Introduction to calculus and analysis / Richard Courant, Fritz John
By: Courant, Richard.
Contributor(s): John, Fritz.
New York : Interscience Publishers, 1965 Description: Vol. 1 - xxiii, 661 p. ; 23 cm.Subject(s): Calculo | Analisis matematicoDDC classification: 515 / C858iItem type | Current location | Collection | Call number | Vol info | Copy number | Status | Notes | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|---|---|---|
Libros | Biblioteca Central | General | 515 / C858i (Browse shelf) | 8001 | 1 | Available | DO | 8010004990 |
The continuum of numbers -- The concept of function -- The elementary functions -- Sequences -- Mathematical
induction -- The limited of a sequence -- Further discussion of the concept of limit -- The concept of limit
for functions of a continous variable -- Limits and the number concept -- Theorems on continuous functions --
Polar coordinates -- Remarks on complex numbers -- The fundamental ideas of the integral and differential
calculus -- The integral -- Elementary examples of integration -- Fundamental rules of integration -- The
integral as a function of the upper limit (Indifinite integral) -- Logarithm defined by an integral --
Exponiental function and powers -- The integral of an arbitrary power of x --The derivative -- The integral,
the primitive function, and the fundamental theorems of the calculus -- The techniques of calculus --
Differentiation and integration of the elementary functions -- The simplest rules for differentiation and
their applications -- The derivative of the inverse function -- Differentiation of composite functions -- Some
applications of the exponential function -- The hyperbolic functions -- Maxima and minima -- The order of
magnitude of functions -- Techniques of integration -- Table of elementary integrals -- The method of
substitution -- Further examples of the substitution method -- Integration by parts -- Integration of rational
functions -- Integration of some other claseses of functions -- Integrals of elementary functions -- Extension
of the concept of integral -- The differential equations of the trigonometric functions -- Applications in
Physics and Geometry -- Theory of plane curves -- Vectors in two dimensions -- Motion of a particle under
given forces -- Free fall of a body resisted by air -- The simplest type of elstic vibration -- Motion on a
given curve -- Motion in a gravitational field -- Work and energy -- Taylor´s expansion -- Expansion of the
Logarithm and the inverse tangent -- Taylor´s theorem -- Expression and estimates for the remainder --
Expansions of the elementary functions -- Numerical meethods -- Computation of integrals -- Other examples of
numerical methods -- Numerical solution of equations -- Infinite sums and products -- The concepts of
convergence and divergence -- Sequences of functions -- Expasion of given functions in power series. Method of
undetermined coefficient -- Trigonometric series -- Periodic functions -- Superposition of harmonic vibrations
-- Fourier series -- Further discussion of convergence -- Aproximation by Trigonometric and rational
polynomials -- Differential equations for the simplest types of vibration -- Vibration problems of mechanics
and physics -- Solution of the homogeneous equation. Free oscillations -- The nonhomogeneous equation. Forced
oscillations --
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