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A Collection of Problems on a Course of Mathematical Analysis
- 1st Edition - July 14, 2014
- Author: G. N. Berman
- Editors: I. N. Sneddon, M. Stark, S. Ulam
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 1 - 6 9 0 3 - 3
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 8 4 8 4 - 5
Collection of Problems on a Course of Mathematical Analysis contains selected problems and exercises on the main branches of a Technical College course of mathematical analysis.… Read more
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Request a sales quoteCollection of Problems on a Course of Mathematical Analysis contains selected problems and exercises on the main branches of a Technical College course of mathematical analysis. This book covers the topics of functions, limits, derivatives, differential calculus, curves, definite integral, integral calculus, methods of evaluating definite integrals, and their applications. Other topics explored include numerical problems related to series and the functions of several variables in differential calculus, as well as their applications. The remaining chapters examine the principles of multiple, line, and surface integrals, the trigonometric series, and the elements of the theory of fields. This book is intended for students studying mathematical analysis within the framework of a technical college course.
Foreword to the Tenth Russian Edition
I. Functions
1. Functions and Methods of Specifying Them
2. Notation for and Classification of Functions
3. Elementary Investigation of Functions
4. Elementary Functions
5. The Inverse Functions. Power, Exponential and Logarithmic Functions
6. The Trigonometric and Inverse Trigonometric Functions
7. Numerical Problems
II. Limits
1. Basic Definitions
2. Orders of Magnitude. Tests for the Existence of a Limit
3. Continuous Functions
4. Finding Limits. Comparison of Infinitesimals
III. Derivatives and Differentials. Differential Calculus
1. Derivatives. The Rate of Change of a Function
2. Differentiation of Functions
3. Differentials. Differentiability of a Function
4. Derivative as Rate of Change (Further Examples)
5. Repeated Differentiation
IV. The Investigation of Functions and Curves
1. The Behaviour of a Function "at a Point"
2. Applications of the First Derivative
3. Applications of the Second Derivative
4. Auxiliary Problems. Solution of Equations
5. Taylor's Formula and its Applications
6. Curvature
7. Numerical Problems
V. The Definite Integral
1. The Definite Integral and its Elementary Properties
2. Fundamental Properties of the Definite Integral
VI. The Indefinite Integral. Integral Calculus
1. Elementary Examples of Integration
2. Basic Methods of Integration
3. Basic Classes of Integrable Functions
VII. Methods of Evaluating Definite Integrals. Improper Integrals
1. Methods of Exact Evaluation of Integrals
2. Approximation Methods
3. Improper Integrals
VIII. Applications of the Integral
1. Some Problems of Geometry and Statics
2. Some Problems of Physics
IX. Series
1. Numerical Series
2. Functional Series
3. Power Series
4. Some Applications of Taylor's Series
5. Numerical Problems
X. Functions of Several Variables. Differential Calculus
1. Functions of Several Variables
2. Elementary Investigation of a Function
3. Derivatives and Differentials of Functions of Several Variables
4. Differentiation of Functions
5. Repeated Differentiation
XI. Applications of the Differential Calculus for Functions of Several Variables
1. Taylor's Formula. Extrema of Functions of Several Variables
2. Plane Curves
3. Vector Functions of a Scalar Argument. Curves in Space. Surfaces
4. Scalar Field. Gradient. Directional Derivative
XII. Multiple Integrals and Iterated Integration
1. Double and Triple Integrals
2. Iterated Integration
3. Integrals in Polar, Cylindrical and Spherical Coordinates
4. Applications of Double and Triple Integrals
5. Improper Integrals. Integrals Depending on a Parameter
XIII. Line and Surface Integrals
1. Line Integrals
2. Coordinate Line Integrals
3. Surface Integrals
XIV. Differential Equations
1. Equations of the First Order
2. Equations of the First Order (Continued)
3. Equations of the Second and Higher Orders
4. Linear Equations
5. Systems of Differential Equations
6. Numerical Problems
XV. Trigonometric Series
1. Trigonometric Polynomials
2. Fourier Series
3. Krylov's Method. Harmonic Analysis
XVI. Elements of the Theory of Fields
Answers
Chapter I
Chapter II
Chapter III
Chapter IV
Chapter V
Chapter VI
Chapter VII
Chapter VIII
Chapter IX
Chapter X
Chapter XI
Chapter XII
Chapter XIII
Chapter XIV
Chapter XV
Chapter XVI
Appendix. Tables
1. Trigonometric Functions
2. Hyperbolic Functions
3. Reciprocals, Square and Cube Roots, Logarithms, Exponential Functions
Index
Other Volumes in the Series in Pure and Applied Mathematics
- No. of pages: 602
- Language: English
- Edition: 1
- Published: July 14, 2014
- Imprint: Pergamon
- Paperback ISBN: 9781483169033
- eBook ISBN: 9781483184845
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