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First Semester Calculus (Westphal, adapted from Open Stax)

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First Semester Calculus (Westphal, adapted from Open Stax)

This text is a first semester calculus text adapted from the OpenStax Calculus 1 text. Some of the material has been re-ordered; the primary change is that derivatives of exponential and log functions are covered earlier in chapter 3 than they were in the OpenStax text.

Mathematics
Author
Karla Westphal
Publisher
Saddleback College
Source
LibreTexts
License
Mixed
Language
EN
Category
Accounting & Auditing
Read online Download PDF (open licence)
Contents· 97 sections
  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.R: Chapter 1 Review Exercises
  14. 02: Limits
  15. 2.00: Prelude to Limits
  16. 2.01: A Preview of Calculus
  17. 2.1.00: Examples of graphing m(x) the function that gives us the slope of a secant line in order to confirm a guess about the value of the slope of the tangent line
  18. 2.1E: Exercises for Section 2.1
  19. 2.02: The Limit of a Function
  20. 2.2E: Exercises for Section 2.2
  21. 2.03: The Limit Laws
  22. 2.3E: Exercises for Section 2.3
  23. 2.04: Continuity
  24. 2.4E: Exercises for Section 2.4
  25. 2.05: The Precise Definition of a Limit
  26. 2.5E: Exercises for Section 2.5
  27. 2.06: Limits at Infinity and Asymptotes
  28. 2.6E: Exercises for Section 2.6
  29. 2.R: Chapter 2 Review Exercises
  30. 03: Derivatives
  31. 3.00: Prelude to Derivatives
  32. 3.01: Defining the Derivative
  33. 3.1E: Exercises for Section 3.1
  34. 3.02: The Derivative as a Function
  35. 3.2E: Exercises for Section 3.2
  36. 3.03: Differentiation Rules
  37. 3.3.00: Basic differentiation rules- constants powers constant multiples sums and differences
  38. 3.3.01: Exponential functions
  39. 3.3.02: The Product and Quotient Rules
  40. 3.3E: Exercises for Section 3.3
  41. 3.04: Derivatives as Rates of Change
  42. 3.4E: Exercises for Section 3.4
  43. 3.05: Derivatives of Trigonometric Functions
  44. 3.5E: Exercises for Section 3.5
  45. 3.06: The Chain Rule
  46. 3.6.00: The Derivative of exponential functions with different bases
  47. 3.6E: Exercises for Section 3.6
  48. 3.07: Implicit Differentiation
  49. 3.7E: Exercises for Section 3.7
  50. 3.08: Derivatives of Inverse Functions
  51. 3.8.00: Preliminary examples- the derivatives of log functions
  52. 3.8.01: Derivatives of inverse functions in general and derivatives of inverse trig functions
  53. 3.8E: Exercises for Section 3.8
  54. 3.09: Reviewing exponential and logarithmic functions and introducing Logarithmic Differentiation
  55. 3.9E: Exercises for Section 3.9
  56. 3.R: Chapter 3 Review Exercises
  57. 04: Applications of Derivatives
  58. 4.00: Prelude to Applications of Derivatives
  59. 4.01: Related Rates
  60. 4.1E: Exercises for Section 4.1
  61. 4.02: Linear Approximations and Differentials
  62. 4.2E: Exercises for Section 4.2
  63. 4.03: Maxima and Minima
  64. 4.3E: Exercises for Section 4.3
  65. 4.04: The Mean Value Theorem
  66. 4.4E: Exercises for Section 4.4
  67. 4.05: Derivatives and the Shape of a Graph
  68. 4.5E: Exercises for Section 4.5
  69. 4.06: Using Calculus (and some algebra too) to graph functions
  70. 4.6E: Exercises for Section 4.6
  71. 4.07: Applied Optimization Problems
  72. 4.7E: Exercises for Section 4.7
  73. 4.08: LHopitals Rule
  74. 4.8E: Exercises for Section 4.8
  75. 4.09: Newtons Method
  76. 4.9E: Exercises for Section 4.9
  77. 4.10: Antiderivatives
  78. 4.10E: Exercises for Section 4.10
  79. 4.R: Chapter 4 Review Exercises
  80. 05: Integration
  81. 5.00: Prelude to Integration
  82. 5.01: Approximating Areas
  83. 5.1E: Exercises for Section 5.1
  84. 5.02: The Definite Integral
  85. 5.2E: Exercises for Section 5.2
  86. 5.03: The Fundamental Theorem of Calculus
  87. 5.3E: Exercises for Section 5.3
  88. 5.04: Integration Formulas and the Net Change Theorem
  89. 5.4E: Exercises for Section 5.4
  90. 5.05: Substitution
  91. 5.5E: Exercises for Section 5.5
  92. 5.06: Integrals Involving Exponential and Logarithmic Functions
  93. 5.6E: Exercises for Section 5.6
  94. 5.07: Integrals Resulting in Inverse Trigonometric Functions
  95. 5.7E: Exercises for Section 5.7
  96. 5.08: Integrals Resulting in Inverse Trigonometric Functions
  97. 5.R: Chapter 5 Review Exercises