Vector and Geometric Calculus (Softcover)
Vector and Geometric Calculus (Softcover)
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From the back cover: This course "is a sequel to the textLinear and Geometric Algebra by the same author. That text is a prerequisite for this one."Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways.
"Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world.
"Differential geometry is used today in many disciplines. A final chapter is devoted to it."
BRIEF CONTENTS
- Preface
- To the Student
- I - Preliminaries
- 1 - Curve and Surface Representations
- 2 - Limits and Continuity
- II - Derivatives
- 3 - The Differential
- 4 - Tangent Spaces
- 5 - The Gradient
- 6 - Extremes
- III - Integrals
- 7 - Integrals over Curves
- 8 - Multiple Integrals
- 9 - Integrals over Surfaces
- IV - The Fundamental Theorem of Calculus
- 10 - The Fundamental Theorem of Calculus
- V - Differential Geometry
- 11 - Differential Geometry in R3
- VI - Appendices
- A - Review of Geometric Algebra
- B - Software
- C - Formulas
- D - Differential Forms
- Index
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PUBLISHER: CreateSpace Independent Publishing Platform
ISBN-13: 9781480132450
ISBN-10: 1480132454