A First Course in Calculus / Edition 5by Serge Lang
Pub. Date: 01/15/1986
Publisher: Springer New York
This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.
Table of Contents
• Numbers and Functions.
• Graphs and Curves. II: Differention and Elementary Functions.
• The Derivative.
• Sine and Cosine.
• The Mean Value Theorem.
• Sketching Curves.
• Inverse Functions
• Exponents and Logarithms. III: Integration.
• Properties of the Integral.
• Techniques of Integration.
• Applications of Integration. IV: Taylor's Formula and Series.
• Taylor's Formula.
• Series. Appendix. V: Functions of Several Variables.
• Differention of Vectors.
• Functions of Several Variables.
• The Chain Rule and the Gradient.
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Serge Lang's text does an effective job of explaining the key concepts in calculus. The principal focus of the text is teaching the reader how to solve calculus problems. Lang clearly explains methods of solution and provides illuminating examples. The challenging exercises reinforce the concepts and foster the skills necessary to solve challenging problems. Answers to the majority of exercises, not just the odd-numbered ones, are provided in an appendix. In some sections, such as max-min problems, Lang provides fully worked out solutions. In addition to teaching you how to solve problems, Lang teaches the reader to think mathematically, proving theorems, deriving results, and only introducing topics after developing their logical foundations. Working through this text, which is more demanding than standard college calculus texts, will provide you with a good foundation for more advanced courses in mathematics. After reviewing prerequisite material, the text covers differentiation, integration, Taylor polynomials, series, and basic concepts from vector calculus. Caveat: keep an eye out for errors.