Vector Calculus And Linear Algebra

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Vector Calculus And Linear Algebra

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Author : Oliver Knill
language : en
Publisher: World Scientific Publishing Company
Release Date : 2025-04-30

Vector Calculus And Linear Algebra written by Oliver Knill and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-30 with Mathematics categories.

This book covers vector calculus up to the integral theorems; linear algebra up to the spectral theorem; and harmonic analysis until the Dirichlet theorem on convergence of Fourier series with applications to partial differential equations. It also contains a unique introduction to proofs, while providing a solid foundation in understanding the proof techniques better.The book incorporates fundamentals from advanced calculus and linear algebra but it is still accessible to a rather general student audience.Students will find materials that are usually left out like differential forms in calculus, the Taylor theorem in arbitrary dimensions or the Jordan normal form in linear algebra, the convergence proof of Fourier series, and how to do calculus on discrete networks.The contents of this book were used to teach in a two-semester course at Harvard University during fall 2018 and spring 2019. For the last 30 years, Oliver Knill has taught calculus, linear algebra, probability theory and differential equations starting at ETH Zürich, moving onward to Caltech, and the University of Arizona, and ever since 2000, at Harvard.

Answers To Selected Problems In Multivariable Calculus With Linear Algebra And Series

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Author : William F. Trench
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Answers To Selected Problems In Multivariable Calculus With Linear Algebra And Series written by William F. Trench and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series contains the answers to selected problems in linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples. The problems and corresponding solutions deal with linear equations and matrices, including determinants; vector spaces and linear transformations; eigenvalues and eigenvectors; vector analysis and analytic geometry in R3; curves and surfaces; the differential calculus of real-valued functions of n variables; and vector-valued functions as ordered m-tuples of real-valued functions. Integration (line, surface, and multiple integrals) is also covered, together with Green's and Stokes's theorems and the divergence theorem. The final chapter is devoted to infinite sequences, infinite series, and power series in one variable. This monograph is intended for students majoring in science, engineering, or mathematics.

Multivariable Mathematics

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Author : Theodore Shifrin
language : en
Publisher: John Wiley & Sons
Release Date : 2004-01-26

Multivariable Mathematics written by Theodore Shifrin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-26 with Mathematics categories.

Multivariable Mathematics combines linear algebra and multivariable calculus in a rigorous approach. The material is integrated to emphasize the role of linearity in all of calculus and the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author addresses all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible and also including complete proofs. By emphasizing the theoretical aspects and reviewing the linear algebra material quickly, the book can also be used as a text for an advanced calculus or multivariable analysis course culminating in a treatment of manifolds, differential forms, and the generalized Stokes’s Theorem.

Introduction To Applied Linear Algebra

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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07

Introduction To Applied Linear Algebra written by Stephen Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Business & Economics categories.

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Vector Calculus

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Author : Paul C. Matthews
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Vector Calculus written by Paul C. Matthews and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Vector calculus is the fundamental language of mathematical physics. It pro vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.

Multivariable Calculus Linear Algebra And Differential Equations

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Author : Stanley I. Grossman
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Multivariable Calculus Linear Algebra And Differential Equations written by Stanley I. Grossman and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Multivariable Calculus, Linear Algebra, and Differential Equations, Second Edition contains a comprehensive coverage of the study of advanced calculus, linear algebra, and differential equations for sophomore college students. The text includes a large number of examples, exercises, cases, and applications for students to learn calculus well. Also included is the history and development of calculus. The book is divided into five parts. The first part includes multivariable calculus material. The second part is an introduction to linear algebra. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in "n" variables, the multivariable mean value theorem, and the implicit function theorem. The fourth section contains detailed discussions of first-order and linear second-order equations. Also included are optional discussions of electric circuits and vibratory motion. The final section discusses Taylor's theorem, sequences, and series. The book is intended for sophomore college students of advanced calculus.

Linear Algebra

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Author : Ted Shifrin
language : en
Publisher: Macmillan Higher Education
Release Date : 2010-07-30

Linear Algebra written by Ted Shifrin and has been published by Macmillan Higher Education this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-30 with Mathematics categories.

Linear Algebra: A Geometric Approach, Second Edition, presents the standard computational aspects of linear algebra and includes a variety of intriguing interesting applications that would be interesting to motivate science and engineering students, as well as help mathematics students make the transition to more abstract advanced courses. The text guides students on how to think about mathematical concepts and write rigorous mathematical arguments.

Concise Calculus

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Author : Sheng Gong
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-02-03

Concise Calculus written by Sheng Gong and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-03 with Mathematics categories.

Mathematics is the fundamental knowledge for every scientist. As an academic at the University of Science and Technology of China, Professor Sheng Gong takes his passion for mathematics teaching even further. Besides imparting knowledge to students from the Department of Mathematics, he has created and developed his method of teaching Calculus to help students from physics, engineering and other sciences disciplines understand Calculus faster and deeper in order to meet the needs of applications in their own fields.This book is based on Professor Sheng Gong's 42 years of teaching experience along with a touch of applications of Calculus in other fields such as computer science, engineering. Science students will benefit from the unique way of illustrating theorems in Calculus and also perceive Calculus as a whole instead of a combination of separate topics. The practical examples provided in the book bring motivation to students to learn Calculus.

Vector And Geometric Calculus

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Author : Alan Macdonald
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2012

Vector And Geometric Calculus written by Alan Macdonald and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. This is the printing of April 2025. The book is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one. Its web page is at faculty.luther.edu/ macdonal/laga. Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways. Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world. Differential geometry is used today in many disciplines. A final chapter is devoted to it. Download the book's table of contents, preface, and index at the book's web site: faculty.luther.edu/ macdonal/vagc. From a review of Linear and Geometric Algebra: Alan Macdonald's text is an excellent resource if you are just beginning the study of geometric algebra and would like to learn or review traditional linear algebra in the process. The clarity and evenness of the writing, as well as the originality of presentation that is evident throughout this text, suggest that the author has been successful as a mathematics teacher in the undergraduate classroom. This carefully crafted text is ideal for anyone learning geometric algebra in relative isolation, which I suspect will be the case for many readers. -- Jeffrey Dunham, William R. Kenan Jr. Professor of Natural Sciences, Middlebury College

An Illustrative Guide To Multivariable And Vector Calculus

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Author : Stanley J. Miklavcic
language : en
Publisher: Springer Nature
Release Date : 2020-02-17

An Illustrative Guide To Multivariable And Vector Calculus written by Stanley J. Miklavcic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-17 with Mathematics categories.

This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.