(Old Edition) Problems In Calculus Of One Variable

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Buy (Old Edition) Problems In Calculus Of One Variable Used Books Online India, Authored by ia maron, Arihant Publications India Limited in paperback binding from Used Book Store.

This is a used (old edition) textbook covering Problems in Calculus of One Variable, written in English. It is an introduction to mathematical analysis, featuring comprehensive coverage of differentiation and integration. The book is structured into eight main parts: 1. Introduction to Mathematical Analysis: This section covers real numbers, absolute values, functions, their domains, investigation, inverse functions, graphical representation, number sequences, limits of sequences, testing sequences for convergence, the limit of a function, calculation of limits, infinitesimals and infinite functions, equivalent infinitesimals, one-sided limits, continuity of functions, points of discontinuity, arithmetic operations on continuous functions, and properties of continuous functions on closed intervals.
2. Differentiation of Functions: This part delves into the definition of the derivative, differentiation of explicit functions (including successive differentiation and Leibnitz’s formula), differentiation of inverse, implicit, and parametrically represented functions, applications of the derivative, the differential of a function, and approximate problems.
3. Application of Differential Calculus to Investigation of Functions: This section explores basic theorems on differentiable functions, evaluation of indeterminate forms using L’Hospital’s Rule, Taylor’s Formula for approximate calculations and limit evaluation, testing functions for monotonicity, finding greatest and least values, solving problems in geometry and physics, convexity and concavity of curves, points of inflection, asymptotes, a general plan for investigating functions and sketching graphs, and approximate solutions of algebraic and transcendental equations.
4. Indefinite Integrals. Basic Methods of Integration: This part covers direct integration, methods of expansion, integration by substitution, integration by parts, and reduction formulas.
5. Basic Classes of Integrable Functions: This section focuses on the integration of rational functions, certain irrational expressions, Euler’s substitutions, other methods for integrating expressions, integration of binomial differentials, integration of trigonometric and hyperbolic functions, integration of certain irrational functions using trigonometric or other transcendental functions, integration of other transcendental functions, and a list of basic forms of integrals.
6. The Definite Integrals: This part explains the attainment of problems, lower and upper integrals, the Newton-Leibniz formula for evaluating definite integrals, estimating integrals, the definite integral as a function of the upper limit, changing variables in a definite integral, simplification of integrals based on symmetry properties, approximating definite integrals, and additional problems.
7. Applications of the Definite Integral: This section covers computing limits of sums, computing areas in rectangular coordinates, areas with parametrically represented curves, areas of curvilinear sectors in polar coordinates, computing volumes of solids, arc length of plane curves in rectangular coordinates and parametrically represented curves, arc length in polar coordinates, geometrical applications, computing pressure, work, and other physical quantities, computing static moments and moments of inertia, and determining coordinates of the center of gravity.
8. Improper Integrals: This part addresses improper integrals with infinite limits, improper integrals of unbounded functions, and geometric and physical applications of improper integrals.

9789388127370 ISBN
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