A Problem Book in Mathematical Analysis

A Problem Book in Mathematical Analysis - G. N. Berman

Table of Contents Perface Chapter I Function 1. Preliminaries 2. Simplest Properties of Functions 3. Basic Elementary Functions 4. Inverse Function. Power, Exponential and Logarithmic Functions 5. Trigonometric and Inverse Trigonometric Functions 6. Computational Problems Chapter II. Limit. Continuity 1. Basic Definitions 2. Infinite Magnitudes. Tests for the Existence of the Limit 3. Continuous Functions 4. Finding Limits. Comparison of Infinitesimals Chapter III. Derivative and Differential. Differential Calculus 1. Derivative. The Rate of Change of a Function 2. Differentiating Functions 3. Differential. Differentiability of a Function 4. The Derivative as the Rate of Change 5. Repeated Differentiation Chapter IV. Investigating Functions and Their Graphs 1. Behavior of a Function 2. Application of the First Derivative 3. Application of the Second Derivative 4. Additional Items. Solving Equations 5. Taylor's Formula and Its Application 6. Curvature 7. Computational Problems Chapter V. The Definite Integral 1. The Definite Integral and Its Simplest Properties 2. Basic Properties of the Definite Integral Chapter VI. Indefinite Integral. Integral Calculus 1. Simplest Integration Rules 2. Basic Methods of Integration 3. Basic Classes of Integrable Functions Chapter VII. Methods for Evaluating Definite Integrals. Improper Integrals 1. Methods for Exact Evaluation of Integrals 2. Approximate Methods 3. Improper Integrals Chapter VIII. Application of Integral Calculus 1. Some Problems in Geometry and statics 2. Some Physics Problems Chapter IX. Series 1. Numerical Series 2. Functional Series 3. Power Series 4. Some Applications of Taylor;s series Chapter X. Functions of Several Variables. Differential Calculus 1. Functions of Several Variables 2. Simplest Properties of Functions 3. Derivatives and Differentials