1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
  2. Support PF! Reminder for those going back to school to buy their text books via PF Here!
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculus Problems in mathematical analysis by Demidovich

  1. Strongly Recommend

    100.0%
  2. Lightly Recommend

    0 vote(s)
    0.0%
  3. Lightly don't Recommend

    0 vote(s)
    0.0%
  4. Strongly don't Recommend

    0 vote(s)
    0.0%
  1. Feb 3, 2013 #1

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award


    Table of Contents:
    Code (Text):

    [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]
     
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 3, 2013 #2
    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.
     
  4. Feb 20, 2014 #3
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Problems in mathematical analysis by Demidovich
Loading...