CLP-1 Differential Calculus

by Joel Feldman, Andrew Rechnitzer & Elyse Yeager

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This textbook covers single variable Differential 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. Licensing
  6. Preface
  7. Dedication
  8. Acknowledgements
  9. Using the exercises in this book
  10. 0: The basics
  11. 0.1: Numbers
  12. 0.2: Sets
  13. 0.3: Other Important Sets
  14. 0.4: Functions
  15. 0.5: Parsing Formulas
  16. 0.6: Inverse Functions
  17. 1: Limits
  18. 1.1: Drawing Tangents and a First Limit
  19. 1.2: Another Limit and Computing Velocity
  20. 1.3: The Limit of a Function
  21. 1.4: Calculating Limits with Limit Laws
  22. 1.5: Limits at Infinity
  23. 1.6: Continuity
  24. 1.7: (Optional) — Making the Informal a Little More Formal
  25. 1.8: (Optional) — Making Infinite Limits a Little More Formal
  26. 1.9: (Optional) — Proving the Arithmetic of Limits
  27. 2: Derivatives
  28. 2.1: Revisiting Tangent Lines
  29. 2.2: Definition of the Derivative
  30. 2.3: Interpretations of the Derivative
  31. 2.4: Arithmetic of Derivatives - a Differentiation Toolbox
  32. 2.5: Proofs of the Arithmetic of Derivatives
  33. 2.6: Using the Arithmetic of Derivatives – Examples
  34. 2.7: Derivatives of Exponential Functions
  35. 2.8: Derivatives of Trigonometric Functions
  36. 2.9: One More Tool – the Chain Rule
  37. 2.10: The Natural Logarithm
  38. 2.11: Implicit Differentiation
  39. 2.12: Inverse Trigonometric Functions
  40. 2.13: The Mean Value Theorem
  41. 2.14: Higher Order Derivatives
  42. 2.15: (Optional) — Is \(\lim_{x\to c}f'(x)\) Equal to \(f'(c)\text{?}\)
  43. 3: Applications of derivatives
  44. 3.1: Velocity and Acceleration
  45. 3.2: Related Rates
  46. 3.3: Exponential Growth and Decay — a First Look at Differential Equations
  47. 3.4: Approximating Functions Near a Specified Point — Taylor Polynomials
  48. 3.5: Optimisation
  49. 3.6: Sketching Graphs
  50. 3.7: L'Hôpital's Rule and Indeterminate Forms
  51. 4: Towards Integral Calculus
  52. 4.1: Introduction to Antiderivatives
  53. Appendix
  54. A - High School Material
  55. A.1 Similar Triangles
  56. A.2 Pythagoras
  57. A.3 Trigonometry — Definitions
  58. A.4 Radians, Arcs and Sectors
  59. A.5 Trigonometry — Graphs
  60. A.6 Trigonometry — Special Triangles
  61. A.7 Trigonometry — Simple Identities
  62. A.8 Trigonometry — Add and Subtract Angles
  63. A.9 Inverse Trigonometric Functions
  64. A.10 Areas
  65. A.11 Volumes
  66. A.12 Powers
  67. A.13 Logarithms
  68. A.14 Highschool Material You Should be Able to Derive
  69. B - Origin of Trig, Area and Volume Formulas
  70. B.1 Theorems about Triangles
  71. B.2 Trigonometry
  72. B.3 Inverse Trigonometric Functions
  73. B.4 Cosine and Sine Laws
  74. B.5 Circles, cones and spheres
  75. C - Root Finding
  76. C.1 Newton's Method
  77. C.2 The Error Behaviour of Newton's Method
  78. C.3 The false position (regula falsi) method
  79. C.4 The secant method
  80. C.5 The Error Behaviour of the Secant Method
  81. D - Hints for Exercises
  82. E - Answers to Exercises
  83. F - Solutions to Exercises
  84. Back Matter
  85. Index
  86. Detailed Licensing