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A Problem book in Mathematical Analysis
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A Problem book in Mathematical Analysis

Rs.180.00

180 INR
    ISBN: 9789385966569
    Author: G.N BERMAN
    Edition: 2016
    Pages: 496
  • Shipping Weight: 421gms
  • Classes: Class 11, Class 12
  • Exams: School Books
  • Subjects: Mathematics
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Product Description
CONTENT
 
Preface
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. Behaviour 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 of Functions of Several Variables
4. Differentiating Functions
5. Repeated Differentiation
Chapter XI. Applications of Differential Calculus of
         Functions of Several Variables
1. Taylor’s Formula. Extrema of Functions of Several Variables
2. Plane Curves
3. Vector Function of a Scalar Argument. Space Curves.Surfaces.
4. Scalar Field.Gradient. Directional Derivative
Chapter XII. Multiple Integrals
1. Double and Triple Integrals
2. Multiple Integration
3. Integrals in Polar, Cylindrical and Spherical Coordinates.
4. Application of Double and Triple Integrals
5. Improper Integrals. Integrals Dependent on Parameters
Chapter XIII. Line Integrals and Surface Integrals
1. Line Integrals with Respect to Arc Length
2. Line Integrals with Respect to Coordinates
3. Surface Integrals
Chapter XIV. Differential Equations
1. Equations of the First Order
2. General Differential Equations of the First Order
3. Equations of the Second and Higher Orders
4. Linear Equations
5. Systems of Differential Equations
6. Computational Problems
Chapter XV. Trigonometric Series
1. Trigonometric Polynomials
2. Fourier Series
3. Krylov’s Method. Harmonic Analysis
Chapter XVI. Elements of Field Theory
Answers
Appendix
 


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