Equations
Mathematical Models and Numerical Methods
2.1 Population Models
2.2 Equilibrium Solutions and Stability
2.3 Acceleration—Velocity Models
2.4 Numerical Approximation: Euler's Method
2.5 A Closer Look at the Euler Method
2.6 The Runge—Kutta Method
Linear Equations of Higher Order
3.1 Introduction: Second-Order Linear Equations
3.2 General Solutions of Linear Equations
3.3 Homogeneous Equations with Constant Coefficients
3.4 Mechanical Vibrations
3.5 Nonhomogeneous Equations and Undetermined Coefficients
3.6 Forced Oscillations and Resonance
3.7 Electrical Circuits
3.8 Endpoint Problems and Eigenvalues
Introduction to Systems of Differential Equations
4.1 First-Order Systems and Applications
4.2 The Method of Elimination
4.3 Numerical Methods for Systems
Linear Systems of Differential Equations
5.1 Matrices and Linear Systems
5.2 The Eigenvalue Method for Homogeneous Systems
5.3 A Gallery of Solution Curves of Linear Systems
5.4 Second-Order Systems and Mechanical Applications
5.5 Multiple Eigenvalue Solutions
5.6 Matrix Exponentials and Linear Systems
5.7 Nonhomogeneous Linear Systems
Nonlinear Systems and Phenomena
6.1 Stability and the Phase Plane
6.2 Linear and Almost Linear Systems
6.3 Ecological Models: Predators and Competitors
6.4 Nonlinear Mechanical Systems
6.5 Chaos in Dynamical Systems
Laplace Transform Methods
7.1 Laplace Transforms and Inverse Transforms
7.2 Transformation of Initial Value Problems
7.3 Translation and Partial Fractions
7.4 Derivatives, Integrals, and Products of Transforms
7.5 Periodic and Piecewise Continuous Input Functions
7.6 Impulses and Delta Functions
Power Series Methods
8.1 Introduction and Review of Power Series
8.2 Series Solutions Near Ordinary Points
8.3 Regular Singular Points
8.4 Method of Frobenius: The Exceptional Cases
8.5 Bessel's Equation
8.6 Applications of Bessel Functions
Fourier Series Methods and Partial Differential Equations
9.1 Periodic Functions and Trigonometric Series
9.2 General Fourier Series and Convergence
9.3 Fourier Sine and Cosine Series
9.4 Applications of Fourier Series
9.5 Heat Conduction and Separation of Variables
9.6 Vibrating Strings and the One-Dimensional Wave Equation
9.7 Steady-State Temperature and Laplace's Equation
Eigenvalue Methods and Boundary Value Problems
10.1 Sturm—Liouville Problems and Eigenfunction Expansions
10.2 Applications of Eigenfunction Series
10.3 Steady Periodic Solutions and Natural Frequencies
10.4 Cylindrical Coordinate Problems
10.5 Higher-Dimensional Phenomena
