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Math 222: Calculus II

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Math 222: Calculus II

Math 222, Calculus II, is the second semester course of the calculus series and is intended as a continuation of the development of single-variable calculus. We will cover the differential calculus of transcendental functions (exponentials, logarithms, inverse trig functions, etc.) as well as continue the integral calculus we began in Math 221, Calculus I. We will introduce techniques of integration such as integration by parts, trigonometric substitution, and partial fraction decompositions.

Mathematics
Publisher
LibreTexts
Source
LibreTexts
Language
EN
Category
Basic Sciences
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Contents· 93 sections
  1. 01: Applications of Integration
  2. 1.00: Prelude to Applications of Integration
  3. 1.01: Areas between Curves
  4. 1.1E: Exercises for Section 1.1
  5. 1.02: Determining Volumes by Slicing
  6. 1.2E: Exercises for Section 1.2
  7. 1.03: Volumes of Revolution - Cylindrical Shells
  8. 1.3E: Exercises for Section 1.3
  9. 1.04: Arc Length of a Curve and Surface Area
  10. 1.4E: Exercises for Section 1.4
  11. 1.05: Physical Applications of Integration
  12. 1.5E: Exercises for Section 1.5
  13. 1.06: Moments and Centers of Mass
  14. 1.6E: Exercises for Section 1.6
  15. 1.07: Integrals Exponential Functions and Logarithms
  16. 1.7E: Exercises for Section 1.7
  17. 1.08: Exponential Growth and Decay
  18. 1.8E: Exercises for Section 1.8
  19. 1.09: Calculus of the Hyperbolic Functions
  20. 1.9E: Exercises for Section 1.9
  21. 1.10: Chapter 1 Review Exercises
  22. 02: Techniques of Integration
  23. 2.00: Prelude to Techniques of Integration
  24. 2.01: Integration by Parts
  25. 2.1E: Exercises for Section 2.1
  26. 2.02: Trigonometric Integrals
  27. 2.2E: Exercises for Section 2.2
  28. 2.03: Trigonometric Substitution
  29. 2.3E: Exercises for Section 2.3
  30. 2.04: Partial Fractions
  31. 2.4E: Exercises for Section 2.4
  32. 2.05: Other Strategies for Integration
  33. 2.5E: Exercises for Section 2.5
  34. 2.06: Numerical Integration
  35. 2.6E: Exercises for Section 2.6
  36. 2.07: Improper Integrals
  37. 2.7E: Exercises for Section 2.7
  38. 2.08: Chapter 2 Review Exercises
  39. 03: Introduction to Differential Equations
  40. 3.00: Prelude to Differential Equations
  41. 3.01: Basics of Differential Equations
  42. 3.1E: Exercises for Section 3.1
  43. 3.02: Direction Fields and Numerical Methods
  44. 3.2E: Exercises for Section 3.2
  45. 3.03: Separable Equations
  46. 3.3E: Exercises for Section 3.3
  47. 3.04: The Logistic Equation
  48. 3.4E: Exercises for Section 3.4
  49. 3.05: First-order Linear Equations
  50. 3.5E: Exercises for Section 3.5
  51. 3.06: Chapter 3 Review Exercises
  52. 04: Sequences and Series
  53. 4.00: Prelude to Sequence and Series
  54. 4.01: Sequences
  55. 4.1E: Exercises for Section 4.1
  56. 4.02: Infinite Series
  57. 4.2E: Exercises for Section 4.2
  58. 4.03: The Divergence and Integral Tests
  59. 4.3E: Exercises for Section 4.3
  60. 4.04: Comparison Tests
  61. 4.4E: Exercises for Section 4.4
  62. 4.05: Alternating Series
  63. 4.5E: Exercises for Section 4.5
  64. 4.06: Ratio and Root Tests
  65. 4.6E: Exercises for Section 4.6
  66. 4.07: Chapter 4 Review Exercises
  67. 05: Power Series
  68. 5.00: Prelude to Power Series
  69. 5.01: Power Series and Functions
  70. 5.1E: Exercises for Section 5.1
  71. 5.02: Properties of Power Series
  72. 5.2E: Exercises for Section 5.2
  73. 5.03: Taylor and Maclaurin Series
  74. 5.3E: Exercises for Section 5.3
  75. 5.04: Working with Taylor Series
  76. 5.4E: Exercises for Section 5.4
  77. 5.05: Chapter 5 Review Exercises
  78. 06: Parametric Equations and Polar Coordinates
  79. 6.00: Prelude to Parametric Equations and Polar Coordinates
  80. 6.01: Parametric Equations
  81. 6.1E: Exercises for Section 6.1
  82. 6.02: Calculus of Parametric Curves
  83. 6.2E: Exercises for Section 6.2
  84. 6.03: Polar Coordinates
  85. 6.3E: Exercises for Section 6.3
  86. 6.04: Area and Arc Length in Polar Coordinates
  87. 6.4E: Exercises for Section 6.4
  88. 6.05: Conic Sections
  89. 6.5E: Exercises for Section 6.5
  90. 6.06: Chapter 6 Review Exercises
  91. 07: Appendices
  92. 7.00: A- Table of Derivatives
  93. 7.01: B- Table of Integrals