Calculus II - Late Transcendentals

by Laimi Cong-Huyen and Vinh Kha-Nguyen

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This Open Educational Resource (OER) textbook is designed for Calculus II using the late transcendentals approach at Evergreen Valley College. It continues the development of single-variable calculus with derivatives and integrals of transcendental functions, applications and techniques of integration, and an introduction to differential equations. The text also covers parametric equations and polar coordinates, sequences and series, and applications of these topics.

Description from LibreTexts.

Publisher
Evergreen Valley College
Subjects
Mathematics
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Transcendental Functions
  7. 1.1: Derivatives of Inverse Functions
  8. 1.1E: Exercises for Section 1.1
  9. 1.2: Derivatives of Exponential and Logarithmic Functions
  10. 1.2E: Exercises for Section 1.2
  11. 1.3: L’Hôpital’s Rule
  12. 1.3E: Exercises for Section 1.3
  13. 1.4: Integrals Involving Exponential and Logarithmic Functions
  14. 1.4E: Exercises for Section 1.4
  15. 1.5: Integrals Resulting in Inverse Trigonometric Functions
  16. 1.5E: Exercises for Section 1.5
  17. 1.6: Chapter 1 Review Exercises
  18. 2: Applications of Integration
  19. 2.1: Areas between Curves
  20. 2.1E: Exercises for Section 2.1
  21. 2.2: Determining Volumes by Slicing
  22. 2.2E: Exercises for Section 2.2
  23. 2.3: Volumes of Revolution - Cylindrical Shells
  24. 2.3E: Exercises for Section 2.3
  25. 2.4: Arc Length of a Curve and Surface Area
  26. 2.4E: Exercises for Section 2.4
  27. 2.5: Physical Applications of Integration
  28. 2.5E: Exercises for Section 2.5
  29. 2.6: Moments and Centers of Mass
  30. 2.6E: Exercises for Section 2.6
  31. 2.7: Integrals, Exponential Functions, and Logarithms
  32. 2.7E: Exercises for Section 2.7
  33. 2.8: Exponential Growth and Decay
  34. 2.8E: Exercises for Section 2.8
  35. 2.9: Calculus of the Hyperbolic Functions
  36. 2.9E: Exercises for Section 2.9
  37. 2.10: Chapter 2 Review Exercises
  38. 3: Techniques of Integration
  39. 3.1: Integration by Parts
  40. 3.1E: Exercises for Section 3.1
  41. 3.2: Trigonometric Integrals
  42. 3.2E: Exercises for Section 3.2
  43. 3.3: Trigonometric Substitution
  44. 3.3E: Exercises for Section 3.3
  45. 3.4: Partial Fractions
  46. 3.4E: Exercises for Section 3.4
  47. 3.5: Other Strategies for Integration
  48. 3.5E: Exercises for Section 3.5
  49. 3.6: Numerical Integration
  50. 3.6E: Exercises for Section 3.6
  51. 3.7: Improper Integrals
  52. 3.7E: Exercises for Section 3.7
  53. 3.8: Chapter 3 Review Exercises
  54. 4: Introduction to Differential Equations
  55. 4.1: Basics of Differential Equations
  56. 4.1E: Exercises for Section 4.1
  57. 4.2: Direction Fields and Numerical Methods
  58. 4.2E: Exercises for Section 4.2
  59. 4.3: Separable Equations
  60. 4.3E: Exercises for Section 4.3
  61. 4.4: The Logistic Equation
  62. 4.4E: Exercises for Section 4.4
  63. 4.5: First-order Linear Equations
  64. 4.5E: Exercises for Section 4.5
  65. 4.6: Chapter 4 Review Exercises
  66. 5: Parametric Equations and Polar Coordinates
  67. 5.1: Parametric Equations
  68. 5.1E: Exercises for Section 5.1
  69. 5.2: Calculus of Parametric Curves
  70. 5.2E: Exercises for Section 5.2
  71. 5.3: Polar Coordinates
  72. 5.3E: Exercises for Section 5.3
  73. 5.4: Area and Arc Length in Polar Coordinates
  74. 5.4E: Exercises for Section 5.4
  75. 5.5: Conic Sections
  76. 5.5E: Exercises for Section 5.5
  77. 5.6: Chapter 5 Review Exercises
  78. 6: Sequences and Series
  79. 6.1: Sequences
  80. 6.1E: Exercises for Section 6.1
  81. 6.2: Infinite Series
  82. 6.2E: Exercises for Section 6.2
  83. 6.3: The Divergence and Integral Tests
  84. 6.3E: Exercises for Section 6.3
  85. 6.4: Comparison Tests
  86. 6.4E: Exercises for Section 6.4
  87. 6.5: Alternating Series
  88. 6.5E: Exercises for Section 6.5
  89. 6.6: Ratio and Root Tests
  90. 6.6E: Exercises for Section 6.6
  91. 6.7: Power Series and Functions
  92. 6.7E: Exercises for Section 6.7
  93. 6.8: Properties of Power Series
  94. 6.8E: Exercises for Section 6.8
  95. 6.9: Taylor and Maclaurin Series
  96. 6.9E: Exercises for Section 6.9
  97. 6.10: Working with Taylor Series
  98. 6.10E: Exercises for Section 6.10
  99. 6.11: Chapter 6 Review Exercises
  100. Back Matter
  101. Index
  102. Glossary
  103. Detailed Licensing