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CLP-2 Integral Calculus

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CLP-2 Integral Calculus

This textbook covers single variable Integral Calculus.

CalculusMathematics
Author
Joel Feldman, Andrew Rechnitzer & Elyse Yeager
Publisher
University of British Columbia
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 59 sections
  1. 01: Integration
  2. 1.01: Definition of the Integral
  3. 1.02: Basic properties of the definite integral
  4. 1.03: The Fundamental Theorem of Calculus
  5. 1.04: Substitution
  6. 1.05: Area between curves
  7. 1.06: Volumes
  8. 1.07: Integration by parts
  9. 1.08: Trigonometric Integrals
  10. 1.09: Trigonometric Substitution
  11. 1.10: Partial Fractions
  12. 1.11: Numerical Integration
  13. 1.12: Improper Integrals
  14. 1.13: More Integration Examples
  15. 02: Applications of Integration
  16. 2.01: Work
  17. 2.02: Averages
  18. 2.03: Centre of Mass and Torque
  19. 2.04: Separable Differential Equations
  20. 03: Sequence and series
  21. 3.01: Sequences
  22. 3.02: Series
  23. 3.03: Convergence Tests
  24. 3.04: Absolute and Conditional Convergence
  25. 3.05: Power Series
  26. 3.06: Taylor Series
  27. 3.07: Optional Rational and irrational numbers
  28. 04: Appendices
  29. 4.01: A: High School Material
  30. 4.1.01: A.1: Similar Triangles
  31. 4.1.02: A.2: Pythagoras
  32. 4.1.03: A.3: Trigonometry — Definitions
  33. 4.1.04: A.4: Radians, Arcs and Sectors
  34. 4.1.05: A.5: Trigonometry — Graphs
  35. 4.1.06: A.6: Trigonometry — Special Triangles
  36. 4.1.07: A.7: Trigonometry — Simple Identities
  37. 4.1.08: A.8: Trigonometry — Add and Subtract Angles
  38. 4.1.09: A.9: Inverse Trigonometric Functions
  39. 4.1.10: A.10: Areas
  40. 4.1.11: A.11: Volumes
  41. 4.1.12: A.12: Powers
  42. 4.1.13: A.13: Logarithms
  43. 4.1.14: A.14: Highschool Material You Should be Able to Derive
  44. 4.1.15: A.15: Cartesian Coordinates
  45. 4.1.16: A.16: Roots of Polynomials
  46. 4.02: B: Complex Numbers and Exponentials
  47. 4.2.01: B.1: Definition and Basic Operations
  48. 4.2.02: B.2: The Complex Exponential
  49. 4.03: C: More About Numerical Integration
  50. 4.3.01: C.1: Richardson Extrapolation
  51. 4.3.02: C.2: Romberg Integration
  52. 4.3.03: C.3: Adaptive Quadrature
  53. 4.04: D: Numerical Solution of ODE's
  54. 4.4.01: D.1: Simple ODE Solvers — Derivation
  55. 4.4.02: D.2: Simple ODE Solvers — Error Behaviour
  56. 4.4.03: D.3: Variable Step Size Methods
  57. 4.05: E: Hints for Exercises
  58. 4.06: F: Answers to Exercises
  59. 4.07: G: Solutions to Exercises