
Multivariable and Vector Calculus
Description
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- Covers the major topics of vector geometry, differentiation, and integration in several variables
- Instructors' ancillaries available upon adoption
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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
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