Test Bank
A First Course In Differential Equations With Modeling
Applications,
By Dennis G. Zill
12th Edition
PAGE 1
, Table Of Contents Are Given Below
Here Is The Table Of Contents For A First Course In Differential Equations With Modeling Applications, 12th
Edition By Dennis G. Zill:
1. Introduction To Differential Equations
o Definitions And Terminology
o Initial-Value Problems
o Differential Equations As Mathematical Models
o Chapter 1 In Review
2. First-Order Differential Equations
o Solution Curves Without A Solution
o Separable Equations
o Linear Equations
o Exact Equations
o Solutions By Substitutions
o A Numerical Method
o Chapter 2 In Review
3. Modeling With First-Order Differential Equations
o Linear Models
o Nonlinear Models
o Modeling With Systems Of First-Order Des
o Chapter 3 In Review
4. Higher-Order Differential Equations
o Theory Of Linear Equations
o Reduction Of Order
PAGE 2
, o Homogeneous Linear Equations With Constant Coefficients
o Undetermined Coefficients—Superposition Approach
o Undetermined Coefficients—Annihilator Approach
o Variation Of Parameters
o Cauchy-Euler Equation
o Green's Functions
o Solving Systems Of Linear Des By Elimination
o Nonlinear Differential Equations
o Chapter 4 In Review
5. Modeling With Higher-Order Differential Equations
o Linear Models: Initial-Value Problems
o Linear Models: Boundary-Value Problems
o Nonlinear Models
o Chapter 5 In Review
6. Series Solutions Of Linear Equations
o Review Of Power Series
o Solutions About Ordinary Points
o Solutions About Singular Points
o Special Functions
o Chapter 6 In Review
7. The Laplace Transform
o Definition Of The Laplace Transform
o Inverse Transform And Transforms Of Derivatives
o Operational Properties I
o Operational Properties Ii
o Dirac Delta Function
o Systems Of Linear Differential Equations
o Chapter 7 In Review
8. Systems Of Linear Differential Equations
PAGE 3
, o Theory Of Linear Systems
o Homogeneous Linear Systems
o Nonhomogeneous Linear Systems
o Matrix Exponential
o Chapter 8 In Review
9. Numerical Solutions Of Ordinary Differential Equations
o Euler Methods And Error Analysis
o Runge-Kutta Methods
o Multistep Methods
o Higher-Order Equations And Systems
o Second-Order Boundary-Value Problems
o Chapter 9 In Review
Appendices:
Appendix A: Integral-Defined Functions
Appendix B: Matrices
Appendix C: Table Of Laplace Transforms
This Comprehensive Structure Provides A Thorough Overview Of Differential Equations And Their Applications,
Supporting Students With Numerous Examples, Explanations, And Review Sections.
PAGE 4
A First Course In Differential Equations With Modeling
Applications,
By Dennis G. Zill
12th Edition
PAGE 1
, Table Of Contents Are Given Below
Here Is The Table Of Contents For A First Course In Differential Equations With Modeling Applications, 12th
Edition By Dennis G. Zill:
1. Introduction To Differential Equations
o Definitions And Terminology
o Initial-Value Problems
o Differential Equations As Mathematical Models
o Chapter 1 In Review
2. First-Order Differential Equations
o Solution Curves Without A Solution
o Separable Equations
o Linear Equations
o Exact Equations
o Solutions By Substitutions
o A Numerical Method
o Chapter 2 In Review
3. Modeling With First-Order Differential Equations
o Linear Models
o Nonlinear Models
o Modeling With Systems Of First-Order Des
o Chapter 3 In Review
4. Higher-Order Differential Equations
o Theory Of Linear Equations
o Reduction Of Order
PAGE 2
, o Homogeneous Linear Equations With Constant Coefficients
o Undetermined Coefficients—Superposition Approach
o Undetermined Coefficients—Annihilator Approach
o Variation Of Parameters
o Cauchy-Euler Equation
o Green's Functions
o Solving Systems Of Linear Des By Elimination
o Nonlinear Differential Equations
o Chapter 4 In Review
5. Modeling With Higher-Order Differential Equations
o Linear Models: Initial-Value Problems
o Linear Models: Boundary-Value Problems
o Nonlinear Models
o Chapter 5 In Review
6. Series Solutions Of Linear Equations
o Review Of Power Series
o Solutions About Ordinary Points
o Solutions About Singular Points
o Special Functions
o Chapter 6 In Review
7. The Laplace Transform
o Definition Of The Laplace Transform
o Inverse Transform And Transforms Of Derivatives
o Operational Properties I
o Operational Properties Ii
o Dirac Delta Function
o Systems Of Linear Differential Equations
o Chapter 7 In Review
8. Systems Of Linear Differential Equations
PAGE 3
, o Theory Of Linear Systems
o Homogeneous Linear Systems
o Nonhomogeneous Linear Systems
o Matrix Exponential
o Chapter 8 In Review
9. Numerical Solutions Of Ordinary Differential Equations
o Euler Methods And Error Analysis
o Runge-Kutta Methods
o Multistep Methods
o Higher-Order Equations And Systems
o Second-Order Boundary-Value Problems
o Chapter 9 In Review
Appendices:
Appendix A: Integral-Defined Functions
Appendix B: Matrices
Appendix C: Table Of Laplace Transforms
This Comprehensive Structure Provides A Thorough Overview Of Differential Equations And Their Applications,
Supporting Students With Numerous Examples, Explanations, And Review Sections.
PAGE 4
