CLP-2 Integral Calculus

by Joel Feldman, Andrew Rechnitzer & Elyse Yeager

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This textbook covers single variable Integral Calculus.

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. Dedication
  9. Acknowledgements
  10. Using the exercises in this book
  11. Feedback about the text
  12. 1: Integration
  13. 1.1: Definition of the Integral
  14. 1.2: Basic properties of the definite integral
  15. 1.3: The Fundamental Theorem of Calculus
  16. 1.4: Substitution
  17. 1.5: Area between curves
  18. 1.6: Volumes
  19. 1.7: Integration by parts
  20. 1.8: Trigonometric Integrals
  21. 1.9: Trigonometric Substitution
  22. 1.10: Partial Fractions
  23. 1.11: Numerical Integration
  24. 1.12: Improper Integrals
  25. 1.13: More Integration Examples
  26. 2: Applications of Integration
  27. 2.1: Work
  28. 2.2: Averages
  29. 2.3: Center of Mass and Torque
  30. 2.4: Separable Differential Equations
  31. 3: Sequence and series
  32. 3.1: Sequences
  33. 3.2: Series
  34. 3.3: Convergence Tests
  35. 3.4: Absolute and Conditional Convergence
  36. 3.5: Power Series
  37. 3.6: Taylor Series
  38. 3.7: Optional — Rational and irrational numbers
  39. Appendices
  40. A: High School Material
  41. A.1: Similar Triangles
  42. A.2: Pythagoras
  43. A.3: Trigonometry — Definitions
  44. A.4: Radians, Arcs and Sectors
  45. A.5: Trigonometry — Graphs
  46. A.6: Trigonometry — Special Triangles
  47. A.7: Trigonometry — Simple Identities
  48. A.8: Trigonometry — Add and Subtract Angles
  49. A.9: Inverse Trigonometric Functions
  50. A.10: Areas
  51. A.11: Volumes
  52. A.12: Powers
  53. A.13: Logarithms
  54. A.14: Highschool Material You Should be Able to Derive
  55. A.15: Cartesian Coordinates
  56. A.16: Roots of Polynomials
  57. B: Complex Numbers and Exponentials
  58. B.1: Definition and Basic Operations
  59. B.2: The Complex Exponential
  60. C: More About Numerical Integration
  61. C.1: Richardson Extrapolation
  62. C.2: Romberg Integration
  63. C.3: Adaptive Quadrature
  64. D: Numerical Solution of ODE's
  65. D.1: Simple ODE Solvers — Derivation
  66. D.2: Simple ODE Solvers — Error Behaviour
  67. D.3: Variable Step Size Methods
  68. E: Hints for Exercises
  69. F: Answers to Exercises
  70. G: Solutions to Exercises
  71. Back Matter
  72. Index
  73. Glossary
  74. Detailed Licensing