launchport.blogg.se - Multivariable calculus pdf engineering

Good diagrams throughout, present whenever needed to help with understanding, e.g., showing the relationship of two different parametrizations when proving that the value of the integral is independent of the parametrization. Nice treatment of multidimensional chain rule via matrix multiplication with one section on the conceptual picture and one on computations. This is not much of an issue for math texts.Įxcellent! Good clear explanations of the ideas behind the theory, e.g., Lagrange multipliers which are sometimes presented as magic, but here are motivated with geometrical ideas.

The mathematics is all correct and the author is honest about where things are being swept under the rug, e.g., in the proof of Green's Theorem. Wobbling means going back and forth which can happen in the plane. He describes torsion as "wobbling" which to me gives the wrong idea. My only complaint here is in the discussion of torsion. I still give this text a 5 for comprehensiveness. In discussing multivariable continuity, it would have been nice to pull out the two path discussion which appears in the text and highlight it as a theorem, but these are all minor points. Some of my favorite examples were missing: e.g., the cycloid and deriving Kepler's laws from Newton's laws, but everybody has their own favorites so I am okay with that. The development was clear enough that I hope most students at this level could get it. I liked the development of differential forms towards the end and having chapter 11 as a teaser for higher level stuff.

Reviewed by Andy Rich, Professor of Mathematics, PALNI, Manchester University on 12/19/19

Journalism, Media Studies & Communications +.

… the presented book is a useful tool for all mathematicians (not only for students) and I find it regrettable that this book was not written when I was a student.” (Andrey Zahariev, zbMATH 1396. The proofs are exposited to encourage understanding, not meaningless rigor. “The main achievement of the authors is that they essentially have simplified the teaching of the old topics to make a place for new ones. Every section of each chapter ends with an excellent collection of exercises, which should be graciously welcomed by independent learners and instructors alike.” (Tushar Das, MAA Reviews, September, 2018) The book is written with a wide range of STEM students in mind, and its exposition remains remarkably fluid without scarificing precision. Even instructors who use standard texts will find much of value in this refreshing first edition. “Lax and Terrell’s sequel to their Calculus With Applications presents a first course in multivariable calculus that fits in just over 400 pages. … I think this book can be recommended since, moreover, it is very pedagogical.” (Richard Becker, Mathematical Reviews, October, 2018) … There are more than 200 figures to help the reader to understand the explanations and about 500 problems. “This book belongs to a collection aimed at third- and fourth-year undergraduate mathematics students at North American universities. Upper-division undergraduates and professionals.” (J.

The text contains over 500 exercises with answers and/or solutions to half provided at the back of the book, enabling students to gauge their understanding of the content as they proceed. “The presentation of the material is guided by applications so that physics and engineering students will find the text engaging and see the relevance of multivariable calculus to their work. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. This text in multivariable calculus fosters comprehension through meaningful explanations.