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Multivariable and Vector Calculus : an Introduction.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Bloomfield :
Mercury Learning & Information,
2015.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Title Page; Copyright; Dedication; Contents; Preface; Acknowledgments; Chapter 1: Vectors and Parametric Curves; 1.1 Points and Vectors on the Plane; 1.2 Scalar Product on the Plane; 1.3 Linear Independence; 1.4 Geometric Transformations in Two Dimensions; 1.5 Determinants in Two Dimensions; 1.6 Parametric Curves on the Plane; 1.7 Vectors in Space; 1.8 Cross Product; 1.9 Matrices in Three Dimensions; 1.10 Determinants in Three Dimensions; 1.11 Some Solid Geometry; 1.12 Cavalieri and the Pappus-Guldin Rules; 1.13 Dihedral Angles and Platonic Solids; 1.14 Spherical Trigonometry.
- 1.15 Canonical Surfaces1.16 Parametric Curves in Space; 1.17 Multidimensional Vectors; Chapter 2: Differentiation; 2.1 Some Topology; 2.2 Multivariable Functions; 2.3 Limits and Continuity; 2.4 Definition of the Derivative; 2.5 The Jacobi Matrix; 2.6 Gradients and Directional Derivatives; 2.7 Levi-Civita and Einstein; 2.8 Extrema; 2.9 Lagrange Multipliers; Chapter 3: Integration; 3.1 Differential Forms; 3.2 Zero-Manifolds; 3.3 One-Manifolds; 3.4 Closed and Exact Forms; 3.5 Two-Manifolds; 3.6 Change of Variables in Double Integrals; 3.7 Change to Polar Coordinates; 3.8 Three-Manifolds.
- 3.9 Change of Variables in Triple Integrals3.10 Surface Integrals; 3.11 Green's, Stokes', and Gauss' Theorems; 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 ElseifB. 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; 1.1 Points and Vectors on the Plane; 1.2 Scalar Product on the Plane; 1.3 Linear Independence; 1.4 Geometric Transformations in Two Dimensions; 1.5 Determinants in Two Dimensions.
- 1.6 Parametric Curves on the Plane1.7 Vectors in Space; 1.8 Cross Product; 1.9 Matrices in Three Dimensions; 1.10 Determinants in Three Dimensions; 1.11 Some Solid Geometry; 1.12 Cavalieri and the Pappus-Guldin Rules; 1.13 Dihedral Angles and Platonic Solids; 1.14 Spherical Trigonometry; 1.15 Canonical Surfaces; 1.16 Parametric Curves in Space; 1.17 Multidimensional Vectors; Chapter 2; 2.1 Some Topology; 2.2 Multivariable Functions; 2.3 Limits and Continuity; 2.4 Definition of the Derivative; 2.5 The Jacobi Matrix; 2.6 Gradients and Directional Derivatives; 2.7 Levi-Civita and Einstein.