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Full Description
For courses in Differential Equations and Linear Algebra.
Now available with MyLab Math
The right balance between concepts, visualization, applications, and skills - now available with MyLab Math
Differential Equations and Linear Algebra provides the conceptual development and geometric visualization of a modern differential equations and linear algebra 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 combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It 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 this text, providing online homework with immediate feedback, the complete eText, and more. Additionally, new presentation slides created by author David Calvis are available in Beamer (LaTeX) and PDF formats. The slides are ideal for classroom lectures and student review, and combined with Calvis' superlative instructional videos offer a level of support not found in any other Differential Equations course.
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MyLab Math is the teaching and learning platform that empowers you 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.
0136743641 / 9780136743644 MYLAB MATH DIGITAL UPDATE WITH PEARSON ETEXT -- ACCESS CARD -- FOR DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA, 4/e
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 Systems and Matrices
3.1 Introduction to Linear Systems
3.2 Matrices and Gaussian Elimination
3.3 Reduced Row-Echelon Matrices
3.4 Matrix Operations
3.5 Inverses of Matrices
3.6 Determinants
3.7 Linear Equations and Curve Fitting
Vector Spaces
4.1 The Vector Space R3
4.2 The Vector Space Rn and Subspaces
4.3 Linear Combinations and Independence of Vectors
4.4 Bases and Dimension for Vector Spaces
4.5 Row and Column Spaces
4.6 Orthogonal Vectors in Rn
4.7 General Vector Spaces
Higher-Order Linear Differential Equations
5.1 Introduction: Second-Order Linear Equations
5.2 General Solutions of Linear Equations
5.3 Homogeneous Equations with Constant Coefficients
5.4 Mechanical Vibrations
5.5 Nonhomogeneous Equations and Undetermined Coefficients
5.6 Forced Oscillations and Resonance
Eigenvalues and Eigenvectors
6.1 Introduction to Eigenvalues
6.2 Diagonalization of Matrices
6.3 Applications Involving Powers of Matrices
Linear Systems of Differential Equations
7.1 First-Order Systems and Applications
7.2 Matrices and Linear Systems
7.3 The Eigenvalue Method for Linear Systems
7.4 A Gallery of Solution Curves of Linear Systems
7.5 Second-Order Systems and Mechanical Applications
7.6 Multiple Eigenvalue Solutions
7.7 Numerical Methods for Systems
Matrix Exponential Methods
8.1 Matrix Exponentials and Linear Systems
8.2 Nonhomogeneous Linear Systems
8.3 Spectral Decomposition Methods
Nonlinear Systems and Phenomena
9.1 Stability and the Phase Plane
9.2 Linear and Almost Linear Systems
9.3 Ecological Models: Predators and Competitors
9.4 Nonlinear Mechanical Systems
Laplace Transform Methods
10.1 Laplace Transforms and Inverse Transforms
10.2 Transformation of Initial Value Problems
10.3 Translation and Partial Fractions
10.4 Derivatives, Integrals, and Products of Transforms
10.5 Periodic and Piecewise Continuous Input Functions
Power Series Methods
11.1 Introduction and Review of Power Series
11.2 Power Series Solutions
11.3 Frobenius Series Solutions
11.4 Bessel Functions
Appendix A: Existence and Uniqueness of Solutions Appendix B: Theory of Determinants APPLICATION MODULES The modules listed below follow the indicated sections in the text. Most provide computing projects that illustrate the corresponding text sections. Many of these modules are enhanced by the supplementary material found at the new Expanded Applications website.
1.3 Computer-Generated Slope Fields and Solution Curves
1.4 The Logistic Equation
1.5 Indoor Temperature Oscillations
1.6 Computer Algebra Solutions
2.1 Logistic Modeling of Population Data
2.3 Rocket Propulsion
2.4 Implementing Euler's Method
2.5 Improved Euler Implementation
2.6 Runge-Kutta Implementation
3.2 Automated Row Operations
3.3 Automated Row Reduction
3.5 Automated Solution of Linear Systems
5.1 Plotting Second-Order Solution Families
5.2 Plotting Third-Order Solution Families
5.3 Approximate Solutions of Linear Equations
5.5 Automated Variation of Parameters
5.6 Forced Vibrations and Resonance
7.1 Gravitation and Kepler's Laws of Planetary Motion
7.3 Automatic Calculation of Eigenvalues and Eigenvectors
7.4 Dynamic Phase Plane Graphics
7.5 Earthquake-Induced Vibrations of Multistory Buildings
7.6 Defective Eigenvalues and Generalized Eigenvectors
7.7 Comets and Spacecraft
8.1 Automated Matrix Exponential Solutions
8.2 Automated Variation of Parameters
9.1 Phase Portraits and First-Order Equations
9.2 Phase Portraits of Almost Linear Systems
9.3 Your Own Wildlife Conservation Preserve
9.4 The Rayleigh and van der Pol Equations
