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Calculus II: Integral Calculus

Nguồn ngoài

Calculus II: Integral Calculus

This second book in a four-part calculus series is designed for both beginners and advanced students, emphasizing a strong conceptual foundation. It explores essential topics such as rates of change and calculating areas and volumes of irregular shapes, with numerous examples and applications across physics, economics, and engineering.

Mathematics
Tác giả
Doli Bambhania, Neelam R. Shukla & Danny Tran
Nhà xuất bản
De Anza 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· 73 mục
  1. 01: Integration
  2. 1.01: Approximating Areas
  3. 1.1E: Exercises for Section 1.1
  4. 1.02: The Definite Integral
  5. 1.2E: Exercises for Section 1.2
  6. 1.03: The Fundamental Theorem of Calculus
  7. 1.3E: Exercises for Section 1.3
  8. 1.04: Integration Formulas and the Net Change Theorem
  9. 1.4E: Exercises for Section 1.4
  10. 1.05: Substitution
  11. 1.5E: Exercises for Section 1.5
  12. 1.06: Integrals Involving Exponential and Logarithmic Functions
  13. 1.6E: Exercises for Section 1.6
  14. 1.07: Integrals Resulting in Inverse Trigonometric Functions
  15. 1.7E: Exercises for Section 1.7
  16. 1.08: Chapter 1 Review Exercises
  17. 02: Applications of Integration
  18. 2.01: Areas between Curves
  19. 2.1E: Exercises for Section 2.1
  20. 2.02: Determining Volumes by Slicing
  21. 2.2E: Exercises for Section 2.2
  22. 2.03: Volumes of Revolution - Cylindrical Shells
  23. 2.3E: Exercises for Section 2.3
  24. 2.04: Arc Length of a Curve and Surface Area
  25. 2.4E: Exercises for Section 2.4
  26. 2.05: Physical Applications of Integration
  27. 2.5E: Exercises for Section 2.5
  28. 2.06: Moments and Centers of Mass
  29. 2.6E: Exercises for Section 2.6
  30. 2.07: Integrals Exponential Functions and Logarithms
  31. 2.7E: Exercises for Section 2.7
  32. 2.08: Exponential Growth and Decay
  33. 2.8E: Exercises for Section 2.8
  34. 2.09: Calculus of the Hyperbolic Functions
  35. 2.9E: Exercises for Section 2.9
  36. 2.10: Chapter 2 Review Exercises
  37. 03: Techniques of Integration
  38. 3.01: Integration by Parts
  39. 3.1E: Exercises for Section 3.1
  40. 3.02: Trigonometric Integrals
  41. 3.2E: Exercises for Section 3.2
  42. 3.03: Trigonometric Substitution
  43. 3.3E: Exercises for Section 3.3
  44. 3.04: Partial Fractions
  45. 3.4E: Exercises for Section 3.4
  46. 3.05: Other Strategies for Integration
  47. 3.5E: Exercises for Section 3.5
  48. 3.06: Numerical Integration
  49. 3.6E: Exercises for Section 3.6
  50. 3.07: Improper Integrals
  51. 3.7E: Exercises for Section 3.7
  52. 3.08: Probability
  53. 3.8E: Exercises for section 3.8
  54. 3.09: Chapter 3 Review Exercises
  55. 04: Parametric Equations
  56. 4.01: Parametric Equations
  57. 4.1E: Exercises for Section 4.1
  58. 4.02: Calculus of Parametric Curves
  59. 4.2E: Exercises for Section 4.2
  60. 4.03: Chapter 4 Review Exercises
  61. 05: Introduction to Differential Equations
  62. 5.01: Basics of Differential Equations
  63. 5.1E: Exercises for Section 5.1
  64. 5.02: Direction Fields and Numerical Methods
  65. 5.2E: Exercises for Section 5.2
  66. 5.03: Separable Equations
  67. 5.3E: Exercises for Section 5.3
  68. 5.04: The Logistic Equation
  69. 5.4E: Exercises for Section 5.4
  70. 5.05: Chapter 5 Review Exercises
  71. 06: Appendices
  72. 6.01: Appendix A- Table of Derivatives
  73. 6.02: Appendix B- Table of Integrals