Problems in Calculus of One Variable

Table of contents :
Front Cover
Title Page
Contents
From the Author
Chapter 1 INTRODUCTION TO MATHEMATICAL ANALYSIS
§ 1.1. Real Numbers. The Absolute Value of a Real Number
§ 1.2. Function. Domain of Definition
§ 1.3. /n'lJestigation of Functions
§ 1.4. /n'Verse Functions
§ 1.5. Graphical Representation of Functions
§ 1.6. Number Sequences. Limit of a Sequence
§ 1.7. Eivaluation of Limits of Sequences
§ 1.8. Testing Sequences for Convergence
§ 1.9. The Limit of a Function
§ 1.10. Calculation of Limits of Functions
§ 1.11. Infinitesimal and Infinite Functions. Their Definition and Comparison
§ 1.12. Equivalent Infinitesimals. Application to Finding Limits
§ 1.13. One-Sided Limits
§ 1.14. Continuity of a Function. Points of Discontinuity and Their Classification
§ 1.15. Arithmetical Operations on Continuous Functions. Continuity of a Composite Function
§ 1.16. The Properties of a Function Continuous on a Closed Interval. Continuity of an Inverse Function
§ 1.17. Additional Problems
Chapter 2 DIFFERENTIATION OF FUNCTIONS
§ 2.1. Definition of the Derivattve
§ 2.2. Differentiation of Explicit Functions
§ 2.3. Successi'Ve Differentiation of Explicit Functions. Leibniz Formula
§ 2.4. Differentiation of ln'Verse, Implicit and Parametrically Represented Functions
§ 2.5. Applications of the Deri'Vati

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