Description

Features

• NEW - Includes a variety of new sections that include discussions on:
  • —Direction fields and Euler's method for first order differential equations.
  • —Row space and column space of a matrix and the rank-nullity theorem.
  • —Non-linear systems of differential equations including phase plane analysis.
  • —Change of variables for differential equations with examples of first order homogeneous DE's, Bernoulli equations, and Ricatti equations. Ex.___

• NEW - Several application problems are introduced in the first section of the text and then used throughout the following chapters.

  • Motivates the study of differential equations. Ex.___

• NEW - Material on second order linear differential equations that was previously in Chapter 9 is now in Chapter 2 and is not dependent on the vector space.
  • —The longer time spent on DE at the beginning of the course gives students a firmer grasp of the differential equation concept early on and also on the solution techniques for this important class of differential equations.
  • —Introduces and reinforces the idea of linearity which can then be used to better motivate and illustrate the vector space ideas.
  • —Placement in Chapter 2 adds flexibility to the text. Since many students have already seem much of this (and the Chapter 1) material in a previous calculus course, some instructors may choose to use this chapter as a review or even omit it altogether. Ex.___

• NEW - Chapters on vector spaces and linear transformations have been completely rewritten:
  • —More emphasis is now placed on Rⁿ before introducing abstract vector spaces.
  • —Two sections discussing the row space and column space of a matrix and the rank nullity theorem have been added.
  • —Material on eigenvalues and eigenvectors (old Chapter 8) now appears in Chapter 7 after the discussion of linear transformations of Rⁿ. Ex.___

• NEW - What were previously Chapters 12 and 13 (Laplace Transforms and Series Solutions of Linear Differential Equations respectively) are now Chapters 3 and 4.

• Provides a better integration of DE and Linear Algebra than other texts in the market.

• Gives students a complete, fundamental introduction to both linear algebra and differential equations.

  • Promotes in-depth understanding (vs. rote memorization)—enabling students to fully comprehend abstract concepts and leave the course with a solid foundation in linear algebra. Ex.___

• Continues to offer one of the most lucid and clearly written narratives on the subject—With material that is accessible to the average student yet challenging to all students.

• Organizes material in a way that is highly flexible—For instructors to tailor the course to meet their needs.

• Presents a greater emphasis on geometry.

  • Help students better visualize the abstract concepts. Ex.___

• Illustrates all concepts with an ample number of worked examples.

• Definitions are highlighted via boxes and/or shading.

New To This Edition

• Includes a variety of new sections that include discussions on:
  • —Direction fields and Euler's method for first order differential equations.
  • —Row space and column space of a matrix and the rank-nullity theorem.
  • —Non-linear systems of differential equations including phase plane analysis.
  • —Change of variables for differential equations with examples of first order homogeneous DE's, Bernoulli equations, and Ricatti equations. Ex.___

• Several application problems are introduced in the first section of the text and then used throughout the following chapters.

  • Motivates the study of differential equations. Ex.___

• Material on second order linear differential equations that was previously in Chapter 9 is now in Chapter 2 and is not dependent on the vector space.
  • —The longer time spent on DE at the beginning of the course gives students a firmer grasp of the differential equation concept early on and also on the solution techniques for this important class of differential equations.
  • —Introduces and reinforces the idea of linearity which can then be used to better motivate and illustrate the vector space ideas.
  • —Placement in Chapter 2 adds flexibility to the text. Since many students have already seem much of this (and the Chapter 1) material in a previous calculus course, some instructors may choose to use this chapter as a review or even omit it altogether. Ex.___

• Chapters on vector spaces and linear transformations have been completely rewritten:
  • —More emphasis is now placed on Rⁿ before introducing abstract vector spaces.
  • —Two sections discussing the row space and column space of a matrix and the rank nullity theorem have been added.
  • —Material on eigenvalues and eigenvectors (old Chapter 8) now appears in Chapter 7 after the discussion of linear transformations of Rⁿ. Ex.___

• What were previously Chapters 12 and 13 (Laplace Transforms and Series Solutions of Linear Differential Equations respectively) are now Chapters 3 and 4.

Table of Contents



 1. First-Order Differential Equations.


 2. Second-Order Linear Differential Equations.


 3. Matrices and Systems of Linear Algebraic Equations.


 4. Determinants.


 5. Vector Spaces.


 6. Linear Transformations and the Eigenvalue/Eigenvector Problem.


 7. Linear Differential Equations of Order n.


 8. Systems of Differential Equations.


 9. The Laplace Transform and Some Elementary Applications.


10. Series Solutions to Differential Equations.


Appendix 1. A Review of Complex Numbers.


Appendix 2. A Review of Partial Fractions.


Appendix 3. A Review of Integration Techniques.


Appendix 4. An Existence and Uniqueness Theorem for First-Order Differential Equations.


Appendix 5. Linearly Independent Solutions to: x2 y" + xp(x) y' + q(x)y = 0.


Answers to Odd Numbered Problems.


Index.

Courses

Differential Equations and Linear Algebra  (Mathematics)

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  This complete introduction to both differential equations and linear algebra presents a carefully balanced and sound integration of the two topics. It promotes in-depth understanding rather than rote memorization, enabling students to fully comprehend abstract concepts and leave the course with a solid foundation in linear algebra. Flexible in format, it explains concepts clearly and logically with an abundance of examples and illustrations, without sacrificing level or rigor. A vast array of problems supports the material, with varying levels from which students/instructors can choose.

   

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