Demidovich's Collection of Problems and Exercises in Mathematical Analysis
by B. P. Demidovich
Translated by Valery Manokhin, PhD
Demidovich's university problem book in mathematical analysis, in first faithful English translation from the original Russian edition. Two parts, eight chapters and 82 numbered sections hold 4,683 numbered problems, each section opening with a short summary of theory: real numbers, sequences, limits and continuity, O-notation, uniform continuity and functional equations; the differential calculus of one variable, from the theorems of Rolle, Lagrange and Cauchy to curvature and evolutes; indefinite and definite integrals with their geometric and physical applications; numerical, functional, power and Fourier series, infinite products and Stirling's formula; the differential calculus of several variables; integrals depending on a parameter, Euler's integrals and the Fourier integral formula; and double, triple, many-fold, line and surface integrals, through the formulas of Green, Stokes and Ostrogradsky to the elements of field theory. Answers, with hints, are at the back. Fourteen figures.
8 chapters · 82 numbered articles · 4683 exercises · 532 pages
Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.
Where this fits in school
Full curriculum table — every book by school year →| United States | University 1–2 | Problem companion to Calculus I–III, advanced calculus and introductory real analysis |
|---|---|---|
| United Kingdom | Undergraduate 1–2 | first- and second-year real analysis and vector calculus |
| Canada | University 1–2 | QC CEGEP 201-NYA / NYB · first- and second-year university calculus and analysis |
How this book fits
See the whole sequence →Work through first
- Kiselev's Calculus$54.95
Covers much of the same ground
The engineering-college collection is smaller — 3,199 problems to 4,683 — but carries a 404-problem chapter on differential equations and an 86-problem chapter on approximate calculations, which this book does not, and opens every section with worked examples. It has no chapter on integrals depending on a parameter.
These overlap heavily. Each note says what that book has which this one does not — the differences are what decide between them.
Problems to work alongside it
- Gunter & Kuzmin$99.95
Table of contents
82 section headings — the printed contents page in full.
Translator's Preface
Part One. Functions of One Independent Variable
Chapter I. Introduction to Analysis10 sections
- Real Numbers
- Theory of Sequences
- The Concept of a Function
- Graphical Representation of a Function
- Limit of a Function
- O-Notation
- Continuity of a Function
- The Inverse Function. Functions Defined Parametrically
- Uniform Continuity of a Function
- Functional Equations
Chapter II. Differential Calculus of Functions of One Variable15 sections
- The Derivative of an Explicit Function
- The Derivative of an Inverse Function. The Derivative of a Function Defined Parametrically. The Derivative of a Function Defined Implicitly
- Geometric Meaning of the Derivative
- The Differential of a Function
- Derivatives and Differentials of Higher Orders
- Theorems of Rolle, Lagrange and Cauchy
- Increase and Decrease of a Function. Inequalities
- Direction of Concavity. Points of Inflection
- Evaluation of Indeterminate Forms
- Taylor's Formula
- Extremum of a Function. The Greatest and Least Values of a Function
- Sketching Graphs of Functions from Characteristic Points
- Problems on the Maximum and Minimum of Functions
- Contact of Curves. Circle of Curvature. Evolute
- Approximate Solution of Equations
Chapter III. The Indefinite Integral6 sections
- The Simplest Indefinite Integrals
- Integration of Rational Functions
- Integration of Certain Irrational Functions
- Integration of Trigonometric Functions
- Integration of Various Transcendental Functions
- Miscellaneous Examples on the Integration of Functions
Chapter IV. The Definite Integral11 sections
- The Definite Integral as the Limit of a Sum
- Evaluation of Definite Integrals by Means of Indefinite Integrals
- Mean Value Theorems
- Improper Integrals
- Computation of Areas
- Computation of Arc Lengths
- Computation of Volumes
- Computation of Areas of Surfaces of Revolution
- Computation of Moments. Coordinates of the Centre of Gravity
- Problems from Mechanics and Physics
- Approximate Evaluation of Definite Integrals
Chapter V. Series11 sections
- Numerical Series. Tests for Convergence of Series with Terms of Constant Sign
- Convergence Tests for Series of Variable Sign
- Operations on Series
- Functional Series
- Power Series
- Fourier Series
- Summation of Series
- Finding Definite Integrals by Means of Series
- Infinite Products
- Stirling's Formula
- Approximation of Continuous Functions by Polynomials
Part Two. Functions of Several Variables
Chapter VI. Differential Calculus of Functions of Several Variables7 sections
- Limit of a Function. Continuity
- Partial Derivatives. Differential of a Function
- Differentiation of Implicit Functions
- Change of Variables
- Geometric Applications
- Taylor's Formula
- Extremum of a Function of Several Variables
Chapter VII. Integrals Depending on a Parameter5 sections
- Proper Integrals Depending on a Parameter
- Improper Integrals Depending on a Parameter. Uniform Convergence of Integrals
- Differentiation and Integration of Improper Integrals under the Integral Sign
- Euler Integrals
- The Fourier Integral Formula
Chapter VIII. Multiple and Line Integrals17 sections
- Double Integrals
- Computation of Areas
- Computation of Volumes
- Computation of Surface Areas
- Applications of Double Integrals to Mechanics
- Triple Integrals
- Evaluation of Volumes by Means of Triple Integrals
- Applications of Triple Integrals to Mechanics
- Improper Double and Triple Integrals
- Many-Fold Integrals
- Line Integrals
- Green's Formula
- Physical Applications of Line Integrals
- Surface Integrals
- Stokes's Formula
- Ostrogradsky's Formula
- Elements of Field Theory
Answers
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $84.95 | — | Gumroad · Instant download | Buy → |
Prices are the publisher list prices. Amazon sets the final price in each store.
Product details
- Publisher
- Northern Star Academic Press
- Language
- English
- Translator
- Valery Manokhin, PhD
- Print length
- 532 pages
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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