CLP-3 Multivariable Calculus

by Joel Feldman, Andrew Rechnitzer, & Elyse Yeager

Read here Read at LibreTextsPDF

This textbook covers multivariable Calculus. There are chapters on vectors and geometry in 2 and 3 dimensions, partial derivatives, and multivariable integrals.

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. Licensing
  6. Colophon
  7. Feedback about the text
  8. Preface
  9. 1: Vectors and Geometry in Two and Three Dimensions
  10. 1.1: Points
  11. 1.2: Vectors
  12. 1.3: Equations of Lines in 2d
  13. 1.4: Equations of Planes in 3d
  14. 1.5: Equations of Lines in 3d
  15. 1.6: Curves and their Tangent Vectors
  16. 1.7: Sketching Surfaces in 3d
  17. 1.8: Cylinders
  18. 1.9: Quadric Surfaces
  19. 2: Partial Derivatives
  20. 2.1: Limits
  21. 2.2: Partial Derivatives
  22. 2.3: Higher Order Derivatives
  23. 2.4: The Chain Rule
  24. 2.5: Tangent Planes and Normal Lines
  25. 2.6: Linear Approximations and Error
  26. 2.7: Directional Derivatives and the Gradient
  27. 2.8: Optional — Solving the Wave Equation
  28. 2.9: Maximum and Minimum Values
  29. 2.10: Lagrange Multipliers
  30. 3: Multiple Integrals
  31. 3.1: Double Integrals
  32. 3.2: Double Integrals in Polar Coordinates
  33. 3.3: Applications of Double Integrals
  34. 3.4: Surface Area
  35. 3.5: Triple Integrals
  36. 3.6: Triple Integrals in Cylindrical Coordinates
  37. 3.7: Triple Integrals in Spherical Coordinates
  38. 3.8: Optional— Integrals in General Coordinates
  39. 4: Appendices
  40. A: Appendices
  41. A.1: Trigonometry
  42. A.2: Powers and Logarithms
  43. A.3: Table of Derivatives
  44. A.4: Table of Integrals
  45. A.5: Table of Taylor Expansions
  46. A.6: 3-D Coordinate Systems
  47. A.7: ISO Coordinate System Notation
  48. A.8: Conic Sections and Quadric Surfaces
  49. B: Hints for Exercises
  50. C: Answers to Exercises
  51. D: Solutions to Exercises
  52. Back Matter
  53. Index
  54. Detailed Licensing