MAT 2410: Calculus 1

by Peggy Beck

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This texts address a three-semester sequence of university-level calculus for a variety of majors including, but not exclusive to, science, engineering, and mathematics. It provides an introduction to single variable calculus; study of limits, continuity, differentiation and its applications, definite and indefinite integrals and the Fundamental Theorem of Calculus.

Description from LibreTexts.

Publisher
Prince George's Community College
Subjects
Mathematics
Licence
CC BY-NC-SA, as LibreTexts states it. Non-commercial use only.
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: Functions and Graphs
  7. 1.1: Prelude to Functions and Graphs
  8. 1.2: Review of Functions
  9. 1.2E: Exercises for Section 1.1
  10. 1.3: Basic Classes of Functions
  11. 1.3E: Exercises for Section 1.2
  12. 1.4: Trigonometric Functions
  13. 1.4E: Exercises for Section 1.3
  14. 1.5: Inverse Functions
  15. 1.5E: Exercises for Section 1.4
  16. 1.6: Exponential and Logarithmic Functions
  17. 1.6E: Exercises for Section 1.5
  18. 1.7: Chapter 1 Review Exercises
  19. 2: Limits
  20. 2.1: Prelude to Limits
  21. 2.2: A Preview of Calculus
  22. 2.2E: Exercises for Section 2.1
  23. 2.3: The Limit of a Function
  24. 2.3E: Exercises for Section 2.2
  25. 2.4: The Limit Laws
  26. 2.4E: Exercises for Section 2.3
  27. 2.5: Continuity
  28. 2.5E: Exercises for Section 2.4
  29. 2.6: The Precise Definition of a Limit
  30. 2.6E: Exercises for Section 2.5
  31. 2.7: Chapter 2 Review Exercises
  32. 3: Derivatives
  33. 3.1: Prelude to Derivatives
  34. 3.2: Defining the Derivative
  35. 3.2E: Exercises for Section 3.1
  36. 3.3: The Derivative as a Function
  37. 3.3E: Exercises for Section 3.2
  38. 3.4: Differentiation Rules
  39. 3.4E: Exercises for Section 3.3
  40. 3.5: Derivatives as Rates of Change
  41. 3.5E: Exercises for Section 3.4
  42. 3.6: Derivatives of Trigonometric Functions
  43. 3.6E: Exercises for Section 3.5
  44. 3.7: The Chain Rule
  45. 3.7E: Exercises for Section 3.6
  46. 3.8: Derivatives of Inverse Functions
  47. 3.8E: Exercises for Section 3.7
  48. 3.9: Implicit Differentiation
  49. 3.9E: Exercises for Section 3.8
  50. 3.10: Derivatives of Exponential and Logarithmic Functions
  51. 3.10E: Exercises for Section 3.9
  52. 3.11: Chapter 3 Review Exercises
  53. 4: Applications of Derivatives
  54. 4.1: Prelude to Applications of Derivatives
  55. 4.2: Related Rates
  56. 4.2E: Exercises for Section 4.1
  57. 4.3: Linear Approximations and Differentials
  58. 4.3E: Exercises for Section 4.2
  59. 4.4: Maxima and Minima
  60. 4.4E: Exercises for Section 4.3
  61. 4.5: The Mean Value Theorem
  62. 4.5E: Exercises for Section 4.4
  63. 4.6: Derivatives and the Shape of a Graph
  64. 4.6E: Exercises for Section 4.5
  65. 4.7: Limits at Infinity and Asymptotes
  66. 4.7E: Exercises for Section 4.6
  67. 4.8: Applied Optimization Problems
  68. 4.8E: Exercises for Section 4.7
  69. 4.9: L’Hôpital’s Rule
  70. 4.9E: Exercises for Section 4.8
  71. 4.10: Newton’s Method
  72. 4.10E: Exercises for Section 4.9
  73. 4.11: Antiderivatives
  74. 4.11E: Exercises for Section 4.10
  75. 4.12: Chapter 4 Review Exercises
  76. 5: Integration
  77. 5.1: Approximating Areas
  78. 5.1E: Exercises for Section 5.1
  79. 5.2: The Definite Integral
  80. 5.2E: Exercises for Section 5.2
  81. 5.3: The Fundamental Theorem of Calculus
  82. 5.3E: Exercises for Section 5.3
  83. 5.4: Integration Formulas and the Net Change Theorem
  84. 5.4E: Exercises for Section 5.4
  85. 5.5: Substitution
  86. 5.5E: Exercises for Section 5.5
  87. 5.6: Integrals Involving Exponential and Logarithmic Functions
  88. 5.6E: Exercises for Section 5.6
  89. 5.7: Integrals Resulting in Inverse Trigonometric Functions
  90. 5.7E: Exercises for Section 5.7
  91. 5.8: Chapter 5 Review Exercises
  92. Back Matter
  93. Index
  94. Glossary
  95. Detailed Licensing