Advanced Calculus: A Geometric View Kindle ´ Advanced

Advanced Calculus: A Geometric View Kindle ´ Advanced


Advanced Calculus: A Geometric View ➜ [Epub] ❧ Advanced Calculus: A Geometric View By James J. Callahan ➦ – Centrumpowypadkowe.co.uk A half century ago, advanced calculus was a well de ned subject at the core of the undergraduate mathematics curriulum The classic texts of Taylor , Buck , Widder , and Kaplan , for example, show A Geometric MOBI í A half century ago, advanced calculus was a well de ned subject at the core of the undergraduate mathematics curriulum The classic texts of Taylor, Buck, Widder, and Kaplan, for example, show some of the ways it was approached Over time, certain aspects Advanced Calculus: PDF or of the course came to be seen as signi cant those seen as giving a rigorous foundation to calculus and they came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core Advanced calculus did Calculus: A Geometric PDF ☆ not, in the process, become less important, but its role in the curriculum changed In fact, a bifurcation occurred 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 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 Multivariable calculusnaturallysplits intothreepartsseveralfunctionsofonevariable,one function of several variables, andseveral 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 To put it another way Green s theorem ts comfortably Stokes and Gauss do not.

    Kindle Welcome to the Kindle ereader store those seen as giving a rigorous foundation to calculus and they came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core Advanced calculus did Calculus: A Geometric PDF ☆ not, in the process, become less important, but its role in the curriculum changed In fact, a bifurcation occurred 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 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 Multivariable calculusnaturallysplits intothreepartsseveralfunctionsofonevariable,one function of several variables, andseveral 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 To put it another way Green s theorem ts comfortably Stokes and Gauss do not."/>
  • Hardcover
  • 526 pages
  • Advanced Calculus: A Geometric View
  • James J. Callahan
  • English
  • 13 July 2019
  • 1441973311

About the Author: James J. Callahan

A Geometric MOBI í James Callahan earned a BA from Marist College and a PhD from New York UniversityIn , Professor Callahan received the Lester R Ford Award of the Mathematical Association of America and at Smith he has received the Faculty Distinguished Teaching Award and the Advanced Calculus: PDF or Sears Roebuck Foundation Award for Teaching Excellence and Campus Leadership He has made research trips to England and FranceCallahan was the director of the Five College Calculus Project funded by the National Science Foundation , and co author of Calculus in Context W H Calculus: A Geometric PDF ☆ Freeman Co, He wrote Geometry of Spacetime Springer Verlag, an undergraduate text in mathematics about relativity, as well as Advanced Calculus a Geometric ViewProfessor Callahan s interests include geometry, dynamical systems, chaos and fractals, catastrophe theory, relativity, most areas of applied analysis and building things.



10 thoughts on “Advanced Calculus: A Geometric View

  1. Adam Lantos Adam Lantos says:

    The emphasis is on intuition but the author does not shy away from advanced concepts.The many diagrams and graphs have practical reasons to be there as they help with understanding The examples that are given in order to motivate the reader do a great job at it There are also some proofs whenever the proof is not very big There are also proofs when the proof directly helps with the understanding.The writing style is also great, mixing a formal type of writing with aconversational style The emphasis is on intuition but the author does not shy away from advanced concepts.The many diagrams and graphs have practical reasons to be there as they help with understanding The examples that are given in order to motivate the reader do a great job at it There are also some proofs whenever the proof is not very big There are also proofs when the proof directly helps with the understanding.The writing style is also great, mixing a formal type of writing with aconversational style.You can find this book at a very low price and it s also hardcover It is of great use to physicists and mathematicians in order to REALLY understand and reinforce your intuition behind these concepts.Also, the author states in the preface that the Feynman Lectures were a great influence due to the way that Feynman explained everything So, this is a strong indication of an author trying and succeeding to write a book on mathematics using that very powerful way of thinking and explaining.Two things that I did not like were 1 The higher dimension derivative is just motivated through the Taylor series of many variables Books like Marsden Tromba s don t even try to motivate it But, I expectedfrom this book I mean, a student coming from only a one variable calculus background would feel a bit overwhelmed while trying to figure out why the derivative indimensions is a matrix and why it is the way it is I figured it out, but I only did so by hard thinking and referencing other books like Colley s books and Hubbard s book But, again, I have skipped some chapters, so I am not very sure that the author did not explain the derivative in higher dimensions.2 I certainly expected to gaingeometrical intuition from the section on the chain rule Sure, no other book explains the geometrical meaning of the chain rule, but this book promises to give the geometrical meaning behind everything that it presents Inexcusable But, again, these points can t make me give this book anything less than a 5 star rating because it s so unique, helpful and well written Any book that concentrates on intuition and motivation without sacrificing essential things is a king in pedagogy

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