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.
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 POST INFO & USER RATINGS ( 0 Votes)
A First Course in Differential Equations with Modeling Applications
Author: Dennis G. Zill Edition:
1111827052 | 9781111827052