Demidovich B.P. (ed.) Problems in Mathematical Analysis

2nd printing. — Trans. from the Russian by G. Yankovsky. — Moscow: Mir Publ., 1986. — 496 p.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 3000 problems covering all branches of higher mathematics given in college courses.Демидович Б.П. (ред.). Задачи и упражнения по математическому анализу для ВТУЗов. 6-е издание. /file/2072608/
Демидович Б.П. (ред.). Сборник задач и упражнений по математическому анализу. 10-е издание. /file/2492787/Introduction to analysis.
Functions.
Graphs of Elementary Functions.
Limits.
Infinitely Small and Large Quantities.
Continuity of Functions.Differentiation of functions.
Calculating Derivatives Directly.
Tabular Differentiation.
The Derivatives of Functions Not Represented Explicitly.
Geometrical and Mechanical Applications of the Derivative.
Derivatives of Higier Orders.
Differentials of First and Higher Orders.
Mean Value Theorems.
Taylor's Formula.
The L’Hospital-Bernoulli Rule for Evaluating Indeterminate Forms.The extrema of a function and the geometric applications of a derivative.
The Extrema of a Function of One Argument.
The Direction of Concavity Points of Inflection.
Asymptotes.
Graphing Functions by Characteristic Points.
Differential of an Arc Curvature.Indefinite integrals.
Direct Integration.
Integration by Substitution.
Integration by Parts.
Standard Integrals Containing a Quadratic Trinomial.
Integration of Rational Functions.
Integration Certain Irrational Functions.
Integrating Trigonemetric Functions.
Integration of Hyperbolic Functions.
Using Trigonometric and Hyperbolic Substitutions tor Finding Integrals.
Integration of Various Transcendental Functions.
Using Reduction Formulas.
Miscellaneous Examples on Integration.Definite integrals.
The Definite Integral as the Limit of a Sum.
Evaluating Definite Integrals by Means of Indefinite Integrals.
Improper Integrals.
Charge of Variable in a Definite Integral.
Integration by Parts.
Mean-Value Theorem.
The Areas of Plane Figures.
The Arc Length of a Curve.
Volumes of Solids.
The Area of a Surface of Revolution.
Moments Centres of Gravity Culdm's Theorems.
Applying Definite Integrals to the Solution of Physical Problems.Functions of several variables.
Basic Notions.
Continuity.
Partial Derivatives.
Total Differential of a Function.
Differentiation of Composite Functions.
Derivative in a Given Direction and the Gradient of a Function.
Higher-Order Derivatives and Differentials.
Integration of Total Differentials.
Differentiation of Implicit Functions.
Change of Variables.
The Tangent Plane and the Normal to a Surface.
Taylor's Formula tor a Function of Several Variables.
The Extremum of a Function of Several Variables.
Finding the Greatest and Smallest Values of Functions.
Singular Points of Plane Curves.
Envelope.
Arc Length of a Space Curve.Multiple and line integrals.
The Double Integral in Rectangular Coordinates.
Change of Variables in a Double Integral.
Computing Areas.
Computing Volumes.
Computing the Areas of Surfaces.
Applications of the Double Integral in Mechanics.
Triple Integrals.
Improper Integrals Dependent on a Parameter. Improper Multiple Integrals.
Line Integrals.
Surface Integrals.
The Ostrogradsky-Gauss Formula.
Fundamentals of Field Theory.Series.
Number Series.
Functional Series.
Taylor’s Series.
Fourier’s Series.Differential equations.
Verifying Solutions. Forming Differential Equations of Families of Curves. Initial Conditions.
First-Order Differential Equations.
First-Order Differential Equations with Variables Separable. Orthogonal Trajectories.
First-Order Homogeneous Differential Equations.
First-Order Linear 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 Exercises on First-Order Differential Equations.
Higher-Order Differential Equations.
Linear Differential Equations.
Linear Differential Equations of Second Order with Constant Coefficients.
Linear Differential Equations of Order Higher than Two with Constant Coefficients.
Euler's Equations.
Systems of Differential Equations.
Integration of Diflerential Equations by Means of Power Series.
Problems on Fourier's Method.Approximate calculations.
Operations on Approximate Numbers.
Interpolation of Functions.
Computing tbo^Roaf Roots of Equations.
Numerical Integration of Functions.
Nunencat Integration of Ordinary DifUrtnliat Equations
Approximating Fourier's Coeficients.Answers.Appendix.
Greek Alphabet.
Some Constants.
Inverse Quantities, Powers, Roots, Logarithms.
Trigonometric Functions.
Exponential, Hyperbolic and Trigonometric Functions.
Some Curves.