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MTH 1 - Calculus I

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MTH 1 - Calculus I

This course is the first in the three-course calculus sequence intended for majors in math, engineering, and physical sciences. The course covers elements of analytic geometry, derivatives, limits and continuity, differentiation of algebraic and trigonometric functions, and the definite integral.

Mathematics
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Chabot College
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LibreTexts
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EN
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Mục lục· 114 mục
  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 1.1
  5. 1.03: Basic Classes of Functions
  6. 1.3E: Exercises for Section 1.2
  7. 1.04: Trigonometric Functions
  8. 1.4E: Exercises for Section 1.3
  9. 1.05: Inverse Functions
  10. 1.5E: Exercises for Section 1.4
  11. 1.06: Exponential and Logarithmic Functions
  12. 1.6E: Exercises for Section 1.5
  13. 1.07: Applied Optimization Problems
  14. 1.7E: Exercises for Section 4.7
  15. 1.08: Chapter 1 Review Exercises
  16. 02: Limits
  17. 2.01: The Idea of Limits
  18. 2.1E: Exercises for Section 2.1
  19. 2.02: Definitions of Limits
  20. 2.2E: Exercises for Section 2.2
  21. 2.03: Techniques for Computing Limits
  22. 2.3E: Exercises for Section 2.3
  23. 2.04: Infinite Limits
  24. 2.4E: Exercises for Section 2.4
  25. 2.05: Limits at Infinity
  26. 2.5E: Exercises for Section 2.5
  27. 2.06: Continuity
  28. 2.6E: Exercises for Section 2.6
  29. 2.07: Precise Definition of a Limit
  30. 2.7E: Exercises for Section 2.7
  31. 2.08: Chapter 2 Review Exercises
  32. 03: Derivatives
  33. 3.01: Introducing the Derivative
  34. 3.1E: Exercises for Section 3.1
  35. 3.02: Differentiation Rules
  36. 3.2E: Exercises for Section 3.2
  37. 3.03: The Product and Quotient Rules
  38. 3.3E: Exercises for Section 3.3
  39. 3.04: Derivatives of Trigonometric Functions
  40. 3.4E: Exercises for Section 3.4
  41. 3.05: Derivatives as Rates of Change
  42. 3.5E: Exercises for Section 3.5
  43. 3.06: The Chain Rule
  44. 3.6E: Exercises for Section 3.6
  45. 3.07: Implicit Differentiation
  46. 3.7E: Exercises for Section 3.7
  47. 3.08: Related Rates
  48. 3.8E: Exercises for Section 3.8
  49. 3.09: Derivatives of Inverse Functions
  50. 3.9E: Exercises for Section 3.9
  51. 3.10: Derivatives of Exponential and Logarithmic Functions
  52. 3.10E: Exercises for Section 3.10
  53. 3.11: Chapter 3 Review Exercises
  54. 04: Applications of Derivatives
  55. 4.01: Maxima and Minima
  56. 4.1E: Exercises for Section 4.1
  57. 4.02: What Derivatives Tell Us
  58. 4.2E: Exercises for Section 4.2
  59. 4.03: Graphing Functions
  60. 4.3E: Exercises for Section 4.3
  61. 4.04: Optimization Problems
  62. 4.4E: Exercises for Section 4.4
  63. 4.05: Linear Approximations and Differentials
  64. 4.5E: Exercises for Section 4.5
  65. 4.06: The Mean Value Theorem
  66. 4.6E: Exercises for Section 4.6
  67. 4.07: LHopitals Rule
  68. 4.7E: Exercises for Section 4.7
  69. 4.08: Newtons Method
  70. 4.8E: Exercises for Section 4.8
  71. 4.09: Antiderivatives
  72. 4.9E: Exercises for Section 4.9
  73. 4.10: Chapter 4 Review Exercises
  74. 05: Integration
  75. 5.01: Approximating Areas
  76. 5.1E: Exercises for Section 5.1
  77. 5.02: The Definite Integral
  78. 5.2E: Exercises for Section 5.2
  79. 5.03: The Fundamental Theorem of Calculus
  80. 5.3E: Exercises for Section 5.3
  81. 5.04: Working with Integrals
  82. 5.4.01: Exercises for Section 5.4
  83. 5.05: Substitution
  84. 5.5E: Exercises for Section 5.5
  85. 5.06: Integrals Involving Exponential and Logarithmic Functions
  86. 5.6E: Exercises for Section 5.6
  87. 5.07: Integrals Resulting in Inverse Trigonometric Functions
  88. 5.7E: Exercises for Section 5.7
  89. 5.08: Chapter 5 Review Exercises
  90. 06: Applications of Integration
  91. 6.01: Numerical Integration
  92. 6.1E: Exercises for Section 6.1
  93. 6.02: Areas Between Curves
  94. 6.2E: Exercises for Section 6.2
  95. 6.03: Determining Volumes by Slicing
  96. 6.3E: Exercises for Section 6.3
  97. 6.04: Volumes of Revolution - Cylindrical Shells
  98. 6.4E: Exercises for Section 6.4
  99. 6.05: Arc Length of a Curve and Surface Area
  100. 6.5E: Exercises for Section 6.5
  101. 6.06: Physical Applications of Integration
  102. 6.6E: Exercises for Section 6.6
  103. 6.07: Moments and Centers of Mass
  104. 6.7E: Exercises for Section 6.8
  105. 6.08: Integrals Exponential Functions and Logarithms
  106. 6.8E: Exercises for Section 6.9
  107. 6.09: Exponential Growth and Decay
  108. 6.9E: Exercises for Section 6.10
  109. 6.10: Calculus of the Hyperbolic Functions
  110. 6.10E: Exercises for Section 6.11
  111. 6.11: Chapter 6 Review Exercises
  112. 07: Appendices
  113. 7.01: A- Table of Derivatives
  114. 7.02: B- Table of Integrals