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MAT 003A: Calculus I

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MAT 003A: Calculus I

Mathematics
Author
Benjamin Fineman
Publisher
Mission College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 87 sections
  1. 01: Functions and Graphs
  2. 1.01: Prelude to Functions and Graphs
  3. 1.02: Review of Functions
  4. 1.2E: Exercises for Section 1.2
  5. 1.03: Basic Classes of Functions
  6. 1.3E: Exercises for Section 1.3
  7. 1.04: Trigonometric Functions
  8. 1.4E: Exercises for Section 1.4
  9. 1.05: Inverse Functions
  10. 1.5E: Exercises for Section 1.5
  11. 1.06: Exponential and Logarithmic Functions
  12. 1.6E: Exercises for Section 1.6
  13. 1.07: Chapter 1 Review Exercises
  14. 02: Limits
  15. 2.01: Prelude to Limits
  16. 2.02: A Preview of Calculus
  17. 2.2E: Exercises for Section 2.1
  18. 2.03: The Limit of a Function
  19. 2.3E: Exercises for Section 2.2
  20. 2.04: The Limit Laws
  21. 2.4E: Exercises for Section 2.3
  22. 2.05: Continuity
  23. 2.5E: Exercises for Section 2.4
  24. 2.06: The Precise Definition of a Limit
  25. 2.6E: Exercises for Section 2.5
  26. 2.07: Chapter 2 Review Exercises
  27. 03: Derivatives
  28. 3.01: Prelude to Derivatives
  29. 3.02: Defining the Derivative
  30. 3.2E: Exercises for Section 3.1
  31. 3.03: The Derivative as a Function
  32. 3.3E: Exercises for Section 3.2
  33. 3.04: Differentiation Rules
  34. 3.4E: Exercises for Section 3.3
  35. 3.05: Derivatives as Rates of Change
  36. 3.5E: Exercises for Section 3.4
  37. 3.06: Derivatives of Trigonometric Functions
  38. 3.6E: Exercises for Section 3.5
  39. 3.07: The Chain Rule
  40. 3.7E: Exercises for Section 3.6
  41. 3.08: Derivatives of Inverse Functions
  42. 3.8E: Exercises for Section 3.7
  43. 3.09: Implicit Differentiation
  44. 3.9E: Exercises for Section 3.8
  45. 3.10: Derivatives of Exponential and Logarithmic Functions
  46. 3.10E: Exercises for Section 3.9
  47. 3.11: Chapter 3 Review Exercises
  48. 04: Applications of Derivatives
  49. 4.01: Prelude to Applications of Derivatives
  50. 4.02: Related Rates
  51. 4.2E: Exercises for Section 4.1
  52. 4.03: Linear Approximations and Differentials
  53. 4.3E: Exercises for Section 4.2
  54. 4.04: Maxima and Minima
  55. 4.4E: Exercises for Section 4.3
  56. 4.05: Rolles Theorem and The Mean Value Theorem
  57. 4.5E: Exercises for Section 4.4
  58. 4.06: Derivatives and the Shape of a Graph
  59. 4.6E: Exercises for Section 4.5
  60. 4.07: Limits at Infinity and Asymptotes
  61. 4.7E: Exercises for Section 4.6
  62. 4.08: Applied Optimization Problems
  63. 4.8E: Exercises for Section 4.7
  64. 4.09: LHopitals Rule
  65. 4.9E: Exercises for Section 4.8
  66. 4.10: Newtons Method
  67. 4.10E: Exercises for Section 4.9
  68. 4.11: Antiderivatives and Indefinite Integrals
  69. 4.11E: Exercises for Section 4.10
  70. 4.12: Chapter 4 Review Exercises
  71. 05: Integration
  72. 5.01: Approximating Areas
  73. 5.1E: Exercises for Section 5.1
  74. 5.02: The Definite Integral
  75. 5.2E: Exercises for Section 5.2
  76. 5.03: The Fundamental Theorem of Calculus
  77. 5.3E: Exercises for Section 5.3
  78. 5.04: Integration Formulas and the Net Change Theorem
  79. 5.4E: Exercises for Section 5.4
  80. 5.05: Substitution
  81. 5.5E: Exercises for Section 5.5
  82. 5.06: Integrals Involving Exponential and Logarithmic Functions
  83. 5.6E: Exercises for Section 5.6
  84. 5.07: Chapter 5 Review Exercises
  85. 06: Appendices
  86. 6.01: A- Table of Derivatives
  87. 6.02: B- Table of Integrals