We now come to Problems in Mathematical Analysis edited by B. P. Demidovich. The list of authors is G. Baranenkov, B. Demidovich, V. Efimenko, S. Kogan, G. Lunts, E. Porshneva, E. Sychera, S. Frolov, R. Shostak and A.  Yanpolsky.This collection of problems and exercises in mathematical analysis 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 branches of higher mathematics (with the exception of analytical 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, differentiation techniques, the graphing of functions, integration techniques, the applications all of definite integrals, series, the solution of differential equations).Since some institutes have extended courses of mathematics, the authors have included problems on field theory, method, and the Fourier approximate calculations. Experience shows that problems given in this book not only fully satisfies the number of the requirements of the student, as far as practical mastering of the various sections of the course goes, but also enables the instructor to supply a varied choice of problems in each section to select problems for tests and examinations.Each chapter begins with a brief theoretical introduction that covers the basic definitions and formulas of that section of the course. Here the most important typical 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 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 Union. It includes, in addition to original problems and examples, a large number of commonly used problems.This book was translated from the Russian by George Yankovsky. The  book was published by first Mir Publishers in 1970.All credits to the original uploader.Thanks Siddharth for providing the link.PDF | OCR | 15.2 MB | Pages: 497 | Table of ContentsPreface 9Chapter I INTRODUCTION TO ANALYSIS Sec. 1. Functions 11Sec. 2. Graphs of Elementary Functions 16Sec. 3 Limits 22Sec. 4 Infinitely Small and Large Quantities 33Sec. 5. Continuity of Functions 36Chapter II DIFFERENTIATION OF FUNCTIONSSec. 1. Calculating Derivatives Directly 42Sec. 2. Tabular Differentiation 46Sec. 3 The Derivatives of Functions Not Represented Explicitly 56Sec. 4. Geometrical and Mechanical Applications of the Derivative 60Sec. 5. Derivatives of Higher Orders 66Sec. 6. Differentials of First and Higher Orders 71Sec. 7. Mean Value Theorems 75Sec. 8. Taylor's Formula 77Sec. 9. The L'Hospital-Bernoulli Rule for Evaluating IndeterminateForms 78Chapter III THE EXTREMA OF A FUNCTION AND THE GEOMETRIC APPLICATIONS OF A DERIVATIVESec. 1. The Extrema of a Function of One Argument 83Sec. 2. The Direction of Concavity. Points of Inflection 91Sec. 3. Asymptotes 93Sec. 4. Graphing Functions by Characteristic Points 96Sec. 5. Differential of an Arc Curvature 101Chapter IV INDEFINITE INTEGRALSSec. 1. Direct Integration 107Sec. 2. Integration by Substitution 113Sec. 3. Integration by Parts 116Sec. 4. Standard Integrals Containing a Quadratic Trinomial 118Sec. 5. Integration of Rational Functions 121Sec. 6. Integrating Certain Irrational Functions 125Sec. 7. Integrating Trigoncrretric Functions 128Sec. 8. Integration of Hyperbolic Functions 133Sec. 9. Using Ingonometric and Hyperbolic Substitutions forFinding integrals of the Form $\int R(x, \sqrt{ax^2 + bx + c}) dx$ R Where Ris a Rational FunctionSec. 10. Integration of Various Transcendental Functions 135Sec. 11. Using Reduction Formulas 135Sec. 12. Miscellaneous Examples on Integration 136Chapter V DEFINITE INTEGRALSSec. 1. The Definite Integral as the Limit of a Sum 138Sec. 2. Evaluating Definite Integrals by Means of Indefinite Integrals 140Sec. 3 Improper Integrals 143Sec. 4. Change of Variable in a Definite Integral 146Sec. 5. Integration by Parts 149Sec. 6. Mean-Value Theorem 150Sec. 7. The Areas of Plane Figures 153Sec 8. The Arc Length of a Curve 158Sec 9 Volumes of Solids 161Sec 10 The Area of a Surface of Revolution 166Sec. 11. Moments. Centres of Gravity. Guldin's Theorems 168Sec. 12. Applying Definite Integrals to the Solution of PhysicalProblems 173Chapter VI. FUNCTIONS OF SEVERAL VARIABLESSec. 1. Basic Notions 180Sec. 2. Continuity 184Sec. 3. Partial Derivatives 185Sec. 4. Total Differential of a Function 187Sec. 5. Differentiation of Composite Functions 190Sec. 6. Derivative in a Given Direction and the Gradient of a Function 193Sec. 7. Higher -Order Derivatives and Differentials 197Sec. 8. Integration of Total Differentials 202Sec. 9. Differentiation of Implicit Functions 205Sec. 10. Change of Variables 211Sec. 11. The Tangent Plane and the Normal to a Surface 217Sec. 12. Taylor's Formula for a Function of Several Variables 220Sec. 13. The Extremum of a Function of Several Variables 222Sec. 14. Finding the Greatest and smallest Values of Functions 227Sec. 15. Singular Points of Plane Curves 230Sec. 16. Envelope 232Sec. 17. Arc Length of a Space Curve 234Sec. 18. The Vector Function of a Scalar Argument 235Sec. 19. The Natural Trihedron of a Space Curve 238Sec. 20. Curvature and Torsion of a Space Curve 242Chapter VII. MULTIPLE AND LINE INTEGRALSSec. 1. The Double Integral in Rectangular Coordinates 246Sec. 2. Change of Variables in a Double Integral 252Sec. 3. Computing Areas 256Sec. 4. Computing Volumes 258Sec. 5. Computing the Areas of Surfaces 259Sec. 6 Applications of the Double Integral in Mechanics 260Sec. 7. Triple Integrals 262Sec. 8. Improper Integrals Dependent on a Parameter. Improper Multiple Integrals  269Sec. 9. Line Integrals 273Sec. 10. Surface Integrals 284Sec. 11. The Ostrogradsky-Gauss Formula 286Sec. 12. Fundamentals of Field Theory 288Chapter VIII. SERIESSec. 1. Number Series 293Sec. 2. Functional Series 304Sec. 3. Taylor's Series 318Sec. 4. Fourier's Series 311Chapter IX DIFFERENTIAL EQUATIONSSec. 1. Verifying Solutions. Forming Differential Equations of Families ofCurves. Initial Conditions 322Sec. 2. First-Order Differential Equations 324Sec. 3. First-Order Diflerential Equations with VariablesSeparable. Orthogonal Trajectories 327Sec. 4. First-Order Homogeneous Differential Equations 330Sec. 5. First-Order Linear Differential Equations. Bernoulli'sEquation 332Sec. 6 Exact Differential Equations. Integrating Factor 335Sec 7 First-Order Differential Equations not Solved for the Derivative 337Sec. 8. The Lagrange and Clairaut Equations 339Sec. 9. Miscellaneous Exercises on First-Order Differential Equations 340Sec. 10. Higher-Order Differential Equations 345Sec. 11. Linear Differential Equations 349Sec. 12. Linear Differential Equations of Second Order with ConstantCoefficients 351Sec. 13. Linear Differential Equations of Order Higher than Two withConstant Coefficients 356Sec. 14. Euler's Equations 357Sec. 15. Systems of Differential Equations 359Sec. 16. Integration of Differential Equations by Means of Power Series 361Sec. 17. Problems on Fourier's Method 363Chapter X. APPROXIMATE CALCULATIONSSec. 1. Operations on Approximate Numbers 367Sec. 2. Interpolation of Functions 372Sec. 3. Computing the Real Roots of Equations 376Sec. 4. Numerical Integration of Functions 382Sec. 5. Numerical Integration of Ordinary Differential Equations 384Sec. 6. Approximating Fourier's Coefficients 393ANSWERS 396APPENDIX 475I. Greek Alphabet 475II. Some Constants 475III. Inverse Quantities, Powers, Roots, Logarithms 476IV. Trigonometric Functions 478V. Exponential, Hyperbolic and Trigonometric Functions 479VI. Some Curves 480