Advanced Calculus

Name: To Put It Another Way: Greenâs Theorem ?ts Comfortably; Stokesâ And Gaussâ Do Not. :- Media
Brand: Springer Nature
SKU: CBAI-105127
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About The In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal..A half-century ago, advanced calculus was a well-de?ned subject at the core of the undergraduate mathematics curriulum

To put it another way: Greenâs theorem ?ts comfortably; Stokesâ and Gaussâ do not. Multivariable calculusnaturallysplits intothreeparts:(1)severalfunctionsofonevariable,(2)one function of several variables, and (3) several functions of several variables. The ?rst two are well-developed in Calculus III, but the third is really too large and varied to be treated satisfactorily in the time remaining at the end of a semester. A half-century ago, advanced calculus was a well-de?ned subject at the core of the undergraduate mathematics curriulum. In fact, a bifurcation occurred. The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III. In my experience, though, it does not manage to accomplish what the old advancedcalculus course did. Advanced calculus did not, in the process, become less important, but its role in the curriculum changed. Over time, certain aspects of the course came to be seen as more signi?cantâthose seen as giving a rigorous foundation to calculusâand they - came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core. In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal. The classic texts of Taylor [19], Buck [1], Widder [21], and Kaplan [9], for example, show some of the ways it was approached.

Books > Mathematics

Advanced Calculus

An Introduction to Mathematical Cryptography

He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

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$Some features of the text: The text is completely self-contained and starts with the real number axioms; The integral is defined as the area under the graph, while the area is defined for every subset of the plane; There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; There are 385 problems with all the solutions at the back of the text.$

Some features of the text: The text is completely self-contained and starts with the real number axioms; The integral is defined as the area under the graph, while the area is defined for every subset of the plane; There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; There are 385 problems with all the solutions at the back of the text.

Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors.This third edition includes corrections as well as some additional material. This text is intended for an honors calculus course or for an introduction to analysis.

The first eleven chapters are aimed at an Upper Division undergraduate audience.

The book is based on lectures given over the years by the author at several places, including UCLA, Brown University, the universities at La Plata and Buenos Aires, Argentina; and the Universidad Autonomo de Valencia, Spain. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis.

4) The section on families of sets has been thoroughly revised, with the focus being on families of sets in general, not necessarily thought of as indexed.

7) All known errors have been corrected. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. 6) A new section called ``You Are the Professor'' has been added to the end of the last chapter. New to the second edition: 1) A new section about the foundations of set theory has been added at the end of the chapter about sets.

A First Course in Calculus

I have not written this course in the style I would use for an advanced monograph, on sophisticated topics. This book is written for the students to give them an immediate, and pleasant, access to the subject. This does not mean that so-called rigor has to be abandoned.

The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III.

Multivariable calculusnaturallysplits intothreeparts:(1)severalfunctionsofonevariable,(2)one function of several variables, and (3) several functions of several variables. The ?rst two are well-developed in Calculus III, but the third is really too large and varied to be treated satisfactorily in the time remaining at the end of a semester.

Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well.

The second edition offersmany additionaltopics for use in the classroom or for independentstudy. There are certain rules that one must abide by in order to create a successful sequel. The rst two chapters, on graph theory and combinatorics, remain largely independent, and may be covered in either order.

He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra.

The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III.

In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal.. The classic texts of Taylor [19], Buck [1], Widder [21], and Kaplan [9], for example, show some of the ways it was approached.

He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.. In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates.

The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III.

In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal. Advanced Calculus Advanced calculus did not, in the process, become less important, but its role in the curriculum changed. Over time, certain aspects of the course came to be seen as more signi?cantâthose seen as giving a rigorous foundation to calculusâand they - came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core.

Advanced Calculus

Books > Mathematics

Specifications of Advanced Calculus

The first eleven chapters are aimed at an Upper Division undergraduate audience.

4) The section on families of sets has been thoroughly revised, with the focus being on families of sets in general, not necessarily thought of as indexed.

A First Course in Calculus

The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III.

Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well.

He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III.

He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III.