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Calculus I Notes

Nguồn ngoài

Calculus I Notes

Mathematics
Tác giả
Kevin Palencia
Nhà xuất bản
Northern Illinois University
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LibreTexts
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CC BY
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EN
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Mục lục· 127 mục
  1. 01: Limits and Continuity
  2. 1.01: The Limit of a Function
  3. 1.02: The Limit Laws
  4. 1.03: Continuity
  5. 02: Derivatives
  6. 2.01: The Definition of the Derivative
  7. 2.02: The Derivative as a Function
  8. 2.03: Differentiation Rules
  9. 2.04: Derivatives as Rates of Change
  10. 2.05: Derivatives of Trigonometric Functions
  11. 2.06: The Chain Rule
  12. 2.07: Derivatives of Inverse Functions
  13. 2.08: Implicit Differentiation
  14. 2.09: Derivatives of Exponential and Logarithmic Functions
  15. 03: Applications of Derivatives
  16. 3.01: Related Rates
  17. 3.02: Linear Approximation
  18. 3.03: The Mean Value Theorem
  19. 3.04: Maxima and Minima
  20. 3.05: Relationship between Derivatives and the Shape of a Graph
  21. 3.06: Limits at Infinity Horizontal Asymptotes and How to Use Calculus to Sketch the Graph of a Function
  22. 3.07: Applied Optimization Problems
  23. 3.08: L'Hopital's Rule
  24. 3.09: Newton's Method
  25. 3.10: Antiderivatives
  26. 04: Introduction to Integrals
  27. 4.01: Riemann Sums
  28. 4.02: The Definite Integral
  29. 4.03: The Fundamental Theorem of Calculus
  30. 4.04: The Substitution Rule
  31. 05: Active Calculus (Boelkins et al.)
  32. 5.01: Understanding the Derivative
  33. 5.1.01: How do we Measure Velocity
  34. 5.1.02: The Notion of Limit
  35. 5.1.03: The Derivative of a Function at a Point
  36. 5.1.04: The Derivative Function
  37. 5.1.05: Interpretating Estimating and Using the Derivative
  38. 5.1.06: The Second Derivative
  39. 5.1.07: Limits Continuity and Differentiability
  40. 5.1.08: The Tangent Line Approximation
  41. 5.1.E: Understanding the Derivative (Exercises)
  42. 5.02: Computing Derivatives
  43. 5.2.01: Elementary Derivative Rules
  44. 5.2.02: The Sine and Cosine Function
  45. 5.2.03: The Product and Quotient Rules
  46. 5.2.04: Derivatives of Other Trigonometric Functions
  47. 5.2.05: The Chain Rule
  48. 5.2.06: Derivatives of Inverse Functions
  49. 5.2.07: Derivatives of Functions Given Implicitly
  50. 5.2.08: Using Derivatives to Evaluate Limits
  51. 5.2.E: Computing Derivatives (Exercises)
  52. 5.03: Using Derivatives
  53. 5.3.01: Using Derivatives to Identify Extreme Values
  54. 5.3.02: Using Derivatives to Describe Families of Functions
  55. 5.3.03: Global Optimization
  56. 5.3.04: Applied Optimization
  57. 5.3.05: Related Rates
  58. 5.3.E: Using Derivatives (Exercises)
  59. 5.04: The Definite Integral
  60. 5.4.01: Determining Distance Traveled from Velocity
  61. 5.4.02: Riemann Sums
  62. 5.4.03: The Definite Integral
  63. 5.4.04: The Fundamental Theorem of Calculus
  64. 5.4.E: The Definite Integral (Exercises)
  65. 5.05: Finding Antiderivatives and Evaluating Integrals
  66. 5.5.01: Construction Accurate Graphs of Antiderivatives
  67. 5.5.02: The Second Fundamental Theorem of Calculus
  68. 5.5.03: Integration by Substitution
  69. 5.5.04: Integration by Parts
  70. 5.5.05: Other Options for Finding Algebraic Derivatives
  71. 5.5.06: Numerical Integration
  72. 5.5.E: Finding Antiderivatives and Evaluating Integrals (Exercises)
  73. 5.06: Using Definite Integrals
  74. 5.6.01: Using Definite Integrals to Find Area and Length
  75. 5.6.02: Using Definite Integrals to Find Volume
  76. 5.6.03: Density Mass and Center of Mass
  77. 5.6.04: Physics Applications - Work Force and Pressure
  78. 5.6.05: Improper Integrals
  79. 5.6.E: Using Definite Integrals (Exercises)
  80. 5.07: Differential Equations
  81. 5.7.01: An Introduction to Differential Equations
  82. 5.7.02: Qualitative Behavior of Solutions to Differential Equations
  83. 5.7.03: Euler's Method
  84. 5.7.04: Separable Differential Equations
  85. 5.7.05: Modeling with Differential Equations
  86. 5.7.06: Population Growth and the Logistic Equation
  87. 5.7.E: Differential Equations (Exercises)
  88. 5.08: Sequences and Series
  89. 5.8.01: Sequences
  90. 5.8.02: Geometric Series
  91. 5.8.03: Series of Real Numbers
  92. 5.8.04: Alternating Series
  93. 5.8.05: Taylor Polynomials and Taylor Series
  94. 5.8.06: Power Series
  95. 5.8.E: Sequences and Series (Exercises)
  96. 5.09: Multivariable and Vector Functions
  97. 5.9.01: Functions of Several Variables and Three Dimensional Space
  98. 5.9.02: Vectors
  99. 5.9.03: Dot Product
  100. 5.9.04: The Cross Product
  101. 5.9.05: Lines and Planes in Space
  102. 5.9.06: Vector-Valued Functions
  103. 5.9.07: Derivatives and Integrals of Vector-Valued Functions
  104. 5.9.08: Arc Length and Curvature
  105. 5.10: Derivatives of Multivariable Functions
  106. 5.10.01: Limits
  107. 5.10.02: First-Order Partial Derivatives
  108. 5.10.03: Second-Order Partial Derivatives
  109. 5.10.04: Linearization- Tangent Planes and Differentials
  110. 5.10.05: The Chain Rule
  111. 5.10.06: Directional Derivatives and the Gradient
  112. 5.10.07: Optimization
  113. 5.10.08: Constrained Optimization - Lagrange Multipliers
  114. 5.11: Multiple Integrals
  115. 5.11.01: Double Riemann Sums and Double Integrals over Rectangles
  116. 5.11.02: Iterated Integrals
  117. 5.11.03: Double Integrals over General Regions
  118. 5.11.04: Applications of Double Integrals
  119. 5.11.05: Double Integrals in Polar Coordinates
  120. 5.11.06: Surfaces Defined Parametrically and Surface Area
  121. 5.11.07: Triple Integrals
  122. 5.11.08: Triple Integrals in Cylindrical and Spherical Coordinates
  123. 5.11.09: Change of Variables
  124. 5.12: Appendices
  125. 5.12.01: A- Short Table of Integrals
  126. 5.12.02: B- Answers to Activities
  127. 5.12.03: C- Answers to Selected Exercises