Elementary Calculus An Infinitesimal Approach

This first-year calculus book is centered around the use of infinitesimals rather than the epsilon-delta approach. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems. Additional subjects include transcendental functions, series, vectors, partial derivatives, and multiple integrals. 2007 edition.

H. Jerome Keisler was a longtime professor at the University of Wisconsin, Madison. He pursued his Ph.D. under the direction of Alfred Tarski at the University of California, Berkeley, and his research included model theory and nonstandard analysis.

Introduction 1. Real and Hyperreal Numbers 2. Differentiation 3. Continous Functions 4. Integration 5. Limits, Analytic Geometry, and Approximations 6. Applications of the Integral 7. Trigonometric Functions 8. Exponential and Logarithmic Functions 9. Infinite Series 10. Vectors 11. Partial Differentiation 12. Multiple Integrals 13. Vector Calculus 14. Differential Equations Epilogue Appendix: Tables Answers to Selected Problems Index