Basic Analysis II

A Modern Calculus in Many Variables

James K. Peterson (Autor)

Buch | Hardcover

530 Seiten

2020
CRC Press (Verlag)
978-1-138-05505-6 (ISBN)

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Basic Analysis II: A Modern Calculus in Many Variables focuses on differentiation in Rn and important concepts about mappings from Rn to Rm, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These topics converge nicely with many other important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a minimal grounding in analysis.

Features

Can be used as a traditional textbook as well as for self-study

Suitable for undergraduates in mathematics and associated disciplines

Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions

James Peterson has been an associate professor in the School of Mathematical and Statistical Sciences since 1990. He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2016. He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University. In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages and from first principles analysis of natural phenomena was absolutely essential to make progress. In both mathematical and applied areas, students often need to use advanced mathematics tools they have not learned properly. So recently, he has written a series of books on analysis to help researchers with the problem of learning new things after their degrees are done and they are practicing scientists. Along the way, he has also written papers in immunology, cognitive science and neural network technology in addition to having grants from NSF, NASA and the Army. He also likes to paint, build furniture and write stories.

1. Beginning Remarks 2.Preliminaries 3.Vector Spaces 4.Linear Transformations 5.Symmetric Matrices 6.Continuity and Topology 7.Abstract Symmetric Matrices 8.Rotations and Orbital Mechanics 9.Determinants and Matrix Manipulations 10.Differentiability 11.Multivariable Extremal Theory 12.The Inverse and Implicit Function Theorems 13.Linear Approximation Applications 14.Integration in Multiple Dimensions 15.Change of Variables and Fubini’s Theorem 16.Line Integrals 17.Differential Forms 18.The Exponential Matrix 19.Nonlinear Parametric Optimization Theory 20.Summing It All Up. References. Index

Erscheinungsdatum	01.06.2020
Zusatzinfo	56 Illustrations, black and white
Verlagsort	London
Sprache	englisch
Maße	178 x 254 mm
Gewicht	1140 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Technik ► Umwelttechnik / Biotechnologie
ISBN-10	1-138-05505-0 / 1138055050
ISBN-13	978-1-138-05505-6 / 9781138055056
Zustand	Neuware