Multivariable and Vector Calculus
An Introduction
2nd Edition
Published on 21. August 2023
450 pages
978-1-68392-918-5 (ISBN)
Description
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. Features: - Includes numerous computer illustrations and tutorials using MATLAB®and Maple®
- Covers the major topics of vector geometry, differentiation, and integration in several variables
- Instructors' ancillaries available upon adoption
- Covers the major topics of vector geometry, differentiation, and integration in several variables
- Instructors' ancillaries available upon adoption
More details
Edition
2nd Revised edition
Language
English
Place of publication
Herndon, VA
United States
Target group
Professional and scholarly
US School Grade: College Graduate Student
Edition type
Revised edition
File size
37,39 MB
ISBN-13
978-1-68392-918-5 (9781683929185)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
02/2023
2nd Edition
Mercury Learning & Information
€89.95
Article not available at the moment
E-Book
02/2023
2nd Edition
Mercury Learning and Information
€119.99
Available for download
Previous edition
E-Book
08/2015
1st Edition
Mercury Learning and Information
€46.99
Available for download
Person
Musa Sarhan M. :
Sarhan M. Musa holds a PhD in electrical engineering and is currently a professor in the electrical and computer engineering department at Prairie View A&M University, Texas.
Sarhan M. Musa holds a PhD in electrical engineering and is currently a professor in the electrical and computer engineering department at Prairie View A&M University, Texas.
Content
- 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
