Discover Calculus

by Peter Keep

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Publisher
Moraine Valley Community College
Subjects
Mathematics
Licence
CC BY 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Limits
  7. 1.1: The Definition of the Limit
  8. 1.2: Evaluating Limits
  9. 1.3: First Indeterminate Forms
  10. 1.4: Limits Involving Infinity
  11. 1.5: The Squeeze Theorem
  12. 1.6: Continuity and the Intermediate Value Theorem
  13. 1.7: Exploration- Limits
  14. 2: Derivatives
  15. 2.1: Introduction to Derivatives
  16. 2.2: Interpreting Derivatives
  17. 2.3: Some Early Derivative Rules
  18. 2.4: The Product and Quotient Rules
  19. 2.5: The Chain Rule
  20. 3: Implicit Differentiation
  21. 3.1: Implicit Differentiation
  22. 3.2: Derivatives of Inverse Functions
  23. 3.3: Logarithmic Differentiation
  24. 4: Applications of Derivatives
  25. 4.1: Mean Value Theorem
  26. 4.2: Increasing and Decreasing Functions
  27. 4.3: Concavity
  28. 4.4: Global Maximums and Minimums
  29. 4.5: Optimization
  30. 4.6: Linear Approximations
  31. 4.7: L’Hôpital’s Rule
  32. 4.8: Exploration- Applications of Derivatives
  33. 5: Antiderivatives and Integrals
  34. 5.1: Antiderivatives and Indefinite Integrals
  35. 5.2: Riemann Sums and Area Approximations
  36. 5.3: The Definite Integral
  37. 5.4: The Fundamental Theorem of Calculus
  38. 5.5: More Results about Definite Integrals
  39. 5.6: Introduction to \(u\) Substitution
  40. 6: Applications of Integrals
  41. 6.1: Integrals as Net Change
  42. 6.2: Area Between Curves
  43. 6.3: Volumes of Solids of Revolution
  44. 6.4: More Volumes- Shifting the Axis of Revolution
  45. 6.5: Arc Length and Surface Area
  46. 6.6: Other Applications of Integrals
  47. 7: Techniques for Antidifferentiation
  48. 7.1: Improper Integrals
  49. 7.2: More on \(u\) Substitution
  50. 7.3: Manipulating Integrands
  51. 7.4: Integration by Parts
  52. 7.5: Integrating Powers of Trigonometric Functions
  53. 7.6: Trigonometric Substitution
  54. 7.7: Partial Fractions
  55. 8: Infinite Series
  56. 8.1: Introduction to Infinite Sequences
  57. 8.2: Introduction to Infinite Series
  58. 8.3: The Divergence Test and the Harmonic Series
  59. 8.4: The Integral Test
  60. 8.5: Alternating Series and Conditional Convergence
  61. 8.6: Common Series Types
  62. 8.7: Comparison Tests
  63. 8.8: The Ratio and Root Tests
  64. 8.9: Exploration- Infinite Series
  65. 9: Power Series
  66. 9.1: Polynomial Approximations of Functions
  67. 9.2: Power Series Convergence
  68. 9.3: How to Build Taylor Series
  69. 9.4: How to Use Taylor Series
  70. 9.5: Exploration- Power Series
  71. 10: Parametric and Polar Curves
  72. 10.1: Parametric Curves
  73. 10.2: Polar Curves
  74. 10.3: Calculus with Parametric Curves
  75. 10.4: Calculus with Polar Curves
  76. Back Matter
  77. Index
  78. Glossary
  79. Detailed Licensing