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Multivariable Mathematics, 4/E
Richard E. Williamson, Dartmouth College
Hale F. Trotter, Princeton University

ISBN-10: 0130672769
ISBN-13: 9780130672766

Publisher: Prentice Hall
Copyright: 2004
Format: Paper; 864 pp
Published: 06/24/2003

Suggested retail price: $73.33
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For courses in second-year calculus, linear calculus and differential equations.

This text explores the standard problem-solving techniques of multivariable mathematics — integrating vector algebra ideas with multivariable calculus and differential equations. This text offers a full year of study and the flexibility to design various one-term and two-term courses.

  • NEW - Increased coverage of phase portraits for second-order equations.

    • Allows students to interpret solutions in the state-space that governs the evolution of a system.

  • NEW - Simple introduction to the geometry of eigenvectors for solutions of systems.

    • Avoids the difficulties of following up this method to the multiple-eigenvalue case, referring ahead to the exponential matrix alternative.

  • NEW - Introduction to vector geometry and matrix algebra—Used extensively in calculus and differential equations.

    • Provides streamlined and unified presentation of these topics for students.

  • NEW - Revised treatment of differentiability—Found in Chapter 5.

    • Presents this topic much more simply and intuitively, with the case of vector-valued functions treated separately.

  • NEW - Early introduction of the gradient vector as the key to differentiability—Presents natural definition with coordinate formula as a consequence of the definition.

    • Allows the later introduction of the derivative matrix to be more natural.

  • NEW - Optional Chapter 3 on general vector spaces—Placed in the context of the preceding two chapters on vector geometry and matrix algebra.

    • Gives those students who want to cover this more theoretical material a multitude of concrete examples.

  • NEW - Java programs available on the Web—For using numerical methods.

    • Provides students with easy access to those useful programs.

  • NEW - Optional numerical methods—Found where applicable.

    • Allows students to produce approximate solutions where closed-form solutions are unavailable.

  • NEW - Optional coverage of moments and centroids.

    • Offers students additional opportunity to practice interpreting and computing multiple integrals.

  • NEW - Simple method for computing the exponential matrix for solution of constant-coefficient linear systems—Found in Chapter 13.

    • Avoids the unnecessarily complicated treatment and aids students in remembering the material.

  • Offers flexibility in coverage—Topics can be covered in a variety of orders, and subsections (which are presented in order of decreasing importance) can be omitted if desired.

    • Allows professor flexibility in lesson planning.

  • Proofs are provided—Includes the definitions and statements of theorems to show how the subject matter can be organized around a few central ideas.

    • Provides a bit of rigor, but not too much.

  • An abundance of applications and worked examples and discussion problems.

    • Reinforces concepts taught in the chapter through a variety of means.

  • Many routine, computational exercises illuminating both theory and practice.

    • Offers students ample opportunity to practice the concepts learned in the chapters.

  • Increased coverage of phase portraits for second-order equations.

    • Allows students to interpret solutions in the state-space that governs the evolution of a system.

  • Simple introduction to the geometry of eigenvectors for solutions of systems.

    • Avoids the difficulties of following up this method to the multiple-eigenvalue case, referring ahead to the exponential matrix alternative.

  • Introduction to vector geometry and matrix algebra—Used extensively in calculus and differential equations.

    • Provides streamlined and unified presentation of these topics for students.

  • Revised treatment of differentiability—Found in Chapter 5.

    • Presents this topic much more simply and intuitively, with the case of vector-valued functions treated separately.

  • Early introduction of the gradient vector as the key to differentiability—Presents natural definition with coordinate formula as a consequence of the definition.

    • Allows the later introduction of the derivative matrix to be more natural.

  • Optional Chapter 3 on general vector spaces—Placed in the context of the preceding two chapters on vector geometry and matrix algebra.

    • Gives those students who want to cover this more theoretical material a multitude of concrete examples.

  • Java programs available on the Web—For using numerical methods.

    • Provides students with easy access to those useful programs.

  • Optional numerical methods—Found where applicable.

    • Allows students to produce approximate solutions where closed-form solutions are unavailable.

  • Optional coverage of moments and centroids.

    • Offers students additional opportunity to practice interpreting and computing multiple integrals.

  • Simple method for computing the exponential matrix for solution of constant-coefficient linear systems—Found in Chapter 13.

    • Avoids the unnecessarily complicated treatment and aids students in remembering the material.



 1. Vectors.


 2. Equations and Matrices.


 3. Vector Spaces and Linearity.


 4. Derivatives.


 5. Differentiability.


 6. Vector Differential Calculus.


 7. Multiple Integration.


 8. Integrals and Derivatives on Curves.


 9. Vector Field Theory.


10. First Order Differential Equations.


11. Second-Order Equations.


12. Introduction to Systems.


13. Matrix Methods.


14. Infinite Series.

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Pearson Higher Education offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students contact your Pearson Higher Education representative.


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