Best book for vector calculus pdf. Prelude This is an ongoing notes project to capture the essence of the subject of vector calculus by providing a variety of examples and visualizations, but also to present the main ideas of vector calculus in conceptual a framework that is adequate for the needs of mathematics, physics, and Download GATE Maths Notes Calculus 2021. Item Weight ‏ : ‎ 2. Dynamics, Statics and Hydrostatics – M. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals. Differential Calculus – Shanti Narayan, PK Mittal. It treatment uses history and the motivation of physical problems to give intuition. In previous articles, we have already seen the basics of Calculus – Differentiation and Integration and all the applications of these. the differentiation and integration both of vectors describing particular bodies, such as the velocity of a particle, and of vector fields, in which a vector is defined as a function of the coordinates throughout some volume (one-, two- or three-dimensional). Each chapter is provided with a excellent examples and problems at the end Authors: Stanley J. ISBN-13 ‏ : ‎ 978-1429215084. CALCULUS CLASS NOTES. , teach-by-examples• Offers extensive opportunities to students for practice and self-evaluation through numerous step-by-step Unfortunately, Calculus courses are taught out of order. a cube. Content Accuracy rating: 5 1. martin’s street, london 1914 For a closed surface S with outer unit normal vector n and surface element d2¾ in 3-D which is the boundary of a volumeV, given any differentiable vector field w on an open set containing S and V, the follow identity (known as Gauss’ theorem or the divergence theorem) holds: Z S Z (w ¢n)d2¾ = Z Z V Z (r¢w)dxdydz: . Differential equations:- Golden series – NP Bali. math. The sum or resultant of A and B, is a vector C formed by placing theinitial pointofB onthe terminalpointofAand then joiningthe initial pointofAto the terminal May 20, 2023 · One of the best Calculus 1 books for self-study are Richard Courant’s Differential and Integral Calculus, Calculus For Dummies by Mark Ryan, and Calculus, Eighth Edition by Howard Anton and Irl C. VECTOR FIELDS301 38. A vector field such as v(x,t) assigns a vector to every point in space. lamar Feb 10, 2020 · Multiple integrals-integration in ℝ. 6 Basis vectors 20 1. The prerequisite is a proof-based course in one-variable calculus. 3. •. 2. This book includes all math that you might possibly need throughout undergraduate and graduate physics/engineering studies. 5 Partial derivatives 35 2. We will have the addition and subtraction of these two vectors to be: Example 3. The 20 best advanced calculus books, such as Calculus, Advanced Calculus and ADVANCED CALCULUS. and. Usually, calculus is used in the development of a mathematical model for getting an optimal solution. turn. Second Year Calculus: From Celestial Mechanics to Special Relativity by Bressoud. (Multiple) Integration. Hardcover ‏ : ‎ 576 pages. To tote the Griffis flag, his EM book handles the introduction to vector Jan 15, 2015 · 2. Boas (July 22, 2005) published by Wiley. Vector Analysis – Shanti Narayan, PK Mittal. 1: Vector Fields. For a line defined by two points a1and a2. (2) Paul's Online notes ( https://tutorial. The object is. For example, f(x) = 3x Basically, vector calculus is the study of applying basic calculus concepts (such as derivatives and integrals) to vectors. Miklavcic. Jan 29, 2016 · 1. a. We therefore present our discussion as a generalization of 2. (6. 6. Ray. It does not require any prerequisites, although, it would be useful to have some knowledge, say of Pre-calculus, and High School Algebra. 2 Surface Integrals 469 7. In this situation, f is called a potential function for F. Includes supplementary material: sn. Key topics include: -vectors and vector fields; -line integrals; -regular k-surfaces; -flux of a vector field; -orientation of a surface; -differential forms; vector calculus - Free ebook download as PDF File (. Jan 10, 2019 · Vector Calculus – GATE Study Material in PDF. Jan 1, 2015 · Fifth edition of a combined vector calculus, linear algebra, and differential forms textbook, including new material such as "an example showing how Google uses the Perron-Frobenius theorem to rank web pages, and an example showing how the singular value decomposition can be used for computer face recognition. Note that different books Nov 22, 2021 · You can check the last chapter of Tristan Needham's Visual Differential Geometry for an easy intuitive explanation of tensors. by f. A scalar field such as s(x,t) assigns a scalar value to every point in space. The difficult, modern concepts are taught first (limits, developed 1800s) and the intuitive foundations are saved for the end (integrals, imagined 250 B. 6 Vectors as derivatives 41 May 28, 2023 · 2206. May 20, 2024 · Download Math’s book pdf of Vector Algebra by Shanti Narayan and PK Mittal best book for b. ). Calculus I and II). That is differential calculus, going from Function . 1/to . 2 Cross product 27 2. 884 kB RES. THE EXTERIOR DIFFERENTIAL OPERATOR313 Calculus. The best one that I know about is Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard & Hubbard; the use of differential forms is key, because it generalizes to higher dimensions, while curl doesn't. It uses differential forms and pullback, but only in low dimensions and very gently. Obviously, · 1 , · 0. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. 1 The equation of a line The equation of the line passing through the point whose position vector is a and lying in the direction of vector b is r = a +λb where λ is a scalar parameter. The zero vector is just a point, and it is denoted by 0. Study calculus online free by downloading volume 1 of OpenStax's college Calculus textbook and using our accompanying online resources. It In this chapter and the next we discuss the calculus of vectors, i. 560. 31 inches. ISBN-10: 0471198269 ISBN-13: 978-0471198260. These top­ ics include fluid dynamics Jun 5, 2011 · I usually think of multivariable calculus as being divided into four parts: (Partial) Differentiation. BSc Books for Free in PDF. Dimensions ‏ : ‎ 8. Important concepts of calculus of real-valued functions of one variable - limit, continuity, derivative, differentiability, and integral are (and it costs less than 10£). Consider the endpoints a; b of the interval [a b] from a to b as the boundary of that interval. Includes over one hundred carefully drawn figures that illustrate the material with clarity and ingenuity. pub/extras. Aug 4, 2010 · Summary. 3 If vectors A = 2i +4k and B = 5j +6k, determine: (a) what planes do these two vectors exist, and (b) their respective magnitudes. Exercises 302 38. It is the second semester in the freshman calculus sequence. The lecture notes [2], the book [3] and the “Vector Calculus Primer” [6] are available online; on the web page [4] of O. Don’t let the title fool you, this book is a math book. Vector calculus also equivalently goes by the name of multivariable calculus, as these are pretty much the same area of mathematics. DEFINITION Let R be a region in the xy plane. Vector calculus Bookreader Item Preview Pdf_module_version 0. This PDF covers the following topics related to Vector Calculus : Fields and vector differential operators, Review of vectors in 3-dimensional Euclidean space, Scalar fields, vector fields and curves, Vector differential operators, Special vector fields and potentials, Total derivatives of a curve, Chain rule for fields and curves, Vector integration, Green’s 2. Jan 13, 2022 at 12:48. Calculus plays an important role in several fields like engineering, science, and navigation. Great book. Due to the comprehensive nature of the material, we are offering the book in three volumes But the best might be Bressoud's Second Year Calculus: From Celestial Mechanics to Special Relativity. The dot (inner, scalar) product · of two vectors and is the number (scalar) defined as. 5 Non-Cartesian unit vectors 14 1. An example of a vector field would be the velocity of the air. 15 Vector Calculus In three dimensions the input point is (x, y, z) and the output vector F has three components. Background307 39. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. 4 Vector addition and multiplication by a scalar 11 1. It's thorough. parentheses. The applications are used to relate the topics to real-world problems. This book gives a comprehensive and thorough introduction to ideas and results in the theory of functions of several variables and modern vector calculus in two and three dimensions. Supplemental Modules (Calculus) Vector Calculus. Before learning vector calculus, you should have a solid understanding of single-variable This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. Linear vector space is to quantum mechanics what calculus is to classical mechanics. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals This book covers calculusin two and three variables. Presenting topics in calculus via examples and applications is perhaps the best feature of this book. Let’s assume that the object with mass M is located at the origin in R Oct 9, 2012 · calculus made easy: being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the differential calculus and the integral calculus. This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. Beside the resources offered by our fellow students, I think there are rigorous resources that worth looking into: (1) Tom Apostol Calculus Vol. 1) f (b) f a = Z b a d f dx x dx; INTRODUCTION. 2 Here, ur = r is the only nonzero component of 푢, and we have. sc engineering and upsc etc exams complete book pdf is given below. This book covers calculusin two and three variables. x/;calculus can find the speed ( velocity) and the slope and the derivative. 1/ There are many good books on vector calculus that will get you up to speed on the basic ideas, illustrated with an abundance of examples. Due to the comprehensive nature of the material, we are offering the book in three volumes May 20, 2024 · Download Math’s book pdf of Vector Algebra by Shanti Narayan and PK Mittal best book for b. Jan 12, 2023 · About the Book. Curves and Surfaces in R3 R 3. The vector is denoted by −−→ PQ. Schoolcraft College. In this chapter the essential ideas of linear vector spaces will be discussed. Students who take this course are expected to already know single-variable differential and integral calculus to the level of an introductory college calculus course. r2 ∂r r r sin θ ∂θ θ r sin θ ∂φ. It was submitted to the Free Digital Textbook Initiative in California and will remain unchanged for at least two years. The latest versions may be found by CONSERVATIVE VECTOR FIELD A vector field F is called a conservative vector field if it is the gradient of some scalar function—that is, if there exists a function f such that F = . The first unit deals Vector Calculus Andrea Moiola. Exercises 309 39. It is divided into three units. Our resource for Vector Calculus includes answers to May 28, 2023 · 16. 3 Stokes’s and Gauss’s Theorems 490 7. Best Sellers Rank: #353,482 in Books ( See Top 100 in Books) #13 in Vector Analysis Mathematics. Its main objective of study is the derivative. 37 x 1 x 10. 1. It's got all the math, plus physics and history. 11/14/19 Multivariate Calculus:Vector CalculusHavens 0. I want to learn multivariable calculus and I need a book suitable for self-study. Study calculus online free by downloading Volume 2 of OpenStax's college Calculus textbook and using our accompanying online resources. between vectors. This pdf contains important questions related to vector calculus important for various examination. In multivariable calculus (also known as multivariate calculus) we study functions of two or more independent variables, For example, f(x, y) = yx or f(x, y, z) = xyz + yz while single variable calculus you study functions of a single independent variable. There's also Spivak's enormous 5 volume A Comprehensive Introduction to Differential Geometry (don't actually buy this to study at your level). Analytic Geometry – Shanti Narayan, DK Jha, HC Sinha and Sharma. 630 15 Vector Calculus 15. 1-2(a). They are also useful for dealing with large-scale behavior such as atmospheric storms or deep-sea ocean currents. However, I most strongly recommend Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach by John Hubbard and Barbara Hubbard. – Babu. BA in Mathematics, University of California. At Quizlet, we’re giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Vector Calculus 6th Edition, you’ll learn how to solve your toughest homework problems. Some familiarity with the complex number system and complex mappings is occa-sionally assumed as well, but the reader can get by without it. Since a vector has no position, we typically indicate a vector field in graphical form by placing the vector f(x, y) with its tail at (x, y). A two-dimensional vector field is a function f that maps each point (x, y) in R2 to a two-dimensional vector hu, vi, and similarly a three-dimensional vector field maps (x, y, z) to hu, v, wi. Given: The two vectors: Vector A1= x 1i + y 1j +z 1k and Vector A = x 2i +y. I have tried to be somewhat rigorous about proving VECTOR CALCULUS Introduction: In this chapter, we shall discuss the vector functions, limits and continuity, differentiation and integration of a vector function. 2 Vector Algebra There are two basic operations with vectors: (a) Vector Addition; (b) Scalar Multiplication. Salient features of the book are summarised below:• Exactly in-sync with the latest GTU syllabus of Linear Algebra and Vector Calculus (2110015)• Lucid writing style and tutorial approach throughout the book, i. Arihant Skills in Mathematics Latest Books pdf download. The study guide for chapter 1 and Index were missing in the PDF version I reviewed. Nov 24, 2022 · This book is an advanced original text on Vector Calculus aiming university students and researchers from engineering and basic sciences who are interested in the analytical aspects of classical Discovery Publishing House, 2010 - Vector analysis - 306 pages Contents: Differentiation and Integration of Vectors, Multiple Vectors, Gradient, Divergence and Curl, Green s Gauss s and Stoke s Theorem. It is suitablefor a one-semester course, normally known as “Vector Calculus”, “Multivariable Calculus”, or simply “Calculus III”. Gilbert Strang’s Calculus textbook is also ideal as a course companion and for self-study. a rhomboid. Vector fields and vector calculus. - free book at FreeComputerBooks. “A Text Book of Vector Analysis” Book Review: This book covers the basics of vectors, including multiplication of vectors by scalars, addition of vectors, vector product, and scalar triple product. Studying the change of the function of a variable May 26, 2023 · The author uses simple terms and easy to follow approach/format. Download Free PDF. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space The term "vector calculus" is sometimes used as a synonym for …. Vector Calculus In this chapter we develop the fundamental theorem of the Calculus in two and three dimensions. Buy Now. Problems 310 39. 18-001 Calculus (f17), Chapter 15: Vector Calculus Chapter 15: Vector Calculus Download File DOWNLOAD. 1 Vector Fields For an ordinary scalar function, the input is a number xand the output is a number f. If you make b a unit vector, r = a+λˆb then λ will represent metric length. Bivens. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. Bressoud focuses on the major motivating problems from physics that necessitated the development of vector calculus. 4 Further Vector Analysis; Maxwell’s Equations 510 True/False Exercises for Chapter Vector calculus is the fundamental language of mathematical physics. Both versions cover the same material, although they are taught by different Jan 20, 2023 · Books. I have tried to be somewhat rigorous about proving The 20 best vector analysis books, such as Vector Analysis, Math Beyond Numbers and Vector And Tensor Analysis. of the unit along . This begins with a slight reinterpretation of that theorem. IMPORTANT FUNCTIONS Let me repeat the right name for the step from . Knill you can find plenty of exercises, lecture notes and graphs. Jul 24, 2008 · A rigorous and comprehensive introductory treatment, it features clear, readable proofs that illustrate the classical theorems of vector calculus, including the inverse and implicit function theorems. x;y/and the output is a two-dimensional vectorF. Thumbnail: Surface with closed boundary . Gilbert Strang A tiny book, with a fair amount of deserved infamy. Guichard and others. These are the lecture notes for my online Coursera course,Vector Calculus for Engineers. You can find other useful books on shelf 515. OpenStax Jul 4, 2021 · Mathew's Vector Calculus is a thin book that covers the basics quite well, and includes some material on suffix notation many texts omit. Answers to Odd-Numbered Exercises311 Chapter 40. 7 Chapter 1 problems 23 2 Vector operations 25 2. 2. 63 (and those nearby) in the University library. THE CALCULUS OF DIFFERENTIAL FORMS 305 Chapter 39. Click To Buy. Marsden and Tromba's Vector Calculus is a standard text, with a reputation of being more difficult. Accessible to anyone with a good background in single-variable calculus, it presents more linear algebra than usually found in a multivariable calculus book. 2 k. a cylinder. 3 Vector components 7 1. May 27, 2015 · It is a bit advanced, but not impossible. #282 in Calculus (Books) We can define differential calculus as a branch of mathematics thanks to which it is possible to solve problems related to the change of variables that can be modeled in a numerical continuum to find the variation of these elements in a given time. Chapter 38. MIT OpenCourseWare offers another version of 18. 25k Accesses. A vector has both magnitude and direction whereas a scalar has only magnitude. Answers to Odd-Numbered Exercises304 Part 10. 4. 3 days ago · Vector Calculus Formulas. Book Name. Offers an in-depth visual approach to multivariable and vector calculus. In order to download these books, you have to click on the Download Button at the end of each section & follow the next steps. com Apr 1, 2020 · 6. "Calculus" by James Stewart. The book is in use at Whitman College and is occasionally updated to correct errors and add new material. , limited st. ISBN-10 ‏ : ‎ 1429215089. The reader is already familiar with vector calculus in three-dimensional Euclidean space E3 (Chapter 1). For texts on a subject better described as multivariable analysis, I • Top 25 Best Solved Calculus • Top 50 Best Advance Calculus. Prerequisites include a knowledge of elementary linear algebra and one-variable calculus. Exercise 38. In these GATE 201 9 Study Notes, you will be introduced to Vector Calculus. The rest of the book is for Geometric intuition building. r. In this book you can also find a great collection of exercises: Easy, Intermediate, Hard and Very Hard ones. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. pdf. It covers many fields including Scalar products, metric geometry, vector products Nov 24, 2022 · This book is an advanced original text on Vector Calculus aiming university students and researchers from engineering and basic sciences who are interested in the analytical aspects of classical Discovery Publishing House, 2010 - Vector analysis - 306 pages Contents: Differentiation and Integration of Vectors, Multiple Vectors, Gradient, Divergence and Curl, Green s Gauss s and Stoke s Theorem. To learn about multiple derivatives of vector-valued functions of vector variables, you might Harvard Mathematics Department : Home page Get "Mathematical Methods in the Physical Sciences" by Mary L. It covers many fields including Scalar products, metric geometry, vector products To compute the left-hand-side of the divergence theorem, we recall the formula for the divergence of a vector field 푢 in spherical coordinates: 1 ∂ 1 ∂ 1 ∂uφ ∇ · 푢 = (r2u ) + (sin θu ) + . 20 Ppi 360 Rcs_key 24143 Republisher_date Aug 21, 2016 · Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. 4 Triple vector product 32 2. Complements existing textbooks on the subject by being concise and portable. Background301 38. First published in 1991 by Wellesley-Cambridge Press, this updated 3rd edition of the book is a useful resource for educators and self-learners alike. This is the free digital calculus text by David R. Answer (Detailed Solution Below) Option 2 : a cylinder. 2 2J + z. To indicate the direction of a vector, we draw an arrow from its initial point to its 1. 02, from the Spring 2006 term. It's probably what you're looking for. This book tries to show that vector analysis and vector calculus are not always at odds with one another. The size (also called dimension or length) of the vector is the number of elements it contains. 3) ·. A vectorfield F assigns to every point (x, y) in R a vector F(x, y) with two components: F(x, y) = M(x, y)i + N(x, y)j. DIFFERENTIAL FORMS307 39. And if you manage this book, you'll be really proud of UPSC Maths Optional Books Paper I & Paper II. pdf) or read book online for free. Differential Calculus. An illustration of two cells of a film strip. This course covers vector and multi-variable calculus. Download Now. Join Our TELEGRAM Channel For Exclusive & FREE IIT JEE & NEET Study Materials. 20 Ppi 360 Rcs_key 24143 Republisher_date Nov 17, 2020 · Calculus. lewisje. Michael Corral. " Several practical methods and many solved exercises are provided. Students should also be familiar with matrices, and be able to compute a three-by-three Textbook. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. The focus is on things like partial derivatives, div, grad, curl, and multiple integrals. 1 Scalar product 25 2. k. Mathematics Paper I. Let’s start with the books of Physics for Bachelor of Science. The prerequisites are the standard courses in single-variable calculus (a. Larson/Edwards: Multivariable Calculus. x/:For a vector field (or vector function), the input is a point . • H. second edition, enlarged macmillan and co. Vector Calculus (Green's Theorem, Stokes' Theorem, Divergence Theorem) For differentiation, you can use Principles of Mathematical Analysis by Rudin (Chapter 9). "A Text Book of Vector Analysis" by Narayan Shanti and Mittal P K. a truncated cone. “Calculus” Book Review: This book presents calculus in a technical manner with well-written chapters that cover topics like functions and limits, derivatives, integrals, inverse functions, polar coordinates, infinite sequence and series, vectors, partial derivatives, and vector calculus. M Schey, “Div, Grad, Curl, and all That” • Jerrold Marsden and Anthony Tromba, “Vector Calculus” Schey develops vector calculus hand in hand with electromagnetism, using Maxwell’s points. 2 is wonderfully written, beside learning calculus using proofs (with a lot of geometric intuition) you will also learn Linear Algebra. Nov 11, 2022 · Books. 2/:When we know the distance or the height or the function f. First published in 1954, this book is now presented as a new edition replacing the 1999 edition. In the below sections, we have shared subject-wise BSc books for free in pdf format. An intro to vector calculus from Michael Corral. and (0 ) is equal to the scalar projection vector along onto the unit vector. An example of a scalar field would be the temperature throughout a room. Jul 15, 2019 · Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. 3 Triple scalar product 30 2. In Mathematics, calculus refers to the branch which deals with the study of the rate of change of a given function. Click To Download. Vector Function: A vector function ⃗ from set D to set R [⃗: D is a rule or corresponding that assigns to each Element t in set D exactly one element y in set R. 1 Parametrized Surfaces 455 7. Unfortunately, the first book is described as targeted at engineering majors (by the author A vector is called the unit vector if 1 . 3 Conservative Vector Fields 439 True/False Exercises for Chapter 6 450 Miscellaneous Exercises for Chapter 6 451 7 Surface Integrals and Vector Analysis 455 7. with a force fields. 0. Vector Calculus, Michael Dec 16, 2011 · Language ‏ : ‎ English. Dec 1, 2004 · This lovely book is an excellent introductory text in vector calculus. e. It is suitable for students because it is written in informal but alluring and almost strict and severe manner, and because it covers all for them indispensable theory together with its applications. (c) the summation of these two vectors. (a) Vector Addition Consider vectors A and B, pictured in Fig. It also explains the geometry of vectors using Cartesian coordinates. This is what makes calculus different from arithmetic and algebra. Differential Vector Calculus. It could be used as a first exposure to these topics, and proofs are supplied. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus. In this notation style, the vector above is written as ( 1:1;0:0;3:6; 7:2): The elements (or entries, coe cients, components) of a vector are the values in the array. x;y/:There is a “field” of vectors, one at every point. This book takes Archimedes’ approach: learn to see what Calculus can do, then layer in the theory as needed. Course Info Instructor Prof. I also like the book Tensor Calculus by Pavel Grinfeld for teaching only the tensor algebra. Its magnitude is the length of the line segment, denoted by ° °−−→PQ°°, and its direction is the same as that of the directed line segment. This text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. An Introduction to Vectors, Vector Operators and Vector Analysis Conceived as s a supplementary text and reference book for undergraduate and graduate students of science and engineering, this book intends communicating the fundamental concepts of vectors and their applications. Colley's Vector Calculus is very good for a more-formal-than-normal treatment of multivariable calculus. Then the fundamental theorem, in this form: (18. It pro­ vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. 1 and Vol. It includes many worked-through exercises, with answers to many of the basic computational ones and hints to many of Mar 26, 2005 · Vector Calculus (3rd Edition) 3rd Edition. There is also an online Instructor’s Manual and a student Study Guide. Vector calculus assignment . cos. 49 pounds. The cosine of angle. (1) This plane vector field involves two functions of two variables. The vector above, for example, has size four; its third entry is 3:6. C. This carefully-designed book covers multivariable and vector calculus, and is appropriate either as a text of a one-semester course, or for self-study. We have given here the best quality and dynamic PDF to download. I looked around on Amazon and found two books that seem to contain the right material: Clark Bray: Multivariable Calculus. Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. The book’s aim is to use multivariable calculus to teach mathematics as 2 days ago · Vector Calculus Question 4: The cross-section along two mutually perpendicular axes of a solid object are a circle and a square, respectively. s. mt pr zh ku rq np rd wf ho tr