A Course of Pure Mathematics Third Edition

by Hardy, G. H.

• ISBN13: 9780486822358
• ISBN10: 0486822354
• Edition: 3rd
• Format: Paperback
• Copyright: 2018-07-18
• Publisher: Dover Publications

Summary

Originally published in 1908, this classic calculus text transformed university teaching and remains a must-read for all students of introductory mathematical analysis. Clear, rigorous explanations of the mathematics of analytical number theory and calculus cover single-variable calculus, sequences, number series, and properties of cos, sin, and log. Meticulous expositions detail the fundamental ideas underlying differential and integral calculus, the properties of infinite series, and the notion of limit.
An expert in the fields of analysis and number theory, author G. H. Hardy taught for decades at both Cambridge and Oxford. A Course of Pure Mathematics is suitable for college and high school students and teachers of calculus as well as fans of pure math. Each chapter includes demanding problem sets that allow students to apply the principles directly, and four helpful Appendixes supplement the text.

Author Biography

English mathematician G. H. Hardy (1877–1947) specialized in number theory and mathematical analysis and is responsible for biology's Hardy-Weinberg principle of population genetics. He mentored Indian mathematician Srinivasa Ramanujan, with whom he coined the Hardy-Ramanujan number, and he wrote the classic essay, "A Mathematician's Apology."

Table of Contents

I. Real Variables

II. Functions of Real Variables

III. Complex Numbers

IV. Limits of Functions of a Positine Integral Variable

V. Limits of Functions of a Continuois Variable. Continuous and Discontinuous Functions

VI. Derivatives and Integrals

VII. Additionsal Theorems in the Differential and Integral Calculus

VIII. The Convergence of Infinite Series and Infinite Integrals

IX. The Logarithmic and Exponential Functions of a Real Variable

X. The General Theory of the Logarithmic, Exponential, and Circular Functions

Appendix I. The Proof that Every Equation has a Root

Appendix II. A Note on Double Limit Problems

Appendix III. The Circular Functions

Appendix IV. The Infinitive in Analysis and Geometry