Differential Equations and Linear Algebra – Edwards & Penney – 3rd Edition

Description

For courses in Equations and Linear Algebra. Acclaimed authors combine core topics in elementary equations with those concepts and of elementary linear needed for a contemporary combined introduction to equations and linear algebra.

Known for its real-world applications and its blend of algebraic and geometric approaches, this text discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications.

In the Third Edition, new graphics and narrative have been added as needed—yet the proven chapter and section remains unchanged, so that class notes and syllabi will not require revision for the new edition.

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  • 1. 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

    2. 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

    3. 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

    4. 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

    5. 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

    6. Eigenvalues and Eigenvectors
    6.1 Introduction to Eigenvalues
    6.2 Diagonalization of Matrices
    6.3 Applications Involving Powers of Matrices

    7. 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 Second-Order Systems and Mechanical Applications
    7.5 Multiple Eigenvalue Solutions
    7.6 Numerical Methods for Systems

    8. Matrix Exponential Methods
    8.1 Matrix Exponentials and Linear Systems
    8.2 Nonhomogeneous Linear Systems
    8.3 Spectral Decomposition Methods

    9. 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

    10. 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

    11. 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

    References for Further Study
    Appendix A: Existence and Uniqueness of Solutions
    Appendix B: Theory of Determinants
    Answers to Selected Problems
    Index
  • Citation

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