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Active Calculus

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Active Calculus

The style of the Active Calculus text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number.

CalculusMathematics
Author
Matthew Boelkins, David Austin & Steven Schlicker
Publisher
Grand Valley State University
Source
LibreTexts
License
CC BY-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 96 sections
  1. 01: Understanding the Derivative
  2. 1.01: How do we Measure Velocity
  3. 1.02: The Notion of Limit
  4. 1.03: The Derivative of a Function at a Point
  5. 1.04: The Derivative Function
  6. 1.05: Interpretating Estimating and Using the Derivative
  7. 1.06: The Second Derivative
  8. 1.07: Limits Continuity and Differentiability
  9. 1.08: The Tangent Line Approximation
  10. 1.E: Understanding the Derivative (Exercises)
  11. 02: Computing Derivatives
  12. 2.01: Elementary Derivative Rules
  13. 2.02: The Sine and Cosine Function
  14. 2.03: The Product and Quotient Rules
  15. 2.04: Derivatives of Other Trigonometric Functions
  16. 2.05: The Chain Rule
  17. 2.06: Derivatives of Inverse Functions
  18. 2.07: Derivatives of Functions Given Implicitely
  19. 2.08: Using Derivatives to Evaluate Limits
  20. 2.E: Computing Derivatives (Exercises)
  21. 03: Using Derivatives
  22. 3.01: Using Derivatives to Identify Extreme Values
  23. 3.02: Using Derivatives to Describe Families of Functions
  24. 3.03: Global Optimization
  25. 3.04: Applied Optimization
  26. 3.05: Related Rates
  27. 3.E: Using Derivatives (Exercises)
  28. 04: The Definite Integral
  29. 4.01: Determining Distance Traveled from Velocity
  30. 4.02: Riemann Sums
  31. 4.03: The Definite Integral
  32. 4.04: The Fundamental Theorem of Calculus
  33. 4.E: The Definite Integral (Exercises)
  34. 05: Finding Antiderivatives and Evaluating Integrals
  35. 5.01: Construction Accurate Graphs of Antiderivatives
  36. 5.02: The Second Fundamental Theorem of Calculus
  37. 5.03: Integration by Substitution
  38. 5.04: Integration by Parts
  39. 5.05: Other Options for Finding Algebraic Derivatives
  40. 5.06: Numerical Integration
  41. 5.E: Finding Antiderivatives and Evaluating Integrals (Exercises)
  42. 06: Using Definite Integrals
  43. 6.01: Using Definite Integrals to Find Area and Length
  44. 6.02: Using Definite Integrals to Find Volume
  45. 6.03: Density Mass and Center of Mass
  46. 6.04: Physics Applications - Work Force and Pressure
  47. 6.05: Improper Integrals
  48. 6.E: Using Definite Integrals (Exercises)
  49. 07: Differential Equations
  50. 7.01: An Introduction to Differential Equations
  51. 7.02: Qualitative Behavior of Solutions to Differential Equations
  52. 7.03: Euler's Method
  53. 7.04: Separable Differential Equations
  54. 7.05: Modeling with Differential Equations
  55. 7.06: Population Growth and the Logistic Equation
  56. 7.E: Differential Equations (Exercises)
  57. 08: Sequences and Series
  58. 8.01: Sequences
  59. 8.02: Geometric Series
  60. 8.03: Series of Real Numbers
  61. 8.04: Alternating Series
  62. 8.05: Taylor Polynomials and Taylor Series
  63. 8.06: Power Series
  64. 8.E: Sequences and Series (Exercises)
  65. 09: Multivariable and Vector Functions
  66. 9.01: Functions of Several Variables and Three Dimensional Space
  67. 9.02: Vectors
  68. 9.03: Dot Product
  69. 9.04: The Cross Product
  70. 9.05: Lines and Planes in Space
  71. 9.06: Vector-Valued Functions
  72. 9.07: Derivatives and Integrals of Vector-Valued Functions
  73. 9.08: Arc Length and Curvature
  74. 10: Derivatives of Multivariable Functions
  75. 10.01: Limits
  76. 10.02: First-Order Partial Derivatives
  77. 10.03: Second-Order Partial Derivatives
  78. 10.04: Linearization- Tangent Planes and Differentials
  79. 10.05: The Chain Rule
  80. 10.06: Directional Derivatives and the Gradient
  81. 10.07: Optimization
  82. 10.08: Constrained Optimization- Lagrange Multipliers
  83. 11: Multiple Integrals
  84. 11.01: Double Riemann Sums and Double Integrals over Rectangles
  85. 11.02: Iterated Integrals
  86. 11.03: Double Integrals over General Regions
  87. 11.04: Applications of Double Integrals
  88. 11.05: Double Integrals in Polar Coordinates
  89. 11.06: Surfaces Defined Parametrically and Surface Area
  90. 11.07: Triple Integrals
  91. 11.08: Triple Integrals in Cylindrical and Spherical Coordinates
  92. 11.09: Change of Variables
  93. 12: Appendices
  94. 12.01: A- Short Table of Integrals
  95. 12.02: B- Answers to Activities
  96. 12.03: C- Answers to Selected Exercises