# A Problem Book in Mathematical Analysis

by

## G N Berman

2 Ratings
Publisher: Arihant (2012)
Price: Rs. 130
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### Book Summary of A Problem Book in Mathematical Analysis

Introduction: Mathematical Analysis
1. Function
• Preliminaries
• Simplest Properties of Functions
• Basic Elementary Functions
• Inverse Function, Power Exponential and Logarithmic Functions
• Trignometric and Inverse Trignometric, Functions
• Computational Problems
2. Limit, Continuity
• Basic Definitions
• Infinite Magnitudes, Tests for the Existence of the Limit
• Continuous Functions
• Finding Limits, Comparison of Infinitesimals

3. Derivative and Differential. Differential Calculus
• Derivative. The Rate of Change of a Function
• Differentiating Functions
• Differential. Differentiability of a Function
• The Derivative as the Rate of Change
• Repeated Differentiation
4. Investigating Functions and Their Graphs
• Behaviour of a Function
• Application of the First Derivative
• Application of the Second Derivative
• Taylor’s Formula and Its Application
• Curvature
• Computational Problems

5. The Definite Integral
• The Definite Integral and Its Simplest Properties
• Basic Properties of the Definite Integral

6. Indefinite Integral. Integral Calculus
• Simplest Integration Rules
• Basic Methods of Integration
• Basic Classes of Integrable Functions

7. Methods for Evaluating Definite Integrals Improper Integrals
• Methods for Exact Evaluation of Integrals
• Approximate Methods
• Improper Integrals
8. Application of Integral Calculus
• Some Problems in Geometry and Statics
• Some Physics Problems
9. Series
• Numerical Series
• Functional Series
• Power Series
• Some Applications of Taylor’s Series
10. Functions of Several Variables. Differential Calculus
• Functions of Several Variables
• Differential Calculus
• Simplest Properties of Functions
• Derivatives and Differentials of Functions of Several Variables
• Differentiating Functions
• Repeated Differentiation
11. Application of Differential Calculus of Functions of Several Variables
• Taylor’s Formula. Extrema of Functions of Several Variables
• Plane Curves
• Vector Function of a Scalar Argument. Space Curves. Surfaces
• Scalar Field. Gradient. Directional Derivative
12. Multiple Integrals
• Double and Triple Integrals
• Multiple Integration
• Integrals in Polar, Cylindrical and Spherical Coordinates
• Application of Double and Triple Integrals
• Improper Integrals. Integrals Dependent on Parameters

13. Line Integrals and Surface Integrals
• Line Integrals with Respect to Arc Length
• Line Integrals with Respect to Coordinates
• Surface Integrals
14. Differential Equations
• Equations of the First Order
• General Differential Equations of the First Order
• Equations of the Second and Higher Orders
• Linear Equations
• Systems of Differential Equations
• Computational Problems
15. Trigonometric Series
• Trigonometric Polynomials
• Fourier Series
• Kryloy’s Method. Harmonic Analysis

16. Elements of Field Theory