Calculus in 3D Geometry Vectors and Multivariate Calculus 1st Edition by Zbigniew Nitecki ISBN 1470443600 9781470443603

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Product details:

ISBN 10: 1470443600

ISBN 13: 978-1470443603

Author:  Zbigniew Nitecki 

Calculus in 3D: Geometry, Vectors, and Multivariate Calculus 1st Edition: 

Calculus in 3D: Geometry, Vectors, and Multivariate Calculus 1st Edition Table of contents:

1. Coordinates and Vectors
1.1 Locating Points in Space
1.2 Vectors and Their Arithmetic
1.3 Lines in Space
1.4 Projection of Vectors; Dot Products
1.5 Planes
1.6 Cross Products
1.7 Applications of Cross Products

2. Curves and Vector-Valued Functions of One Variable
2.1 Conic Sections
2.2 Parametrized Curves
2.3 Calculus of Vector-Valued Functions
2.4 Regular Curves
2.5 Integration along Curves

3. Differential Calculus for Real-Valued Functions of Several Variables
3.1 Continuity and Limits
3.2 Linear and Affine Functions
3.3 Derivatives
3.4 Level Curves
3.5 Surfaces and Tangent Planes I: Graphs and Level Surfaces
3.6 Surfaces and Tangent Planes II: Parametrized Surfaces
3.7 Extrema
3.8 Higher Derivatives
3.9 Local Extrema

4. Integral Calculus for Real-Valued Functions of Several Variables
4.1 Integration over Rectangles
4.2 Integration over General Planar Regions
4.3 Changing Coordinates
4.4 Integration Over Surfaces
4.5 Integration in Three Variables

5. Integral Calculus for Vector Fields and Differential Forms
5.1 Line Integrals of Vector Fields and 1-Forms
5.2 The Fundamental Theorem for Line Integrals
5.3 Green’s Theorem
5.4 Green’s Theorem and 2-forms in R²
5.5 Oriented Surfaces and Flux Integrals
5.6 Stokes’ Theorem
5.7 2-forms in R³
5.8 The Divergence Theorem
5.9 3-forms and the Generalized Stokes Theorem (Optional)

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Zbigniew Nitecki,Calculus,3D,Geometry Vectors,Multivariate Calculus