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Calculus Problems in mathematical analysis by Demidovich

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  1. Feb 3, 2013 #1

    Table of Contents:
    Code (Text):

    [*] Preface
    [*] 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 Higher Orders
    [*] Differentials of First and Higher Orders
    [*] Mean Value Theorems
    [*] Taylor's Formula
    [*] The L'Hospital-Bernoulli Rule for Evaluating Indeterminate Forms
    [*] The Etrema 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
    [*] 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
    [*] 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 Guldin'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 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
    [*] 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 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
    [*] Approximate Calculations
    [*] 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
    [*] Answers
    [*] Appendix
    [*] Greek Alphabet
    [*] Some Constants
    [*] Inverse Quantities, Powers, Roots, Logarithms
    [*] Trigonometric Functions
    [*] Exporential, Hyperbolic and Trigonometric Functions
    [*] Some Curves
    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.
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