Demidovich's Collection of Problems and Exercises in Mathematical Analysis for Engineering Colleges
by B. P. Demidovich (editor)
Translated by Valery Manokhin, PhD
The problem collection in mathematical analysis written for engineering colleges by ten authors under the editorship of B. P. Demidovich, in faithful English translation from the original Russian edition. Ten chapters and 102 numbered sections hold 3,199 numbered problems, each section opening with a summary of theory and worked examples: functions, limits and continuity; differentiation and its geometrical and mechanical applications; extrema, asymptotes and curve sketching; the indefinite and the definite integral, with areas, volumes, centres of gravity and physical problems; functions of several variables, through directional derivatives, envelopes and the curvature and torsion of space curves; multiple, line and surface integrals and the elements of field theory; number, functional, Taylor and Fourier series; a full chapter of 404 problems on differential equations; and a chapter of approximate calculations — interpolation, real roots of equations, numerical integration of functions and of differential equations. Answers follow, with hints and, for the problems marked with two asterisks, solutions. 107 numbered figures and six appendix tables.
10 chapters · 102 numbered articles · 3199 exercises · 504 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, a first course in ODEs and numerical methods |
|---|---|---|
| United Kingdom | Undergraduate 1–2 | first- and second-year engineering mathematics |
| Canada | University 1–2 | QC CEGEP 201-NYA / NYB · first- and second-year engineering calculus |
How this book fits
See the whole sequence →Work through first
- Kiselev's Calculus$54.95
Covers much of the same ground
The general collection has 4,683 problems to 3,199 and a whole chapter on integrals depending on a parameter — Euler’s integrals, the Fourier integral formula — plus sections on uniform continuity, functional equations and infinite products that this book lacks. It has no differential equations and no chapter of approximate calculations.
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
108 section headings — the printed contents page in full.
Translator's Preface
From the Authors' Preface
Chapter I. Introduction to Analysis5 sections
- The Concept of a Function
- Graphs of Elementary Functions
- Limits
- Infinitesimals and Infinitely Large Quantities
- Continuity of Functions
Chapter II. Differentiation of Functions9 sections
- Direct Computation of Derivatives
- Tabular Differentiation
- Derivatives of Functions Not Given Explicitly
- Geometrical and Mechanical Applications of the Derivative
- Derivatives of Higher Orders
- Differentials of the First and Higher Orders
- Mean Value Theorems
- Taylor's Formula
- The L'Hospital–Bernoulli Rule for Evaluating Indeterminate Forms
Chapter III. Extrema of a Function and Geometric Applications of the Derivative5 sections
- Extrema of a Function of One Argument
- Direction of Concavity. Points of Inflection
- Asymptotes
- Sketching Graphs of Functions by Characteristic Points
- Differential of an Arc. Curvature
Chapter IV. The Indefinite Integral12 sections
- Direct Integration
- The Method of Substitution
- Integration by Parts
- The Simplest Integrals Containing a Quadratic Trinomial
- Integration of Rational Functions
- Integration of Certain Irrational Functions
- Integration of Trigonometric Functions
- Integration of Hyperbolic Functions
- Application of Trigonometric and Hyperbolic Substitutions for Finding Integrals of the Form ∫R(x, √(ax² + bx + c)) dx, Where R Is a Rational Function
- Integration of Various Transcendental Functions
- Using Reduction Formulae
- Integration of Miscellaneous Functions
Chapter V. The Definite Integral12 sections
- The Definite Integral as the Limit of a Sum
- Evaluating Definite Integrals by Means of Indefinite Integrals
- Improper Integrals
- Change of Variable in a Definite Integral
- Integration by Parts
- The Mean Value Theorem
- Areas of Plane Figures
- The Arc Length of a Curve
- Volumes of Solids
- Area of a Surface of Revolution
- Moments. Centres of Gravity. Guldin's Theorems
- Applications of Definite Integrals to the Solution of Physical Problems
Chapter VI. Functions of Several Variables20 sections
- Basic Notions
- Continuity
- Partial Derivatives
- The Total Differential of a Function
- Differentiation of Composite Functions
- The Derivative in a Given Direction and the Gradient of a Function
- Derivatives and Differentials of Higher Orders
- Integration of Total Differentials
- Differentiation of Implicit Functions
- Change of Variables
- The Tangent Plane and the Normal to a Surface
- Taylor's Formula for a Function of Several Variables
- The Extremum of a Function of Several Variables
- Problems on Finding the Greatest and Least Values of Functions
- Singular Points of Plane Curves
- Envelope
- Arc Length of a Space Curve
- Vector Functions of a Scalar Argument
- Natural Trihedron of a Space Curve
- Curvature and Torsion of a Space Curve
Chapter VII. Multiple and Line Integrals12 sections
- The Double Integral in Rectangular Coordinates
- Change of Variables in a Double Integral
- Computation of Areas of Figures
- Computation of Volumes of Solids
- Computation of Areas of Surfaces
- Applications of the Double Integral to Mechanics
- Triple Integrals
- Improper Integrals Depending on a Parameter. Improper Multiple Integrals
- Line Integrals
- Surface Integrals
- The Ostrogradsky–Gauss Formula
- Elements of Field Theory
Chapter VIII. Series4 sections
- Number Series
- Functional Series
- Taylor Series
- Fourier Series
Chapter IX. Differential Equations17 sections
- Verification of Solutions. Formation of Differential Equations of Families of Curves. Initial Conditions
- First-Order Differential Equations
- First-Order Differential Equations with Separable Variables. Orthogonal Trajectories
- Homogeneous First-Order Differential Equations
- Linear First-Order Differential Equations. Bernoulli's Equation
- Exact Differential Equations. Integrating Factor
- First-Order Differential Equations Not Solved for the Derivative
- The Lagrange and Clairaut Equations
- Miscellaneous First-Order Differential Equations
- Higher-Order Differential Equations
- Linear Differential Equations
- Second-Order Linear Differential Equations with Constant Coefficients
- Linear Differential Equations with Constant Coefficients of Order Higher than the Second
- Euler's Equations
- Systems of Differential Equations
- Integration of Differential Equations by Means of Power Series
- Problems on the Fourier Method
Chapter X. Approximate Calculations6 sections
- Operations on Approximate Numbers
- Interpolation of Functions
- Computation of the Real Roots of Equations
- Numerical Integration of Functions
- Numerical Integration of Ordinary Differential Equations
- Approximate Computation of Fourier Coefficients
Answers
Appendices6 sections
- I. The Greek Alphabet
- II. Some Constants
- III. Reciprocals, Powers, Roots, Logarithms
- IV. Trigonometric Functions
- V. Exponential, Hyperbolic and Trigonometric Functions
- VI. Some Curves (for Reference)
Formats and editions
| Format | Price | ISBN-13 | Where | Buy |
|---|---|---|---|---|
| $64.95 | — | 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
- 504 pages
Published by Northern Star Academic Press · First faithful English translation from the original Russian edition
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