Calculus; Early Vectors / Edition 1by James Stewart, Columba Stewart
Pub. Date: 01/28/1999
Publisher: Cengage Learning
Once again keeping a keen ear to the needs of the evolving calculus community, Stewart created this text at the suggestion and with the collaboration of professors in the mathematics department at Texas A&M University. With an early introduction to vectors and vector functions, the approach is ideal for engineering students who use vectors early in their curriculum. Stewart begins by introducing vectors in Chapter 1, along with their basic operations, such as addition, scalar multiplication, and dot product. The definition of vector functions and parametric curves is given at the end of Chapter 1 using a two-dimensional trajectory of a projectile as motivation. Limits, derivatives, and integrals of vector functions are interwoven throughout the subsequent chapters.
As with the other texts in his Calculus series, in Early Vectors Stewart makes us of heuristic examples to reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject. This heuristic or discovery approach in the examples give students an intuitive feeling for analysis.
In the Preliminary Edition, Stewart incorporates a focus on problem solving; meticulously attends to accuracy; patiently explains the concepts and examples; and includes the same carefully graded problems that make his other texts work so well for a wide range of students.
Table of ContentsReview and Preview. 2. Limits and Rates of Change. 3. Derivatives. 4. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions. 5. Applications of Differentiation. 6. Integrals. 7. Applications of Integration. 8. Techniques of Integration. 9. Further Applications of Integration. 10. Infinite Sequences and Series. 11. Three-Dimensional Analytic Geometry and Vectors. 12. Partial Derivatives. 13. Multiple Integrals. 14. Vector Calculus. 15. Second-Order Differential Equations. Appendix A. Numbers, Inequalities, and Absolute Values. Appendix B. Coordinate Geometry and Lines. Appendix C. Graphs of Second-Degree Equations. Appendix D. Trigonometry. Appendix E. Mathematical Induction. Appendix F. Proofs of Theorems. Appendix G. Lies My Calculator and Computer Told Me. Appendix H. Complex Numbers. Appendix I. Conic Sections. Appendix J. Conic Sections in Polar Coordinates. Appendix K. Answers to Odd-Numbered Exercises. Index.
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