Description
Book SynopsisCalculus is important for first-year undergraduate students pursuing mathematics, physics, economics, engineering, and other disciplines where mathematics plays a significant role. The book provides a thorough reintroduction to calculus with an emphasis on logical development arising out of geometric intuition. The author has restructured the subject matter in the book by using Tarski''s version of the completeness axiom, introducing integration before differentiation and limits, and emphasizing benefits of monotonicity before continuity. The standard transcendental functions are developed early in a rigorous manner and the monotonicity theorem is proved before the mean value theorem. Each concept is supported by diverse exercises which will help the reader to understand applications and take them nearer to real and complex analysis.
Table of ContentsIntroduction; 1. Real Numbers and Functions; 2. Integration; 3. Limits and Continuity; 4. Differentiation; 5. Techniques of Integration; 6. Mean Value Theorems and Applications; 7. Sequences and Series; 8. Taylor and Fourier Series; A. Solutions to Odd-Numbered Exercises; Bibliography; Index.
