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Buy A Problem Book in Mathematical Analysis: Book

A Problem Book in Mathematical Analysis


G N Berman

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

Table of Contents
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
  • Additional Items. Solving Equations
  • 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


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