Problems in mathematical analysis by Demidovich

[micromass]

• Author: B.P. Demidovich
• Title: Problems in mathematical analysis
• Amazon link https://www.amazon.com/dp/B0007BNL1W/?tag=pfamazon01-20

Table of Contents:

[LIST]
[*] Preface
[*] Introduction to Analysis
[LIST]
[*] Functions
[*] Graphs of Elementary Functions
[*] Limits
[*] Infinitely Small and Large Quantities
[*] Continuity of Functions
[/LIST]
[*] Differentiation of Functions
[LIST]
[*] Calculating Derivatives Directly
[*] Tabular Differentiation
[*] The Derivatives of Functions Not Represented Explicitly
[*] Geometrical and Mechanical Applications of the Derivative
[*] Derivatives of Higher Orders
[*] Differentials of First and Higher Orders
[*] Mean Value Theorems
[*] Taylor's Formula
[*] The L'Hospital-Bernoulli Rule for Evaluating Indeterminate Forms
[/LIST]
[*] The Etrema of a Function and the Geometric Applications of a Derivative
[LIST]
[*] 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
[/LIST]
[*] Indefinite Integrals
[LIST]
[*] Direct Integration
[*] Integration by Substitution
[*] Integration by Parts
[*] Standard Integrals Containing a Quadratic Trinomial
[*] Integration of Rational Functions
[*] Integrating Certain Irrational Functions
[*] Integrating Trigonometric Functions
[*] Integration of Hyperbolic Functions
[*] Using Ingonometric and Hyperbolic Substitutions for Finding Integrals of the Form \int R(x,\sqrt{ax^2 + bx + c})dx Where R is a Rational Function
[*] Integration of Various Transcendental Functions
[*] Using Reduction Formulas
[*] Miscellaneous Examples on Integration
[/LIST]
[*] Definite Integrals
[LIST]
[*] 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 Guldin's Theorems
[*] Applying Definite Integrals to the Solution of Physical Problems
[/LIST]
[*] Functions of Several Variables
[LIST]
[*] 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 for 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
[*] The Vector Function of a Scalar Argument
[*] The Natural Trihedron of a Space Curve
[*] Curvature and Torsion of a Space Curve
[/LIST]
[*] Multiple and Line Integrals
[LIST]
[*] 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
[/LIST]
[*] Series
[LIST]
[*] Number Series
[*] Functional Series
[*] Taylor's Series
[*] Fourier's Series
[/LIST]
[*] Differential Equations
[LIST]
[*] Verifying Solutions. Forming Differential Equations of Families of Curves. Initial Conditions
[*] First-Order Differential Equations
[*] First-Order Diflerential Equations with Variables Separable. Orthogonal Trajectories
[*] First-Order Homogeneous Differential Equations
[*] First-Order Linear Diflerential 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 Differential Equations by Means of Power Series
[*] Problems on Fourier's Method
[/LIST]
[*] Approximate Calculations
[LIST]
[*] Operations on Approximate Numbers
[*] Interpolation of Functions
[*] Computing the Real Roots of Equations
[*] Numerical Integration of Functions
[*] Numerical Integration of Ordinary Differential Equations
[*] Approximating Fourier's Coefficients
[/LIST]
[*] Answers
[*] Appendix
[LIST]
[*] Greek Alphabet
[*] Some Constants
[*] Inverse Quantities, Powers, Roots, Logarithms
[*] Trigonometric Functions
[*] Exporential, Hyperbolic and Trigonometric Functions
[*] Some Curves
[/LIST]
[/LIST]

 

[fourier jr]

Not exactly analysis, there are a total of 3193 problems on what you would call precalculus, calculus I, II, III & intro DE. There's usually a short intro at the beginning of each section or chapter on how to solve the following problems. I've gotten through about 2/3 of the probs after feeling stupid/guilty for having not tried any considering who previously owned my copy (his name is crossed out on the title page). I was up to >100/day at one point which I thought was pretty good. There's plenty of stuff I'd never seen before & I doubt I would have encountered it elsewhere.

 

[honzazostravy]

Excellent collection of problems. I have russian original. When I had Calculus courses I computed all exercises. In my point of view, one of the best collection of problems of calculus of the world.