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文件名称: 吉米多维奇工科数学分析习题集（可搜索）（带书签）
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 详细说明：吉米多维奇工科数学分析习题集英文版，可搜索，带书签G. Baran nkov, B. Demidovich V. Efimenko, S. Kogan G. Lunts, E. Porshneva, e. St, chet a, s. FrolcU, R. Shostak A. Yanpolsky PROBLEMS iN MATHEMATICAL ANALYSIS Under the editorship B. DEMIDOVICH Translated from the Russian b G. YAN KOVSKY MIR PUBLISHERS Mosco TO THE READER MIR Publishers would be glad to have your opinion of the translation and t he design of this book Please send your suggest tons to 2, Pervy Rizhsk Pereulok, Moscow, U. S.s.R. Second Printing Printed in the Union of soviet soclallst Republics CONTENTS Preface Chapter I. INTRODUCTION TO ANALYSIS Sec.1. functions Sec. 2 Graphs of Elementary Functions ....... Sec.3 Limits 22 Sec. 4 Infinitely Small and Lat ge Quantities 33 Sec. 5. Continuity of Functions 36 Chapter II DIFFERENTIATION OF FUNCTIONS Sec 1. Calculating Derivatives directly Sec 2 Tabular Differentiation Sec. 3 The Derivat 'ves of Functions Not Re presented Explicitly Sec. 4. Geometrical and Mechanical Applications of the Derivative Sec 5 Derivatives of higher Orders Sec 6 Differentials of First and Higher Orders Sec 7 Mean Value Theorems 6606757 Sec.8 Tay lor's For mula Sec 9 The L Hospital-Bernoulli Rule for Evaluating Indeterminate orms Chapter III THE EXTREMA OF A FUNCTION AND THE GEOMETRIC APPLICATIONS OF A DERIVATIVE Sec. 1. The Extrema of a function of One argumen Sec. 2 The Direction of Concavity points of Inflection 91 Sec 3 Asymptotes Sec 4. Graphing Functions by Characteristic Points Sec. 5. Differential of an Arc Curvature Chapter IV INDEFINITE INTEGRALS Sec. 1 Direct Integration sec2 Integration by substitution,.。。 113 cec 3 Integration by Parts l16 Sec. 4 Standard Integrals Containing a Quadratic trinomial l18 Sec. 5. Integration of Rational Functions 。。.121 Contents Sec. 6. Integrating Certain Irrational Functions ,,,。。,。125 Sec 7. Integrating Trigonometric Functions Sec.8 Integration of Hyper bolic Functions Sec 9. Using Trigonometric and Hy Fer bolic Substitutions for Finding Integrals of the Form R(x, Vax+bx+c)dx. Where R is a Ra- tional function 133 Sec i0 integration of various Transcendental functions 135 Sec l1 Using Reduction Formulas Sec. 12. Miscellaneous Examples on Integration Chapter V DEFINITE INTEGRALS Sec. 1. The Definite Integral as the limit of a Sum 。。。。,.138 Sec 2 Evaluating [ofir ite Integrals by Means of indefinite Integrals 140 Sec. 3 Improper Integrals cec 4 Charge of varia ble in a De finite Integral 146 5. Integration by Part 149 Sec 6 Mean-Value theorem 。。150 Sec. 7. The Areas of plane figures 153 Sec 8. The Arc Length of a curve 58 Sec 9 volumes of solids 161 Sec 10 The Area of a Surface of Revolution 166 Sec 11 Norents Centres of Cravity Culdin's Theorems ,168 cec 12. Applying Cefrite Integrals to the Solution of Physical Prcb lems ,。.,173 Chapter VI. FUNCTIONS OF SEVERAL VARIABLES Sec. 1. Basic Notions Sec. 2. Continuity 184 sec3 Partial Derivatives,,,,,.,。,,,,·.,,,, Sec 4 total Diflerential of a function 187 Sec 5 Differentiation of Composite functions 190 Sec. 6. Derivative in a given direction and the gradient of a function 193 Sec. 7 Higher- Crder derivatives and differentials ,,197 Sec 8 Integration of total Diferential 202 Sec 9 Dif erentiation of implicit Functions ,,。,,,,,205 Sec 10 Change of variables 2l1 Sec. 11. The T d the ne Surf Sec 12 l aylor's Formula for a function of several variables 220 Sec. 13 The Extremum of a function of Several variables ,。222 Sec 14 Fir dire the Createst and mallest Values of Functions 227 Sec 15 Singular points of Plane Cu 230 Sec 16 Envelope 232 Sec. 17. Arc Length of a Space Curve 234 Contents Sec. 18. The Vector Function of a Scalar Argument 235 Sec. 19 The Natural Trihedron of a Space Curve 238 Sec. 20. Curvature and Torsion of a Space Curve 242 Chapter VII. MULTIPLE AND LINE INTEGRALS Sec. 1 The double Integral in Rectangular Coor dinates......246 Sec. 2 Change of Variables in a Double Integral 252 Sec. 3. Computing Areas 256 Sec. 4. Com puting volumes 258 Sec. 5. Computing the Areas of Surfaces ,,,,259 Sec. 6 Applications of the Double Integral in Mechanics .... 250 Sec. 7. Triple Integrals 262 Sec. 8. Improper Integrals Dependent on a Parameter. Improper Multi le Integrals ●··· 。.,,,,,,。269 Sec. 9 Line Integrals 273 Sec. 10. Surface Integrals 284 Sec. 11. The Ostrogradsky- Gauss Formula 286 Sec. 12. Fundamentals of Field Theory 288 Chapter VIII. SERIES Sec. 1. Number series 293 Sec. 2. Functional Series 304 Sec. 3. Taylors series ,,,,3l1 Sec. 4. Fouriers series 3l8 Chapter IX DIFFERENTIAL EQUATIONS Sec. 1. Verifying Solutions. Forming Differential Equations of Fami lies of Curves. Initial Conditions ,,,,,,,,,,322 Sec.2 First-Order Differential Equations 324 Sec. 3. First-Or der Diflerential Equations with Variables Se parable. Orthogonal Trajectories 327 Sec. 4 First-Order Homogeneous Differential Equations Sec. 5. First-Order Linear Differential equations. Bernoullis Equation 332 Sec. 6 Exact Differential Equations. Integrating Factor 335 Sec 7 First-Order differential equations not solved for the derivative 337 Sec.8. The Lagrange and clairaut Equations 339 Sec. 9. Miscellaneous Exercises on First-Order Differential Equations 340 Sec. 10. Higher-Order Differential Equations 345 Sec. 11. Linear Differential equations 349 Sec. 12. Linear Differential Equations of Second Order with Constant Coefficients,,,,,,,,。,,,,,,。 35l Contents Sec. 13. Line ar Differential Equations of Order Higher than Two with Constant Coefficients 356 Sec 14. Euler's equations 。.,。,,,,。,357 Sec 15. Systems of Differential Equations 359 Sec. 16. Integration of Diflerential Equations by means of Power se TIes Sec 17. froblenis on fouriers method ,,,,,,。.363 Chapter X. APPROXIMATE CALCULATIONS Sec.1 O tions on appr proxima ate Numbers 367 Sec. 2. Inter polation of Functions 372 Sec. 3. Coniputing the Rcal roots of equations 376 Sec. 4 NuInerical Integration of functions 382 Sec. 5. Nun er:cal Integration of Crdirary Diflerential e quations . 384 Cec. 6. Approximating F(utricr's Cce ficients 鲁 393 ANSWERS ,,,,,,,,,,。396 APPENDIX ,475 I. Greek Alphabet 475 I. Some Constants 475 Ill. Inverse Quantities, Powers, Roots, Logarithms 470 Iv Trigonometric Functions 478 V. Exporer tial, IlyFerbolic and Trigonoilfetric Functions 。479 VI. Some Curves 480 PREFACE This collection of problems and exercises in mathematical anal- ysis covers the maximum requirements of general courses in higher mathematics for higher technical schools. It contains over 3,000 problems sequentially arranged in Chapters I to X covering all branches of higher mathematics(with the exception of ana- lytical geometry) given in college courses. Particular attention is given to the most important sections of the course that require established skills(the finding of limits, diferentiation techniques the graphing of functions, integration techniques, the applications of definite integrals, series, the solution of diferential equations). Since some institutes have extended courses of mathematics the authors have included problems on field theory, the Fourier method, and approximate calculations. Experience shows that the number of problems given in this book not only fully satisfies the requiremen s of the student, as far as practical mas ering of the various sections of the course goes, but also enables the in- structor to sup ply a varied choice of problems in each section and to select problems for tests and examinations. Each chap, er begins with a brief theoretical introduction th covers the basic definitions and formulas of that section of the course. Here the nost important ty pical problems are worked out in full We believe that this will greatly simplify the work of the student. Answers are given to all computational problems; one asterisk indicates that hints to the solution are given in the answers, two asterisks, that the solution is given the problems are frequently illustrated by drawings This collection of problems is the result of many years of teaching higher mathematics in the technical schools of the Soviet ples, a large number of commonly used problems,ms and exam- Union. It includes, in addition to original probler Chapter I INTRO DUCTION TO ANALYSIS Sec. 1. Functions 1. Real nur ters r ationa irrationa num mber a s collectively known as real numbers the absolute of a real num understood to be the nonnegative number | al defined by the conditions'al=a if a>0, and a a if a0, that is, if x >l. Thus, the domain of the function is a set of two inter vals:-∞
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