# Problems in mathematical analysis by Demidovich

• micromass
In summary, "Problems in Mathematical Analysis" by B.P. Demidovich is a comprehensive collection of 3,193 problems covering precalculus, calculus I, II, III, and introductory differential equations. The book provides a short introduction at the beginning of each section and covers a wide range of topics, including limits, derivatives, integrals, functions of several variables, series, and differential equations. The problems are challenging and the book is highly recommended for anyone looking to improve their mathematical skills.

## For those who have use this book

• ### Strongly don't Recommend

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Code:
[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]
[*] Appendix
[LIST]
[*] Greek Alphabet
[*] Some Constants
[*] Inverse Quantities, Powers, Roots, Logarithms
[*] Trigonometric Functions
[*] Exporential, Hyperbolic and Trigonometric Functions
[*] Some Curves
[/LIST]
[/LIST]

Last edited by a moderator:
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.

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.

## 1. What is "Problems in mathematical analysis by Demidovich" about?

"Problems in mathematical analysis by Demidovich" is a comprehensive collection of mathematical problems covering a wide range of topics in mathematical analysis, such as limits, derivatives, integrals, series, and differential equations.

## 2. Is "Problems in mathematical analysis by Demidovich" suitable for beginners?

No, this book is not suitable for beginners as it assumes a strong foundation in mathematical concepts and techniques. It is better suited for advanced undergraduate or graduate students in mathematics or related fields.

## 3. How many problems are included in "Problems in mathematical analysis by Demidovich"?

There are over 3000 problems included in this book, divided into 26 chapters based on different topics in mathematical analysis.

## 4. Are there solutions provided for the problems in "Problems in mathematical analysis by Demidovich"?

Yes, this book includes solutions for all the problems, making it a valuable resource for self-study and practice.

## 5. How can "Problems in mathematical analysis by Demidovich" be used in teaching or studying mathematics?

This book can be used as a supplement to a textbook or as a source for practice problems in mathematical analysis courses. It can also be used for self-study to improve problem-solving skills and deepen understanding of mathematical concepts.

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