Math 400: Calculus I - Differential Calculus

by Roy Simpson

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This text explores the basic concepts of analytic geometry, limits (including indeterminate forms), derivatives, and integrals. The topics covered will include graphs, derivatives, and integrals of algebraic, trigonometric, exponential, logarithmic, and hyperbolic functions. Standard proofs will be covered, such as delta-epsilon proofs and proofs of some theorems. Applications will be covered, including those involving rectilinear motion, differentials, related rates, graphing, and optimization.

Description from LibreTexts.

Publisher
Cosumnes River College
Subjects
Mathematics
Licence
CC BY-SA, 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. Preface for the Instructor
  5. Table of Contents
  6. Licensing
  7. Preface to the Student
  8. Templates
  9. 1: Learning Limits
  10. 1.1: Numerical Investigation of Limits
  11. 1.1.1: Resources and Key Concepts
  12. 1.1.2: Homework
  13. 1.1.3: Additional Exercises
  14. 1.2: Graphical Investigation of Limits
  15. 1.2.1: Resources and Key Concepts
  16. 1.2.2: Homework
  17. 1.2.3: Additional Exercises
  18. 1.3: Limit Laws and the Squeeze Theorem
  19. 1.3.1: Resources and Key Concepts
  20. 1.3.2: Homework
  21. 1.3.3: Additional Exercises
  22. 1.4: Algebraic Manipulations and the Limit Laws
  23. 1.4.1: Resources and Key Concepts
  24. 1.4.2: Homework
  25. 1.4.3: Additional Exercises
  26. 1.5: Limits at Infinity
  27. 1.5.1: Resources and Key Concepts
  28. 1.5.2: Homework
  29. 1.5.3: Additional Exercises
  30. 1.6: The Precise Definition of a Limit
  31. 1.6.1: Resources and Key Concepts
  32. 1.6.2: Homework
  33. 1.6.3: Additional Exercises
  34. 1.7: The Precise Definitions of Limits Involving Infinity
  35. 1.7.1: Resources and Key Concepts
  36. 1.7.2: Homework
  37. 1.7.3: Additional Exercises
  38. 1.8: Continuity
  39. 1.8.1: Resources and Key Concepts
  40. 1.8.2: Homework
  41. 1.8.3: Additional Exercises
  42. 1.9: Defining the Derivative
  43. 1.9.1: Resources and Key Concepts
  44. 1.9.2: Homework
  45. 1.9.3: Additional Exercises
  46. 1.10: The Derivative as a Function
  47. 1.10.1: Resources and Key Concepts
  48. 1.10.2: Homework
  49. 1.10.3: Additional Exercises
  50. 2: Discovering Derivatives
  51. 2.1: Derivatives of Polynomial Functions
  52. 2.1.1: Resources and Key Concepts
  53. 2.1.2: Homework
  54. 2.1.3: Additional Exercises
  55. 2.2: Differentiation Techniques - The Product and Quotient Rules
  56. 2.2.1: Resources and Key Concepts
  57. 2.2.2: Homework
  58. 2.2.3: Additional Exercises
  59. 2.3: Derivatives of Trigonometric Functions
  60. 2.3.1: Resources and Key Concepts
  61. 2.3.2: Homework
  62. 2.3.3: Additional Exercises
  63. 2.4: Differentiation Techniques - The Chain Rule
  64. 2.4.1: Resources and Key Concepts
  65. 2.4.2: Homework
  66. 2.4.3: Additional Exercises
  67. 2.5: An Interlude - Hyperbolic Functions
  68. 2.5.1: Resources and Key Concepts
  69. 2.5.2: Homework
  70. 2.5.3: Additional Exercises
  71. 2.6: Derivatives of Exponential and Hyperbolic Functions
  72. 2.6.1: Resources and Key Concepts
  73. 2.6.2: Homework
  74. 2.6.3: Additional Exercises
  75. 2.7: Implicit Differentiation and the Derivatives of the Inverse Trigonometric and Hyperbolic Functions
  76. 2.7.1: Resources and Key Concepts
  77. 2.7.2: Homework
  78. 2.7.3: Additional Exercises
  79. 2.8: Derivatives of Logarithms and Logarithmic Differentiation
  80. 2.8.1: Resources and Key Concepts
  81. 2.8.2: Homework
  82. 2.8.3: Additional Exercises
  83. 2.9: Related Rates
  84. 2.9.1: Resources and Key Concepts
  85. 2.9.2: Homework
  86. 2.9.3: Additional Exercises
  87. 2.10: Linear Approximations and Differentials
  88. 2.10.1: Resources and Key Concepts
  89. 2.10.2: Homework
  90. 2.10.3: Additional Exercises
  91. 3: Advancing with Applications
  92. 3.1: Extrema
  93. 3.1.1: Resources and Key Concepts
  94. 3.1.2: Homework
  95. 3.2: The Mean Value Theorem
  96. 3.2.1: Resources and Key Concepts
  97. 3.2.2: Homework
  98. 3.3: Shapes of Curves
  99. 3.3.1: Resources and Key Concepts
  100. 3.3.2: Homework
  101. 3.4: l'Hôpital's Rule and Indeterminate Forms
  102. 3.4.1: Resources and Key Concepts
  103. 3.4.2: Homework
  104. 3.5: Graphing Using Calculus
  105. 3.5.1: Resources and Key Concepts
  106. 3.5.2: Homework
  107. 3.6: Optimization
  108. 3.6.1: Resources and Key Concepts
  109. 3.6.2: Homework
  110. 3.7: Newton’s Method
  111. 3.7.1: Resources and Key Concepts
  112. 3.7.2: Homework
  113. 4: Investigating Integrals
  114. 4.1: Antiderivatives and Indefinite Integrals
  115. 4.1.1: Resources and Key Concepts
  116. 4.1.2: Homework
  117. 4.2: Approximating Areas
  118. 4.2.1: Resources and Key Concepts
  119. 4.2.2: Homework
  120. 4.3: The Definite Integral
  121. 4.3.1: Resources and Key Concepts
  122. 4.3.2: Homework
  123. 4.4: The Fundamental Theorem of Calculus
  124. 4.4.1: Resources and Key Concepts
  125. 4.4.2: Homework
  126. 4.5: The Net Change Theorem, Distances, and Symmetry
  127. 4.5.1: Resources and Key Concepts
  128. 4.5.2: Homework
  129. 4.6: Integration by Substitution
  130. 4.6.1: Resources and Key Concepts
  131. 4.6.2: Homework
  132. 5: Appendix
  133. 5.1: A.1- Algebraic Manipulations Critical for Calculus
  134. 5.1.1: A.1.1- Homework
  135. 5.2: A.2- Functions
  136. 5.2.1: A.2.1- Homework
  137. 5.3: A.3- Basic Classes of Functions and Their Graphs
  138. 5.3.1: A.3.1- Homework
  139. 5.4: A.4- Inverse Functions
  140. 5.4.1: A.4.1- Homework
  141. 5.5: A.5- Exponential and Logarithmic Functions
  142. 5.5.1: A.5.1- Homework
  143. 5.6: A.6- Trigonometry
  144. 5.6.1: A.6.1- Homework
  145. 5.7: A.7- Tangent Lines and Velocity
  146. 5.7.1: A.7.1- Homework
  147. 5.8: A.8- Answers to Selected Exercises
  148. 5.8.1: A.8.1- Chapter 1 Answers
  149. 5.8.2: Chapter 2 Answers
  150. 5.8.3: Chapter 3 Answers
  151. 5.8.4: Chapter 4 Answers
  152. 5.9: Diagnostic Examples
  153. 5.9.1: Chapter 1 Diagnostics
  154. Back Matter
  155. Detailed Licensing
  156. Index
  157. Glossary
  158. Detailed Licensing