Calculus and Linear Algebra, vol. 2 - Wilfred Kaplan

Calculus and Linear Algebra. Vol. 2: Vector Spaces, Many-Variable Calculus, and Differential Equations.

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Advanced Calculus - Wilfred Kaplan

The Fifth Edition of this leading text offers substantial training in vectors and matrices, vector analysis, and partial differential equations. Vectors are introduced at the outset and serve at many points to indicate geometrical and physical significance of mathematical relations. Numerical methods are touched upon at various points, because of their practical value and the insights they give about theory. Vectors and Matrices; Differential Calculus of Functions of Several Variables; Vector Differential Calculus; Integral Calculus of Functions of Several Variables; Vector Integral Calculus; Two-Dimensional Theory; Three-Dimensional Theory and Applications; Infinite Series; Fourier Series and Orthogonal Functions; Functions of a Complex Variable; Ordinary Differential Equations; Partial Differential Equations. For all readers interested in advanced calculus.

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Theory of Functions of a Real Variable - S. Sternberg

I have taught the beginning graduate course in real variables and functional analysis three times in the last five years, and this book is the result. The course assumes that the student has seen the basics of real variable theory and point set topology. The elements of the topology of metrics spaces are presented (in the nature of a rapid review) in Chapter I. The course itself consists of two parts: 1) measure theory and integration, and 2) Hilbert space theory, especially the spectral theorem and its applications. In Chapter II I do the basics of Hilbert space theory, i.e. what I can do without measure theory or the Lebesgue integral. The hero here (and perhaps for the first half of the course) is the Riesz representation theorem. Included is the spectral theorem for compact self-adjoint operators and applications of this theorem to elliptic partial differential equations. The pde material follows closely the treatment by Bers and Schecter in Partial Differential Equations by Bers, John and Schecter AMS (1964).

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Calculo Infinitesimal - Spivak, M.

En esta segunda edición, existen apéndices especiales para temas que antes se hallaban tratados sólo superficialmente. Algunos temas, tales como operaciones con series de potencias, han sido desarrollados con más detalle en el texto y sobre los mismos hay ahora más ejercicios. Se presentan alrededor de 160 problemas nuevos, muchos de los cuales están, en cuanto a dificultad, en un término medio entre los pocos ejercicios de rutina del comienzo de cada capítulo y los más difíciles que aparecen más adelante.

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Calculus On Manifolds - Spivak, M.

This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.

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Advanced Calculus, 3rd Edition - Taylor Angus & Wiley.Fayez

The concept of a curse in advanced calculus has a long history in American colleges and universities.

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Calculus, Vol. 2 Multi - Variable Calculus - Tom M. Apostol

Now available in paperback! An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

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Calculus, Vol. 1 One - Variable Calculus- Tom M. Apostol

O cálculo é uma ciência dedutiva e um ramo da matamática pura. Ao mesmo tempo é muito importante lembrar que o Cálculo tem raízes profundas em problemas físicos e que muita da sua potência e beleza deriva da variedade de suas aplicações. É possívelcombinar um desenvolvimento teórico profundo com uma sadia formação técnica.

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Cálculo, Volume 2 - Mauricio A. Vilches

Esta notas são a continuação natural do livro CÁLCULO: VOLUME I, que é prérequisito para este livro. Da mesma forma que o Cálculo Diferencial e Integral de uma variável, os conceitos centrais do Cálculo Diferencial e Integral de várias variáveis são relativamente profundos e não se espera que possam ser assimilados de uma só vez. Neste nível, o importante é que o leitor desenvolva a habilidade de calcular e adquira a compreensão geométrica dos problemas. Esperamos que o livro permita ao leitor um acesso rápido e agradável ao Cálculo Diferencial e Integral de uma variável. Não podemos deixar de recomendar aos alunos a utilização, criteriosa, dos softwares de Cálculo existente no mercado, pois eles são um complemento útil ao aprendizado da disciplina. Desejamos agradecer aos nossos colegas do Departamento de Análise e do IMEUERJ que, de algum modo, nos motivaram e deram condições para escrever estas notas e à Sra. Sonia Maria Alves pela digitação. Certamente, todos os erros são exclusivamente de responsabilidade dos autores.

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