Exterior Calculus: Theory and Cases

Cover
Title
Copyright
End User License Agreement
Contents
Foreword
Preface
Acknowledgements
Dedication
List of Credits
List of Symbols
Part I. Heaviside-Gibbs Algebra
	Chapter 1. Vector Algebra on ℝ² and ℝ³
		1.1. Normed Vector Space: ????(????)
		1.2. Basic operators
		1.3. Vector-Valued Functions
		1.4. Vector Theorems
		1.5. Remarks
		1.6. Exercises
Part II. Grassmann Algebra
	Chapter 2. Geometric Algebra on ????₂
		2.1. Geometric Algebra on ????₂
		2.2. Properties on ????₂
		2.3. Reflections and Rotations on a Plane
		2.4. Geometric Representation of a Line on ℝ²
		2.5. Geometric Representation of a Plane on ℝ²
		2.6. Remarks
		2.7. Exercises
	Chapter 3. Geometric Algebra on ????₃
		3.1. Geometric Algebra on ????₃
		3.2. Properties on ????₃
		3.3. Reflections and Rotations in Space
		3.4. Geometric Representation of a Line on ℝ³
		3.5. Geometric Representation of a Plane on ℝ³
		3.6. Remarks
		3.7. Exercises
	Chapter 4. Geometric Algebra on ????ₙ
		4.1. Preliminaries
		4.2. Geometric Algebra on ????ₙ
		4.3. Properties on ????ₙ
		4.4. Reflections and Rotations on ????ₙ
		4.5. Analytical Representation of a Line in Rⁿ
		4.6. Analytical Representation of a Plane in Rⁿ
		4.7. Remarks
		4.8. Exercises
	Chapter 5. Differentiation
		5.1. Differential of a Function
		5.2. Differential Forms
		5.3. Differentiation of Forms
		5.4. Remarks
		5.5. Exercises
	Chapter 6. Integration
		6.1. Preliminaries
		6.2. Integration of 0−Forms
		6.3. Integration of 1−Forms
		6.4. Integration of 2−Forms
		6.5. Integration of 3−Forms
		6.6. Integration of k−Forms
		6.7. Remarks
		6.8. Exercises
	Chapter 7. Fundamental Theorem of Calculus
	7.1. Preliminaries
	7.2. Green Theorem
	7.3. Stokes’ Theorem
	7.4. Gauss’ Theorem
	7.5. Fundamental Theorem of Calculus
	7.6. Remarks
	7.7. Exercises
Part III. Applications
	Chapter 8. Applications
		8.1. Mathematical Epidemiology
		8.2. Structural Proteomics
		8.3. Ampere’s Law
		8.4. Remarks
Chapter 9. Solutions
	Solution 1.1.
	Solution 1.5.
	Solution 2.1.
	Solution 2.17.
	Solution 3.1.
	Solution 3.17.
	Solution 4.1.
	Solution 4.13.
	Solution 5.1.
	Solution 5.8.
	Solution 5.10.
	Solution 6.1.
	Solution 6.11.
	Solution 7.1.
	Solution 7.5.
	Solution 7.6.
	Solution 7.8.
	Solution 7.9.
	Solution 7.10.
References
[20]
Subject Index
G-Z