CLP-4 Vector Calculus (Feldman, Rechnitzer, and Yeager)

by Joel Feldman, Andrew Rechnitzer and Elyse Yeager

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This textbook covers Vector Calculus. There are chapters on curves, vector fields, surface integrals and integral theorems (such as the divergence theorem).

Description from LibreTexts.

Publisher
University of British Columbia
Subjects
Mathematics, Calculus
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Colophon
  6. Licensing
  7. Preface
  8. Feedback about the text
  9. 1: Curves
  10. 1.1: Derivatives, Velocity, Etc.
  11. 1.2: Reparametrization
  12. 1.3: Curvature
  13. 1.4: Curves in Three Dimensions
  14. 1.5: A Compendium of Curve Formula
  15. 1.6: Integrating Along a Curve
  16. 1.7: Sliding on a Curve
  17. 1.8: Optional — Polar Coordinates
  18. 1.9: Optional — Central Forces
  19. 1.10: Optional — Planetary Motion
  20. 1.11: Optional — The Astroid
  21. 1.12: Optional — Parametrizing Circles
  22. 2: Vector Fields
  23. 2.1: Definitions and First Examples
  24. 2.2: Optional — Field Lines
  25. 2.3: Conservative Vector Fields
  26. 2.4: Line Integrals
  27. 2.5: Optional — The Pendulum
  28. 3: Surface Integrals
  29. 3.1: Parametrized Surfaces
  30. 3.2: Tangent Planes
  31. 3.3: Surface Integrals
  32. 3.4: Interpretation of Flux Integrals
  33. 3.5: Orientation of Surfaces
  34. 4: Integral Theorems
  35. 4.1: Gradient, Divergence and Curl
  36. 4.2: The Divergence Theorem
  37. 4.3: Green's Theorem
  38. 4.4: Stokes' Theorem
  39. 4.5: Optional — Which Vector Fields Obey ∇ × F = 0
  40. 4.6: Really Optional — More Interpretation of Div and Curl
  41. 4.7: Optional — A Generalized Stokes' Theorem
  42. 5: True/False and Other Short Questions
  43. 5.2: Exercises
  44. Appendices
  45. A: Appendices
  46. A.1: Trigonometry
  47. A.2: Powers and Logarithms
  48. A.3: Table of Derivatives
  49. A.4: Table of Integrals
  50. A.5: Table of Taylor Expansions
  51. A.6: 3d Coordinate Systems
  52. A.7: ISO Coordinate System Notation
  53. A.8: Conic Sections and Quadric Surfaces
  54. A.9: Review of Linear Ordinary Differential Equations
  55. B: Hints for Exercises
  56. C: Answers to Exercises
  57. D: Solutions to Exercises
  58. Back Matter
  59. Index
  60. Glossary
  61. Detailed Licensing