Collection of Problems on a Course of Mathematical Analysis (eBook)

G. N. Berman (Autor)

I. N. Sneddon, M. Stark, S. Ulam (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
602 Seiten
Elsevier Science (Verlag)
978-1-4831-8484-5 (ISBN)

Infos

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. 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.

Inhalt

Front Cover 1
A Collection of Problems on a Course of Mathematical Analysis 4
Copyright Page 5
Table of Contents 6
Foreword to the Tenth Russian Edition 10
CHAPTER I. FUNCTIONS 14
1. Functions and Methods of Specifying Them 14
2. Notation for and Classification of Functions 16
3. Elementary Investigation of Functions 20
4. Elementary Functions 26
5. The Inverse Functions. Power, Exponential and Logarithmic 
33 
6. The Trigonometric and Inverse Trigonometric Functions 37
7. Numerical Problems 42
CHAPTER 
44 
1. Basic Definitions 44
2. Orders of Magnitude. Tests for the Existence of a Limit 47
3. Continuous Functions 50
4. Finding Limits. Comparison of Infinitesimals 53
CHAPTER 
67 
1. Derivatives. The Rate of Change of a Function 67
2. Differentiation of Functions 71
3. Differentials. Differentiability of a Function 95
4. Derivative as Rate of Change (Further Examples) 100
5. Repeated Differentiation 110
CHAPTER 
119 
1. The Behaviour of a Function "at a Point'' 119
2. Applications of the First Derivative 120
3. Applications of the Second Derivative 133
4. Auxiliary Problems. Solution of Equations 138
5. Taylor's Formula and its Applications 148
6. Curvature 151
7. Numerical Problems 155
CHAPTER 
157 
1. The Definite Integral and its Elementary Properties 157
2. Fundamental Properties of the Definite Integral 162
CHAPTER 
169 
1. Elementary Examples of Integration 169
2. Basic Methods of Integration 174
3. Basic Classes of Integrable Functions 181
CHAPTER 
190 
1. Methods of Exact Evaluation of Integrals 190
2. Approximation Methods 200
3. Improper Integrals 205
CHAPTER 
211 
1. Some Problems of Geometry and Statics 211
2. Some Problems of Physics 234
CHAPTER 
247 
1. Numerical Series 247
2. Functional Series 252
3. Power Series 257
4. Some Applications of Taylor's Series 261
5. Numerical Problems 265
CHAPTER 
267 
1. Functions of Several Variables 267
2. Elementary Investigation of a Function 270
3. Derivatives and Differentials of Functions of Several Variables 276
4. Differentiation of Functions 281
5. Repeated Differentiation 286
CHAPTER 
292 
1. Taylor's Formula. Extrema of Functions of Several Variables 292
2. Plane Curves 300
3. Vector Functions of a Scalar Argument. Curves in Space Surfaces 302
4. Scalar Field. Gradient. Directional Derivative 310
CHAPTER 
314 
1. Double and Triple Integrals 314
2. Iterated Integration 315
3. Integrals in Polar, Cylindrical and Spherical Coordinates 320
4. Applications of Double and Triple Integrals 324
5. Improper Integrals. Integrals Depending on a Parameter 337
CHAPTER 
346 
1. Line Integrals 346
2. Coordinate Line Integrals 350
3. Surface Integrals 358
CHAPTER 
362 
1. Equations of the First Order 362
2. Equations of the First Order (Continued) 378
3. Equations of the Second and Higher Orders 383
4. Linear Equations 389
5. Systems of Differential Equations 397
6. Numerical Problems 400
CHAPTER 
403 
1. Trigonometric Polynomials 403
2. Fourier Series 404
3. Krylov's Method. Harmonic Analysis 409
CHAPTER 
410 
ANSWERS 419
APPENDIX: TABLES 593
Index 598
Other Volumes in the Series in Pure and Applied Mathematics 602

Produkt-Details

• Erscheint lt. Verlag: 14.7.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• ISBN-10: 1-4831-8484-6 / 1483184846
• ISBN-13: 978-1-4831-8484-5 / 9781483184845