Multivariable and Vector Calculus : An Introduction / Sarhan M. Musa.

Format:

Book

Author/Creator:

Musa, Sarhan M., author.

Language:

English

Subjects (All):

Vector analysis.

Physical Description:

1 online resource (455 pages)

Edition:

Second edition.

Place of Publication:

Mercury Learning and Information 2023

Dulles, VA : Mercury Learning and Information, [2023]

Summary:

This book is designed primarily for undergraduates in mathematics, engineering, and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. Furthermore, it can be used to impower the mathematical knowledge for Artificial Intelligence (AI) concepts. It also provides numerous computer illustrations and tutorials using MATLAB®and Maple®, that bridge the gap between analysis and computation. Partial solutions and instructor ancillaries available for use as a textbook.FEATURESIncludes numerous computer illustrations and tutorials using MATLAB®and Maple®Covers the major topics of vector geometry, differentiation, and integration inseveral variablesInstructors' ancillaries available upon adoption

Contents:

Cover

Half-Title

Title

Copyright

Dedication

Contents

Preface

Acknowledgments

Chapter 1: Vectors and Parametric Curves

1.1 Points and Vectors on the Plane

Exercises 1.1

1.2 Scalar Product on the Plane

Exercises 1.2

1.3 Linear Independence

Exercises 1.3

1.4 Geometric Transformations in Two Dimensions

Exercises 1.4

1.5 Determinants in Two Dimensions

Exercises 1.5

1.6 Parametric Curves on the Plane

Exercises 1.6

1.7 Vectors in Space

Exercises 1.7

1.8 Cross Product

Exercises 1.8

1.9 Matrices in Three Dimensions

Exercises 1.9

1.10 Determinants in Three Dimensions

Exercises 1.10

1.11 Some Solid Geometry

Exercises 1.11

1.12 Cavalieri and the Pappus-Guldin Rules

Exercises 1.12

1.13 Dihedral Angles and Platonic Solids

Exercises 1.13

1.14 Spherical Trigonometry

Exercises 1.14

1.15 Canonical Surfaces

Exercises 1.15

1.16 Parametric Curves in Space

Exercises 1.16

1.17 Multidimensional Vectors

Exercises 1.17

Chapter 2: Differentiation

2.1 Some Topology

Exercises 2.1

2.2 Multivariable Functions

Exercises 2.2

2.3 Limits and Continuity

Exercises 2.3

2.4 Definition of the Derivative

Exercises 2.4

2.5 The Jacobi Matrix

Exercises 2.5

2.6 Gradients and Directional Derivatives

Exercises 2.6

2.7 Levi-Civitta and Einste

Exercises 2.7

2.8 Extrema

Exercises 2.8

2.9 Lagrange Multipliers

Exercises 2.9

Chapter 3: Integration

3.1 Differential Forms

Exercises 3.1

3.2 Zero-Manifolds

Exercises 3.2

3.3 One Manifold

Exercises 3.3

3.4 Closed and Exact Forms

Exercises 3.4

3.5 Two-Manifolds

Exercises 3.5

3.6 Change of Variables in Double Integrals

Exercises 3.6

3.7 Change to Polar Coordinates

Exercises 3.7

3.8 Three-Manifolds

Exercises 3.8.

3.9 Change of Variables in Triple Integrals

Exercises 3.9

3.10 Surface Integrals

Exercises 3.10

3.11 Green's, Stokes', and Gauss' Theorems

Exercises 3.11

Appendix A: Maple

A.1 Getting Started and Windows of Maple

A.2 Arithmetic

A.3 Symbolic Computation

A.4 Assignments

A.5 Working with Output

A.6 Solving Equations

A.7 Plots with Maple

A.8 Limits and Derivatives

A.9 Integration

A.10 Matrix

Appendix B: Matlab

B.1 Getting Started and Windows of MATLAB

B.1.1 Using MATLAB in Calculations

B.2 Plotting

B.2.1 Two-dimensional Plotting

B.2.2 Three-Dimensional Plotting

B.3 Programming in MATLAB

B.3.1 For Loops

B.3.2 While Loops

B.3.3 If, Else, and Elseif

3.3.4 Switch

B.4 Symbolic Computation

B.4.1 Simplifying Symbolic Expressions

B.4.2 Differentiating Symbolic Expressions

B.4.3 Integrating Symbolic Expressions

B.4.4 Limits Symbolic Expressions

B.4.5 Taylor Series Symbolic Expressions

B.4.6 Sums Symbolic Expressions

B.4.7 Solving Equations as Symbolic Expressions

Appendix C: Answers to Odd-Numbered Exercises

Chapter 1

Chapter 2

Chapter 3

Appendix D: Formulas

D.1 Trigonometric Identities

D.2 Hyperbolic Functions

D.3 Table of Derivatives

D.4 Table of Integrals

D.5 Summations (Series)

D.5.1 Finite Element of Terms

D.5.2 Infinite Element of Terms

D.6 Logarithmic Identities

D.7 Exponential Identities

D.8 Approximations for Small Quantities

D.9 Vectors

D.9.1 Vector Derivatives

D.9.2 Vector Identity

D.9.3 Fundamental Theorems

Bibliography

Index.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Other Format:

Print version: Musa, Sarhan M. Multivariable and Vector Calculus

ISBN:

9781683929185

1683929187

9781683929178

1683929179