Problems in Mathematical Analysis

[4685/96%]

B. P. Demidovich

Chapter 1Introduction to Analysis[860/96%]

Section 1.1Real Numbers[41/98%]

Section 1.2Theory of Sequences[111/99%]

Section 1.3The Concept of a Function[91/95%]

Section 1.4Graphical Representation of Functions[153/98%]

Section 1.5Limits of Functions[285/93%]

Section 1.6Orders of infinitesimals and infinities of functions[18/100%]

Section 1.7Continuity of Functions[97/100%]

Section 1.8Inverse Functions. Functions Given Parametrically[26/100%]

Section 1.9Uniform continuity of a function[26/92%]

Section 1.10Functional Equations[12/100%]

Chapter 2Differential Calculus of Functions of One Variable[845/96%]

Section 2.1Derivatives of Explicit Functions[221/97%]

Section 2.2Derivatives of Inverse Functions. Derivatives of Functions Given Parametrically. Derivatives of Implicit Functions[21/100%]

Section 2.3Geometric Meaning of the Derivative[30/93%]

Section 2.4Differentials of Functions[29/100%]

Section 2.5Higher-Order Derivatives and Differentials[126/98%]

Section 2.6Rolle's, Lagrange's, and Cauchy's Theorems[36/97%]

Section 2.7Increase and Decrease of a Function. Inequalities[30/100%]

Section 2.8Concavity and Convexity. Inflection Points[21/100%]

Section 2.9Methods for Evaluating Indeterminate Forms[65/89%]

Section 2.10Taylor's Formula[47/81%]

Section 2.11Extrema of a Function. Maximum and Minimum Values of a Function[59/97%]

Section 2.12Sketching the Graph of a Function from Its Characteristic Points[88/97%]

Section 2.13Problems on Maxima and Minima of Functions[35/100%]

Section 2.14Tangency of Curves. Circle of Curvature. Evolute[26/100%]

Section 2.15Approximate Solution of Equations[11/100%]

Chapter 3Indefinite Integrals[563/98%]

Section 3.1The Simplest Indefinite Integrals[243/98%]

Section 3.2Integration of rational functions[60/100%]

Section 3.3Integration of Irrational Functions[65/100%]

Section 3.4Integration of trigonometric functions[76/99%]

Section 3.5Integration of various transcendental functions[63/95%]

Section 3.6Various examples of the integration of functions[56/98%]

Chapter 4The Definite Integral[396/94%]

Section 4.1The Definite Integral as the Limit of a Sum[29/86%]

Section 4.2Methods for Computing Definite Integrals Using Indefinite Integrals[111/100%]

Section 4.3Mean Value Theorems[20/95%]

Section 4.4Improper integrals[67/94%]

Section 4.5Methods of Computing Area[44/80%]

Section 4.6Computation of Arc Length[29/86%]

Section 4.7Methods for Computing Volume[33/100%]

Section 4.8Computing the surface area of a solid of revolution[15/100%]

Section 4.9Computation of Moments. Coordinates of the Centroid[18/83%]

Section 4.10Problems in mechanics and physics[15/100%]

Section 4.11Approximate Methods for Evaluating Definite Integrals[15/100%]

Chapter 5Series[617/96%]

Section 5.1Numerical series, tests for convergence of series of constant sign[123/89%]

Section 5.2Tests for the convergence of series with variable sign[48/94%]

Section 5.3Operations on Series[16/94%]

Section 5.4Function series[99/97%]

Section 5.5Power Series[130/96%]

Section 5.6Fourier Series[50/100%]

Section 5.7Methods of Summing Series[48/100%]

Section 5.8Evaluating Definite Integrals Using Series[17/100%]

Section 5.9Infinite Products[60/100%]

Section 5.10Stirling's Formula[10/100%]

Section 5.11Approximating Continuous Functions by Polynomials[16/100%]

Chapter 6Differential Calculus of Functions of Several Variables[595/97%]

Section 6.1Limits and Continuity of Functions of Several Variables[84/89%]

Section 6.2Partial Derivatives. Differentials of Functions of Several Variables[154/97%]

Section 6.3Differentiation of implicit functions[74/96%]

Section 6.4Change of Variables[97/100%]

Section 6.5Applications in Geometry[53/100%]

Section 6.6Taylor's Formula[40/100%]

Section 6.7Extrema of Functions of Several Variables[93/97%]

Chapter 7Integrals Depending on a Parameter[206/94%]

Section 7.1Proper Integrals Depending on a Parameter[33/94%]

Section 7.2Improper Integrals with a Parameter. Uniform Convergence of Integrals[52/83%]

Section 7.3Change of variable in improper integrals. Differentiation and integration under the integral sign for improper integrals[59/97%]

Section 7.4Euler Integrals[42/100%]

Section 7.5Fourier Integral Formulas[20/100%]

Chapter 8Multiple Integrals and Curvilinear Integrals[603/94%]

Section 8.1Double Integrals[83/100%]

Section 8.2Methods of Computing Area[25/84%]

Section 8.3Methods for Computing Volume[32/97%]

Section 8.4Methods for Computing Surface Area[19/79%]

Section 8.5Applications of Double Integrals in Mechanics[26/96%]

Section 8.6Triple Integrals[25/100%]

Section 8.7Computing volumes by means of triple integrals[35/86%]

Section 8.8Applications of Triple Integrals in Mechanics[33/91%]

Section 8.9Double and Triple Improper Integrals[40/100%]

Section 8.10Multiple Integrals[20/100%]

Section 8.11Curve Integrals[80/94%]

Section 8.12Green's Formula[31/97%]

Section 8.13Physical Applications of Curve Integrals[15/100%]

Section 8.14Surface Integrals[30/87%]

Section 8.15Stokes' Formula[9/100%]

Section 8.16The Ostrogradsky Formula[26/96%]

Section 8.17Elements of Field Theory[74/88%]