Phu Xuan University Library
|
PXU E-LIB
Sign in
Math 400: Calculus I - Differential Calculus

External

Math 400: Calculus I - Differential Calculus

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.

Mathematics
Author
Roy Simpson
Publisher
Cosumnes River College
Source
LibreTexts
License
CC BY-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 145 sections
  1. 01: Learning Limits
  2. 1.01: Numerical Investigation of Limits
  3. 1.1.01: Resources and Key Concepts
  4. 1.1.02: Homework
  5. 1.1.03: Additional Exercises
  6. 1.02: Graphical Investigation of Limits
  7. 1.2.01: Resources and Key Concepts
  8. 1.2.02: Homework
  9. 1.2.03: Additional Exercises
  10. 1.03: Limit Laws and the Squeeze Theorem
  11. 1.3.01: Resources and Key Concepts
  12. 1.3.02: Homework
  13. 1.3.03: Additional Exercises
  14. 1.04: Algebraic Manipulations and the Limit Laws
  15. 1.4.01: Resources and Key Concepts
  16. 1.4.02: Homework
  17. 1.4.03: Additional Exercises
  18. 1.05: Limits at Infinity
  19. 1.5.01: Resources and Key Concepts
  20. 1.5.02: Homework
  21. 1.5.03: Additional Exercises
  22. 1.06: The Precise Definition of a Limit
  23. 1.6.01: Resources and Key Concepts
  24. 1.6.02: Homework
  25. 1.6.03: Additional Exercises
  26. 1.07: The Precise Definitions of Limits Involving Infinity
  27. 1.7.01: Resources and Key Concepts
  28. 1.7.02: Homework
  29. 1.7.03: Additional Exercises
  30. 1.08: Continuity
  31. 1.8.01: Resources and Key Concepts
  32. 1.8.02: Homework
  33. 1.8.03: Additional Exercises
  34. 1.09: Defining the Derivative
  35. 1.9.01: Resources and Key Concepts
  36. 1.9.02: Homework
  37. 1.9.03: Additional Exercises
  38. 1.10: The Derivative as a Function
  39. 1.10.01: Resources and Key Concepts
  40. 1.10.02: Homework
  41. 1.10.03: Additional Exercises
  42. 02: Discovering Derivatives
  43. 2.01: Derivatives of Polynomial Functions
  44. 2.1.01: Resources and Key Concepts
  45. 2.1.02: Homework
  46. 2.1.03: Additional Exercises
  47. 2.02: Differentiation Techniques - The Product and Quotient Rules
  48. 2.2.01: Resources and Key Concepts
  49. 2.2.02: Homework
  50. 2.2.03: Additional Exercises
  51. 2.03: Derivatives of Trigonometric Functions
  52. 2.3.01: Resources and Key Concepts
  53. 2.3.02: Homework
  54. 2.3.03: Additional Exercises
  55. 2.04: Differentiation Techniques - The Chain Rule
  56. 2.4.01: Resources and Key Concepts
  57. 2.4.02: Homework
  58. 2.4.03: Additional Exercises
  59. 2.05: An Interlude - Hyperbolic Functions
  60. 2.5.01: Resources and Key Concepts
  61. 2.5.02: Homework
  62. 2.5.03: Additional Exercises
  63. 2.06: Derivatives of Exponential and Hyperbolic Functions
  64. 2.6.01: Resources and Key Concepts
  65. 2.6.02: Homework
  66. 2.6.03: Additional Exercises
  67. 2.07: Implicit Differentiation and the Derivatives of the Inverse Trigonometric and Hyperbolic Functions
  68. 2.7.01: Resources and Key Concepts
  69. 2.7.02: Homework
  70. 2.7.03: Additional Exercises
  71. 2.08: Derivatives of Logarithms and Logarithmic Differentiation
  72. 2.8.01: Resources and Key Concepts
  73. 2.8.02: Homework
  74. 2.8.03: Additional Exercises
  75. 2.09: Related Rates
  76. 2.9.01: Resources and Key Concepts
  77. 2.9.02: Homework
  78. 2.9.03: Additional Exercises
  79. 2.10: Linear Approximations and Differentials
  80. 2.10.01: Resources and Key Concepts
  81. 2.10.02: Homework
  82. 2.10.03: Additional Exercises
  83. 03: Advancing with Applications
  84. 3.01: Extrema
  85. 3.1.01: Resources and Key Concepts
  86. 3.1.02: Homework
  87. 3.02: The Mean Value Theorem
  88. 3.2.01: Resources and Key Concepts
  89. 3.2.02: Homework
  90. 3.03: Shapes of Curves
  91. 3.3.01: Resources and Key Concepts
  92. 3.3.02: Homework
  93. 3.04: l'Hopital's Rule and Indeterminate Forms
  94. 3.4.01: Resources and Key Concepts
  95. 3.4.02: Homework
  96. 3.05: Graphing Using Calculus
  97. 3.5.01: Resources and Key Concepts
  98. 3.5.02: Homework
  99. 3.06: Optimization
  100. 3.6.01: Resources and Key Concepts
  101. 3.6.02: Homework
  102. 3.07: Newtons Method
  103. 3.7.01: Resources and Key Concepts
  104. 3.7.02: Homework
  105. 04: Investigating Integrals
  106. 4.01: Antiderivatives and Indefinite Integrals
  107. 4.1.01: Resources and Key Concepts
  108. 4.1.02: Homework
  109. 4.02: Approximating Areas
  110. 4.2.01: Resources and Key Concepts
  111. 4.2.02: Homework
  112. 4.03: The Definite Integral
  113. 4.3.01: Resources and Key Concepts
  114. 4.3.02: Homework
  115. 4.04: The Fundamental Theorem of Calculus
  116. 4.4.01: Resources and Key Concepts
  117. 4.4.02: Homework
  118. 4.05: The Net Change Theorem Distances and Symmetry
  119. 4.5.01: Resources and Key Concepts
  120. 4.5.02: Homework
  121. 4.06: Integration by Substitution
  122. 4.6.01: Resources and Key Concepts
  123. 4.6.02: Homework
  124. 05: Appendix
  125. 5.01: A.1- Algebraic Manipulations Critical for Calculus
  126. 5.1.01: A.1.1- Homework
  127. 5.02: A.2- Functions
  128. 5.2.01: A.2.1- Homework
  129. 5.03: A.3- Basic Classes of Functions and Their Graphs
  130. 5.3.01: A.3.1- Homework
  131. 5.04: A.4- Inverse Functions
  132. 5.4.01: A.4.1- Homework
  133. 5.05: A.5- Exponential and Logarithmic Functions
  134. 5.5.01: A.5.1- Homework
  135. 5.06: A.6- Trigonometry
  136. 5.6.01: A.6.1- Homework
  137. 5.07: A.7- Tangent Lines and Velocity
  138. 5.7.01: A.7.1- Homework
  139. 5.08: A.8- Answers to Selected Exercises
  140. 5.8.01: A.8.1- Chapter 1 Answers
  141. 5.8.02: Chapter 2 Answers
  142. 5.8.03: Chapter 3 Answers
  143. 5.8.04: Chapter 4 Answers
  144. 5.09: Diagnostic Examples
  145. 5.9.01: Chapter 1 Diagnostics