An Illustrative Guide To Multivariable And Vector Calculus
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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.
Introduction To Modeling And Numerical Methods For Biomedical And Chemical Engineers
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Author : Edward Gatzke
language : en
Publisher: Springer Nature
Release Date : 2021-09-02
Introduction To Modeling And Numerical Methods For Biomedical And Chemical Engineers written by Edward Gatzke and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-02 with Technology & Engineering categories.
This textbook introduces the concepts and tools that biomedical and chemical engineering students need to know in order to translate engineering problems into a numerical representation using scientific fundamentals. Modeling concepts focus on problems that are directly related to biomedical and chemical engineering. A variety of computational tools are presented, including MATLAB, Excel, Mathcad, and COMSOL, and a brief introduction to each tool is accompanied by multiple computer lab experiences. The numerical methods covered are basic linear algebra and basic statistics, and traditional methods like Newton’s method, Euler Integration, and trapezoidal integration. The book presents the reader with numerous examples and worked problems, and practice problems are included at the end of each chapter.
A Mathematical Introduction To Data Science
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Author : Yi Sun
language : en
Publisher: Springer Nature
Release Date : 2025-07-09
A Mathematical Introduction To Data Science written by Yi Sun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-09 with Computers categories.
This textbook provides a comprehensive foundation in the mathematics needed for data science for students and self-learners with a basic mathematical background who are interested in the principles behind computational algorithms in data science. It covers sets, functions, linear algebra, and calculus, and delves deeply into probability and statistics, which are key areas for understanding the algorithms driving modern data science applications. Readers are guided toward unlocking the secrets of algorithms like Principal Component Analysis, Singular Value Decomposition, Linear Regression in two and more dimensions, Simple Neural Networks, Maximum Likelihood Estimation, Logistic Regression and Ridge Regression, illuminating the path from mathematical principles to algorithmic mastery. It is designed to make the material accessible and engaging, guiding readers through a step-by-step progression from basic mathematical concepts to complex data science algorithms. It stands out for its emphasis on worked examples and exercises that encourage active participation, making it particularly beneficial for those with limited mathematical backgrounds but a strong desire to learn. This approach facilitates a smoother transition into more advanced topics. The authors expect readers to be proficient in handling numbers in various formats, including fractions, decimals, percentages, and surds. They should also have a knowledge of introductory algebra, such as manipulating simple algebraic expressions, solving simple equations, and graphing elementary functions, along with a basic understanding of geometry including angles, trigonometry and Pythagoras’ theorem.
The Mathematica Guidebook For Numerics
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Author : Michael Trott
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-27
The Mathematica Guidebook For Numerics written by Michael Trott 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 2006-10-27 with Computers categories.
Provides the reader with working knowledge of Mathematica and key aspects of Mathematica's numerical capabilities needed to deal with virtually any "real life" problem Clear organization, complete topic coverage, and an accessible writing style for both novices and experts Website for book with additional materials: http://www.MathematicaGuideBooks.org Accompanying DVD containing all materials as an electronic book with complete, executable Mathematica 5.1 compatible code and programs, rendered color graphics, and animations
Multivariable Calculus
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Author : Don Shimamoto
language : en
Publisher:
Release Date : 2019-11-17
Multivariable Calculus written by Don Shimamoto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-17 with Calculus categories.
This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking, the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and, finally, the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise, the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required. Latest corrected printing: January 8, 2020. Updated information available online at the Open Textbook Library.
Understanding Vector Calculus
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Author : Jerrold Franklin
language : en
Publisher: Courier Dover Publications
Release Date : 2021-01-13
Understanding Vector Calculus written by Jerrold Franklin and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-13 with Mathematics categories.
This concise text is a workbook for using vector calculus in practical calculations and derivations. Part One briefly develops vector calculus from the beginning; Part Two consists of answered problems. 2020 edition.
Advanced Calculus Revised Edition
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Author : Lynn Harold Loomis
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-26
Advanced Calculus Revised Edition written by Lynn Harold Loomis 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 2014-02-26 with Mathematics categories.
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
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
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Author : Rolland Trapp
language : en
Publisher:
Release Date : 2019
Multivariable Calculus written by Rolland Trapp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.
Multivariable Calculus is an introductory textbook in the field of multivariable calculus, which utilises interactive 3D graphing software to develop students' understanding.
Calculus On Manifolds
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Author : Michael Spivak
language : en
Publisher: Westview Press
Release Date : 1965
Calculus On Manifolds written by Michael Spivak and has been published by Westview Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Science categories.
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.