Multivariable and Vector Calculus : An Introduction

• Autore: Musa Sarhan M
• Pubblicazione: Edinburgh : , : Mercury Learning & Information, , 2023; ©2023
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (455 pages)
• Soggetto non controllato: Calculus; Vector Analysis; Mathematics
• Nota di contenuto: 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.
• Sommario/riassunto: 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
• Titolo autorizzato: Multivariable and Vector Calculus
• ISBN: 9781683929185; 9781683929192
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910838379003321
• Lo trovi qui: Univ. Federico II