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Math C185: Calculus II

Nguồn ngoài

Math C185: Calculus II

Second course in the calculus sequence. It satisfies the requirement for majors in mathematics, science, or engineering. Topics include techniques and applications of integration, calculus applied to parametric curves and polar curves, analytic geometry, sequences, series, and an introduction to differential equations.

Mathematics
Tác giả
Michael Everett
Nhà xuất bản
Coastline 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· 106 mục
  1. 01: Calculus I Review
  2. 1.01: Derivatives of Exponential and Logarithmic Functions
  3. 1.02: Exercises on Derivatives of Logarithms and Exponential Functions
  4. 1.03: Derivatives of the Inverse Trigonometric Functions
  5. 02: Integration
  6. 2.01: Antiderivatives
  7. 2.1E: Antiderivative and Indefinite Integral Exercises
  8. 2.02: Prelude to Integration
  9. 2.03: Approximating Areas
  10. 2.3E: Approximating Areas (Exercises)
  11. 2.04: The Definite Integral
  12. 2.05: The Fundamental Theorem of Calculus
  13. 2.06: Integration Formulas and the Net Change Theorem
  14. 2.07: Substitution
  15. 2.08: 5.5E and 5.6E u-Substitution Exercises
  16. 2.09: Integrals Involving Exponential and Logarithmic Functions
  17. 2.10: Integrals Resulting in Inverse Trigonometric Functions and Related Integration Techniques
  18. 2.10E: Exercises for Integrals Resulting in Inverse Trigonometric Functions
  19. 2.11: Chapter 5 Review Exercises
  20. 03: Applications of Integration
  21. 3.01: Prelude to Applications of Integration
  22. 3.02: Areas between Curves
  23. 3.2E: Exercises for Section 6.1
  24. 3.03: Determining Volumes by Slicing
  25. 3.3E: Exercises for Volumes of Common Cross-Section and Disk Washer Method
  26. 3.04: Volumes of Revolution- The Shell Method
  27. 3.4b: Volumes of Revolution- Cylindrical Shells OS
  28. 3.4E: Exercises for the Shell Method
  29. 3.05: Arc Length and Surface Area
  30. 3.06: Arc Length of a Curve and Surface Area
  31. 3.07: Exercises for Section 6.4
  32. 3.08: Using Integration to Determine Work
  33. 3.09: More Physical Applications of Integration
  34. 3.10: Exercises on Work
  35. 3.11: Moments and Centers of Mass
  36. 3.11E: Exercises for Section 6.6
  37. 3.12: Integrals Exponential Functions and Logarithms
  38. 3.12E: Exercises for Section 6.7
  39. 3.13: Exponential Growth and Decay
  40. 3.13E: Exercises for Section 6.8
  41. 3.14: Calculus of the Hyperbolic Functions
  42. 3.14E: Exercises for Section 6.9
  43. 3.15: Chapter 6 Review Exercises
  44. 04: Techniques of Integration
  45. 4.01: Prelude to Techniques of Integration
  46. 4.02: Integration by Parts
  47. 4.2E: Exercises for Integration by Parts
  48. 4.03: Trigonometric Integrals
  49. 4.3E: Exercises for Trigonometric Integrals
  50. 4.04: Trigonometric Substitution
  51. 4.4E: Exercises for Trigonometric Substitution
  52. 4.05: Partial Fractions
  53. 4.5E: Exercises for Integration by Partial Fractions
  54. 4.06: Other Strategies for Integration
  55. 4.6E: Exercises for Section 7.5
  56. 4.07: Numerical Integration
  57. 4.7E: Exercises for Numerical Integration
  58. 4.08: L'Hopital's Rule
  59. 4.8E: Exercises for L'Hopital's Rule
  60. 4.09: Improper Integrals
  61. 4.9E: Exercises for Improper Integrals
  62. 4.10: Chapter 7 Review Exercises
  63. 05: Introduction to Differential Equations
  64. 5.01: Prelude to Differential Equations
  65. 5.02: Basics of Differential Equations
  66. 5.2E: Exercises for Basics of Differential Equations
  67. 5.03: Direction Fields and Numerical Methods
  68. 5.3E: Exercises for Direction Fields and Numerical Methods
  69. 5.04: Separable Differential Equations
  70. 5.4E: Exercises for Separable Differential Equations
  71. 5.05: The Logistic Equation
  72. 5.5E: Exercises for the Logistic Equation
  73. 5.06: First-order Linear Equations
  74. 5.6E: Exercises for Section 8.5
  75. 5.07: Chapter 8 Review Exercises
  76. 06: Sequences and Series
  77. 6.01: Prelude to Sequence and Series
  78. 6.02: Sequences
  79. 6.2E: Exercises for Sequences
  80. 6.03: Infinite Series
  81. 6.3E: Exercises for Infinite Series
  82. 6.04: The Divergence and Integral Tests
  83. 6.4E: Exercises for Divergence and Integral Tests
  84. 6.05: Comparison Tests
  85. 6.5E: Exercises for Comparison Test
  86. 6.06: Alternating Series
  87. 6.6E: Exercises for Alternating Series
  88. 6.07: Ratio and Root Tests
  89. 6.7E: Exercises for Ratio and Root Tests
  90. 6.08: Chapter 9 Review Exercises
  91. 07: Power Series
  92. 7.01: Prelude to Power Series
  93. 7.02: Power Series and Functions
  94. 7.2E: Exercises for Section 10.1
  95. 7.03: Properties of Power Series
  96. 7.3E: Exercises for Section 10.2
  97. 7.04: Taylor and Maclaurin Series
  98. 7.4E: Exercises for Taylor Polynomials and Taylor Series
  99. 7.05: Working with Taylor Series
  100. 7.5E: Exercises for Section 10.4
  101. 7.06: Chapter 10 Review Exercises
  102. 08: Appendices
  103. 8.01: Trigonometric Identities
  104. 8.02: Review of Derivative Rules
  105. 8.03: Table of Derivatives
  106. 8.04: Table of Integrals