A revision of McGraw-Hill's leading calculus text for the 3-semester sequence taken primarily by math, engineering, and science majors. The revision is substantial and has been influenced by students, instructors in physics, engineering, and mathematics, and participants in the national debate on the future of calculus. Revision focused on these key areas: Upgrading graphics and design, expanding range of problem sets, increasing motivation, strengthening multi-variable chapters, and building a stronger support package.
1. An Overview of Calculus.
2. Functions, Limits, and Continuity.
3. The
Derivative.
4. Applications of the Derivative.
5. The Definite Integral.
6.
Topics in Differential Calculus.
7. Computing Antiderivatives.
8.
Applications of the Definite Integral.
9. Plane Curves and Polar Coordinates.
10. Series.
11. Power Series and Complex Numbers.
12. Vectors.
13. The
Derivative of a Vector Function.
14. Partial Derivatives.
15. Definite
Integrals over Plane and Solid Regions.
16. Green's Theorem.
17. The
Divergence Theorem and Stokes' Theorem. Appendices:A. Real Numbers. B. Graphs
and Lines. C. Topics in Algebra. D. Exponents. E. Mathematical Induction. F.
The Converse of a Statement. G. Conic Sections. H. Logarithms and
Exponentials Defined through Calculus.I. The Taylor Series for f(x,y). J.
Theory of Limits. K. The Interchange of Limits. L. The Jacobian. M. Linear
Differential Equations with Constant Coefficients.
Sherman Stein, received his Ph.D. from Columbia University. After a one-year instructorship at Princeton University, he joined the faculty at the University of California, Davis, where he taught until 1993. His main mathematical interests are in algebra, combinatorics, and pedagogy. He has been the recipient of two MAA awards; the Lester R. Ford Award for Mathematical Exposition, and the Beckenbach Book Prize for Algebra and Tiling (with Sandor Szabo). He also received The Distinguished Teaching Award from the University of California, Davis, and an honorary Doctor of Humane Letters from Marietta College.
