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.

Table of Contents

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

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