A First Course in Differential Equations with Modeling Applications – Dennis G. Zill – 10th Edition


A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 10th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations.

This proven and accessible book speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, “Remarks” boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, the book provides a thorough treatment of boundary-value problems and partial differential equations.

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  • Chapter 1: Introduction to Differential Equations
    1.1: Definitions and Terminology
    1.2: Initial-Value Problems
    1.3: Differential Equations as Mathematical Models

    Chapter 2: First-Order Differential Equations
    2.1: Solution Curves Without a Solution
    2.2: Separable Equations
    2.3: Linear Equations
    2.4: Exact Equations
    2.5: Solutions by Substitutions
    2.6: A Numerical Method

    Chapter 3: Modeling With First-Order Differential Equations
    3.1: Linear Models
    3.2: Nonlinear Models
    3.3: Modeling with Systems of First-Order Des

    Chapter 4: Higher-Order Differential Equations
    4.1: Preliminary Theory_Linear Equations
    4.2: Reduction of Order
    4.3: Homogeneous Linear Equations with Constant Coefficients
    4.4: Undetermined Coefficients_Superposition Approach
    4.5: Undetermined Coefficients_Annihilator Approach
    4.6: Variation of Parameters
    4.7: Cauchy-Euler Equation
    4.8: Green's Function
    4.9: Solving Systems of Linear Des by Elimination
    4.10: Nonlinear Differential Equations

    Chapter 5: Modeling With Higher-Order Differential Equations
    5.1: Linear Models: Initial-Value Problems
    5.2: Linear Models: Boundary-Value Problems
    5.3: Nonlinear Models

    Chapter 6: Series Solutions of Linear Equations
    6.1: Review of Power Series
    6.2: Solutions About Ordinary Points
    6.3: Solutions About Singular Points
    6.4: Special Functions

    Chapter 7: The Laplace Transform
    7.1: Definition of the Laplace Transform
    7.2: Inverse Transforms and Transforms of Derivatives
    7.3: Operational Properties I
    7.4: Operational Properties II
    7.5: The Dirac Delta Function
    7.6: Systems of Linear Differential Equations

    Chapter 8: Systems of Linear First-Order Differential Equations
    8.1: Preliminary Theory_Linear Systems
    8.2: Homogeneous Linear Systems
    8.3: Nonhomogeneous Linear Systems
    8.4: Matrix Exponential

    Chapter 9: Numerical Solutions of Ordinary Differential Equations
    9.1: Euler Methods and Error Analysis
    9.2: Runge-Kutta Methods
    9.3: Multistep Methods
    9.4: Higher-Order Equations and Systems
    9.5: Second-Order Boundary-Value Problems

    Chapter A: Appendixes
    A.1: Gamma Function
    A.2: Matrices
    A.3: Laplace Transforms
  • Citation
    • Full Title: A First Course in Differential Equations with Modeling Applications
    • Author/s:
    • ISBN-10: 1111827052
    • ISBN-13: 9781111827052
    • Edition: 10th Edition
    • Publication date: 2014
    • Topic: Math
    • Subtopic: Differential Equations
    • File Type: eBook
    • Idioma: English

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