Calculus: Concepts and Connections (Paperback) (微積分：概念與連結)

Description

This modern calculus textbook places a strong emphasis on developing students' conceptual understanding and on building connections between key calculus topics and their relevance for the real world. It is written for the average student -- one who is mostly unfamiliar with the subject and who requires significant motivation. It follows a relatively standard order of presentation, with early coverage of transcendentals, and integrates thought-provoking applications, examples and exercises throughout. The text also provides balanced guidance on the appropriate role of technology in problem-solving, including its benefits and its potential pitfalls. Wherever practical, concepts are developed from graphical, numerical, algebraic and verbal perspectives (the "Rule of Four") to give students a complete understanding of calculus.

Table of Contents

 

0 Preliminaries

1 Limits and Continuity

2 Differentiation

3 Applications of Differentiation

4 Integration

5 Applications of the Definite Integral

6 Differential Equations

7 Infinite Series

8 Vectors and the Geometry of Space

9 Vector-Valued Functions

10 Functions of Several Variables and Differentiation

11 Multiple Integrals

12 Vector Calculus

Appendix A Additional Polar Graphs

Appendix B Formal Definition of the Limit

Appendix C Derivation of Sine Function

Appendix D The Natural Logarithm as an Integral

Appendix E Conic Sections in Polar Coordinates

Appendix F Proofs of Selected Theorems

Appendix G Answers to Odd-Numbered Exercises