# MTG A Problem book in Mathematical Analysis

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Rs.180.00
"MTG™s ORIGINAL MASPTERPIECE is a series of collection of books that started their journey as best sellers and continue as a chart-topper generation after generation. Even today these books are considered as a masterpiece among the teachers and students fraternity which is passionate about the subject.
The USP of MTG™s ORIGINAL MASTERPIECE Series lies in the fact that the work has been reproduced from the Original artifact and remains as true to the original work as possible.
The book â€œA Problem Book In Mathematical Analysisâ€œ is a collection of problems and exercises that are systematically selected and arranged in compliance with the major sections of the course in mathematical analysis.
Thought the theoretical information is not given in this book, the huge number of questions are more than enough for thorough practice of the various concepts covered under the sphere of mathematical analysis. For convenience, 16 chapters are further subdivided into parts. Necessary information is given before problems on physics. More difficult problems (indicated by an asterisk) are supplied with hints for their solution to be found in the Answers.
It also includes tables of the values of basic elementary functions compiled in the Appendix.
At the end of the book answers and solutions to all the problems have also been provided. As the book covers the varied aspects of Mathematical Analysis with the help of ample number of examples, it is enough to give an idea about the depth of questions expected from each chapter in the syllabus.
This books is well suited for the students aspiring for JEE Main and especially JEE Advanced. This is also consulted by the students studying in Higher Technical Education.
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"CONTENTS 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. Taylorâ€™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 Taylorâ€™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. Taylorâ™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 "

## Details

"CONTENTS 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. Taylorâ€™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 Taylorâ€™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. Taylorâ™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 "