E-Book, Englisch, 602 Seiten, Web PDF
Berman / Sneddon / Stark A Collection of Problems on a Course of Mathematical Analysis
1. Auflage 2014
ISBN: 978-1-4831-8484-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 602 Seiten, Web PDF
Reihe: International Series in Pure and Applied Mathematics
ISBN: 978-1-4831-8484-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;A Collection of Problems on a Course of Mathematical Analysis;4
3;Copyright Page;5
4;Table of Contents;6
5;Foreword to the Tenth Russian Edition;10
6;CHAPTER I. FUNCTIONS;14
6.1;1. Functions and Methods of Specifying Them;14
6.2;2. Notation for and Classification of Functions;16
6.3;3. Elementary Investigation of Functions;20
6.4;4. Elementary Functions;26
6.5;5. The Inverse Functions. Power, Exponential and Logarithmic
Functions;33
6.6;6. The Trigonometric and Inverse Trigonometric Functions;37
6.7;7. Numerical Problems;42
7;CHAPTER
II. LIMITS;44
7.1;1. Basic Definitions;44
7.2;2. Orders of Magnitude. Tests for the Existence of a Limit;47
7.3;3. Continuous Functions;50
7.4;4. Finding Limits. Comparison of Infinitesimals;53
8;CHAPTER
III. DERIVATIVES AND DIFFERENTIALS DIFFERENTIAL CALCULUS;67
8.1;1. Derivatives. The Rate of Change of a Function;67
8.2;2. Differentiation of Functions;71
8.3;3. Differentials. Differentiability of a Function;95
8.4;4. Derivative as Rate of Change (Further Examples);100
8.5;5. Repeated Differentiation;110
9;CHAPTER
IV. THE INVESTIGATION OF FUNCTIONS AND CURVES;119
9.1;1. The Behaviour of a Function "at a Point'';119
9.2;2. Applications of the First Derivative;120
9.3;3. Applications of the Second Derivative;133
9.4;4. Auxiliary Problems. Solution of Equations;138
9.5;5. Taylor's Formula and its Applications;148
9.6;6. Curvature;151
9.7;7. Numerical Problems;155
10;CHAPTER
V. THE DEFINITE INTEGRAL;157
10.1;1. The Definite Integral and its Elementary Properties;157
10.2;2. Fundamental Properties of the Definite Integral;162
11;CHAPTER
VI. THE INDEFINITE INTEGRAL. INTEGRAL CALCULUS;169
11.1;1. Elementary Examples of Integration;169
11.2;2. Basic Methods of Integration;174
11.3;3. Basic Classes of Integrable Functions;181
12;CHAPTER
VII. METHODS OF EVALUATING DEFINITE INTEGRALS IMPROPER INTEGRALS;190
12.1;1. Methods of Exact Evaluation of Integrals;190
12.2;2. Approximation Methods;200
12.3;3. Improper Integrals;205
13;CHAPTER
VIII. APPLICATIONS OF THE INTEGRAL;211
13.1;1. Some Problems of Geometry and Statics;211
13.2;2. Some Problems of Physics;234
14;CHAPTER
IX. SERIES;247
14.1;1. Numerical Series;247
14.2;2. Functional Series;252
14.3;3. Power Series;257
14.4;4. Some Applications of Taylor's Series;261
14.5;5. Numerical Problems;265
15;CHAPTER
X. FUNCTIONS OF SEVERAL VARIABLES DIFFERENTIAL CALCULUS;267
15.1;1. Functions of Several Variables;267
15.2;2. Elementary Investigation of a Function;270
15.3;3. Derivatives and Differentials of Functions of Several Variables;276
15.4;4. Differentiation of Functions;281
15.5;5. Repeated Differentiation;286
16;CHAPTER
XI. APPLICATIONS OF THE DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES;292
16.1;1. Taylor's Formula. Extrema of Functions of Several Variables;292
16.2;2. Plane Curves;300
16.3;3. Vector Functions of a Scalar Argument. Curves in Space Surfaces;302
16.4;4. Scalar Field. Gradient. Directional Derivative;310
17;CHAPTER
XII. MULTIPLE INTEGRALS AND ITERATED INTEGRATION;314
17.1;1. Double and Triple Integrals;314
17.2;2. Iterated Integration;315
17.3;3. Integrals in Polar, Cylindrical and Spherical Coordinates;320
17.4;4. Applications of Double and Triple Integrals;324
17.5;5. Improper Integrals. Integrals Depending on a Parameter;337
18;CHAPTER
XIII. LINE AND SURFACE INTEGRALS;346
18.1;1. Line Integrals;346
18.2;2. Coordinate Line Integrals;350
18.3;3. Surface Integrals;358
19;CHAPTER
XIV. DIFFERENTIAL EQUATIONS;362
19.1;1. Equations of the First Order;362
19.2;2. Equations of the First Order (Continued);378
19.3;3. Equations of the Second and Higher Orders;383
19.4;4. Linear Equations;389
19.5;5. Systems of Differential Equations;397
19.6;6. Numerical Problems;400
20;CHAPTER
XV. TRIGONOMETRIC SERIES;403
20.1;1. Trigonometric Polynomials;403
20.2;2. Fourier Series;404
20.3;3. Krylov's Method. Harmonic Analysis;409
21;CHAPTER
XVI. ELEMENTS OF THE THEORY OF FIELDS;410
22;ANSWERS;419
23;APPENDIX: TABLES;593
24;Index;598
25;Other Volumes in the Series in Pure and Applied Mathematics;602
