Vector Calculus

Description

• NEW – Thorough coverage of constrained optimization/Lagrange multipliers—Along with second derivative tests.

  • Determines the nature of constrained local extrema. Ex.___

• NEW – Student-tested laboratory and writing exercises.

  • Helps students investigate mathematical problems using software tools, and encourages them to practice their writing skills through experiences in the laboratory. Ex.___

• NEW – More than 200 new exercises—Includes drills, applications, proofs, and “technologically active” projects.

  • Challenges students to use computer graphics and symbolic algebra in ways that enhance their understanding. Ex.___

• NEW – Many new examples—Now total approximately 300

  • Many include new figures to aid students in visualization, others include new applications.

• Emphasis on parameterization.

  • Encourages students to visualize with the aid of hand drawings and computers, in order to enhance their geometric intuition. Ex.___

• Presentation/use of linear algebra as a tool.

  • Provides students with many conceptual and formal parallels with single-variable calculus. Ex.___

• Early introduction to geometry in three-dimensional space—Along with Cylindrical and Spherical coordinates.

  • Prepares students for their later use in connection with the Chain Rule, and change of variables in double and triple integrals. Ex.___

• Early introduction to matrix notation and the rudiments of linear algebra.

  • Familiarizes students with these topics so that it is easier to understand and build upon later material throughout the text. Ex.___

• Technology oriented exercises and projects.

  • Gives students the opportunity to practice what they have learned, including using computers to produce a solution. Ex.___

• Application motivated definitions.

  • Supplies students with a connection between “theory” and “applications.” Ex.___

This brief book presents an accessible treatment of multivariable calculus with an early emphasis on linear algebra as a tool. The organization of the text draws strong analogies with the basic ideas of elementary calculus (derivative, integral, and fundamental theorem). Traditional in approach, it is written with an assumption that the student may have computing facilities for two- and three-dimensional graphics, and for doing symbolic algebra.

1. Coordinate and Vector Geometry.

2. Geometry and Linear Algebra in Rⁿ.

3. Differentiation.

4. Applications of Differentiation.

5. Integration.

6. Fundamental Theorems.

7. Laboratory Writing Projects.

Bibliography.

Answers to Selected Exercises.

Index.

• Thorough coverage of constrained optimization/Lagrange multipliers—Along with second derivative tests.

  • Determines the nature of constrained local extrema. Ex.___

• Student-tested laboratory and writing exercises.

  • Helps students investigate mathematical problems using software tools, and encourages them to practice their writing skills through experiences in the laboratory. Ex.___

• More than 200 new exercises—Includes drills, applications, proofs, and “technologically active” projects.

  • Challenges students to use computer graphics and symbolic algebra in ways that enhance their understanding. Ex.___

• Many new examples—Now total approximately 300

  • Many include new figures to aid students in visualization, others include new applications.