Multivariable Mathematics, 4th edition

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 stu

• 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.