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Math 3A: Calculus 1

Nguồn ngoài

Math 3A: Calculus 1

This is the first part of the three-semester calculus sequence. Topics include functions, limits, continuity, differentiation and integration, and applications for polynomial and transcendental functions.

Mathematics
Tác giả
Max Sklar
Nhà xuất bản
Mission College
Nguồn
LibreTexts
Giấy phép
CC BY-NC-SA
Ngôn ngữ
EN
Danh mục
Khoa học cơ bản
Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 88 mục
  1. 01: Functions and Graphs
  2. 1.00: Prelude to Functions and Graphs
  3. 1.01: Review of Functions
  4. 1.1E: Exercises for Section 1.1
  5. 1.02: Basic Classes of Functions
  6. 1.2E: Exercises for Section 1.2
  7. 1.03: Trigonometric Functions
  8. 1.3E: Exercises for Section 1.3
  9. 1.04: Inverse Functions
  10. 1.4E: Exercises for Section 1.4
  11. 1.05: Exponential and Logarithmic Functions
  12. 1.5E: Exercises for Section 1.5
  13. 1.06: Chapter 1 Review Exercises
  14. 02: Limits
  15. 2.00: Prelude to Limits
  16. 2.01: A Preview of Calculus
  17. 2.1E: Exercises for Section 2.1
  18. 2.02: The Limit of a Function
  19. 2.2E: Exercises for Section 2.2
  20. 2.03: The Limit Laws
  21. 2.3E: Exercises for Section 2.3
  22. 2.04: Continuity
  23. 2.4E: Exercises for Section 2.4
  24. 2.05: The Precise Definition of a Limit
  25. 2.5E: Exercises for Section 2.5
  26. 2.06: Chapter 2 Review Exercises
  27. 03: Derivatives
  28. 3.00: Prelude to Derivatives
  29. 3.01: Defining the Derivative
  30. 3.1E: Exercises for Section 3.1
  31. 3.02: The Derivative as a Function
  32. 3.2E: Exercises for Section 3.2
  33. 3.03: Differentiation Rules
  34. 3.3E: Exercises for Section 3.3
  35. 3.04: Derivatives as Rates of Change
  36. 3.4E: Exercises for Section 3.4
  37. 3.05: Derivatives of Trigonometric Functions
  38. 3.5E: Exercises for Section 3.5
  39. 3.06: The Chain Rule
  40. 3.6E: Exercises for Section 3.6
  41. 3.07: Derivatives of Inverse Functions
  42. 3.7E: Exercises for Section 3.7
  43. 3.08: Implicit Differentiation
  44. 3.8E: Exercises for Section 3.8
  45. 3.09: Derivatives of Exponential and Logarithmic Functions
  46. 3.9E: Exercises for Section 3.9
  47. 3.10: Chapter 3 Review Exercises
  48. 04: Applications of Derivatives
  49. 4.00: Prelude to Applications of Derivatives
  50. 4.01: Related Rates
  51. 4.1E: Exercises for Section 4.1
  52. 4.02: Linear Approximations and Differentials
  53. 4.2E: Exercises for Section 4.2
  54. 4.03: Maxima and Minima
  55. 4.3E: Exercises for Section 4.3
  56. 4.04: The Mean Value Theorem
  57. 4.4E: Exercises for Section 4.4
  58. 4.05: Derivatives and the Shape of a Graph
  59. 4.5E: Exercises for Section 4.5
  60. 4.06: Limits at Infinity and Asymptotes
  61. 4.6E: Exercises for Section 4.6
  62. 4.07: Applied Optimization Problems
  63. 4.7E: Exercises for Section 4.7
  64. 4.08: LHopitals Rule
  65. 4.8E: Exercises for Section 4.8
  66. 4.09: Newtons Method
  67. 4.9E: Exercises for Section 4.9
  68. 4.10: Antiderivatives
  69. 4.10E: Exercises for Section 4.10
  70. 4.11: Chapter 4 Review Exercises
  71. 05: Integration
  72. 5.00: Prelude to Integration
  73. 5.01: Approximating Areas
  74. 5.1E: Exercises for Section 5.1
  75. 5.02: The Definite Integral
  76. 5.2E: Exercises for Section 5.2
  77. 5.03: The Fundamental Theorem of Calculus
  78. 5.3E: Exercises for Section 5.3
  79. 5.04: Integration Formulas and the Net Change Theorem
  80. 5.4E: Exercises for Section 5.4
  81. 5.05: Substitution
  82. 5.5E: Exercises for Section 5.5
  83. 5.06: Integrals Involving Exponential and Logarithmic Functions
  84. 5.6E: Exercises for Section 5.6
  85. 5.07: Chapter 5 Review Exercises
  86. 06: Appendices
  87. 6.00: A- Table of Derivatives
  88. 6.01: B- Table of Integrals