Active Calculus

by Matthew Boelkins, David Austin & Steven Schlicker

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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.

Description from LibreTexts.

Publisher
Grand Valley State University
Subjects
Mathematics
Licence
CC BY-SA 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Understanding the Derivative
  7. 1.1: How do we Measure Velocity?
  8. 1.2: The Notion of Limit
  9. 1.3: The Derivative of a Function at a Point
  10. 1.4: The Derivative Function
  11. 1.5: Interpretating, Estimating, and Using the Derivative
  12. 1.6: The Second Derivative
  13. 1.7: Limits, Continuity, and Differentiability
  14. 1.8: The Tangent Line Approximation
  15. 1.9: Understanding the Derivative (Exercises)
  16. 2: Computing Derivatives
  17. 2.1: Elementary Derivative Rules
  18. 2.2: The Sine and Cosine Function
  19. 2.3: The Product and Quotient Rules
  20. 2.4: Derivatives of Other Trigonometric Functions
  21. 2.5: The Chain Rule
  22. 2.6: Derivatives of Inverse Functions
  23. 2.7: Derivatives of Functions Given Implicitly
  24. 2.8: Using Derivatives to Evaluate Limits
  25. 2.9: Computing Derivatives (Exercises)
  26. 3: Using Derivatives
  27. 3.1: Using Derivatives to Identify Extreme Values
  28. 3.2: Using Derivatives to Describe Families of Functions
  29. 3.3: Global Optimization
  30. 3.4: Applied Optimization
  31. 3.5: Related Rates
  32. 3.6: Using Derivatives (Exercises)
  33. 4: The Definite Integral
  34. 4.1: Determining Distance Traveled from Velocity
  35. 4.2: Riemann Sums
  36. 4.3: The Definite Integral
  37. 4.4: The Fundamental Theorem of Calculus
  38. 4.5: The Definite Integral (Exercises)
  39. 5: Finding Antiderivatives and Evaluating Integrals
  40. 5.1: Construction Accurate Graphs of Antiderivatives
  41. 5.2: The Second Fundamental Theorem of Calculus
  42. 5.3: Integration by Substitution
  43. 5.4: Integration by Parts
  44. 5.5: Other Options for Finding Algebraic Derivatives
  45. 5.6: Numerical Integration
  46. 5.7: Finding Antiderivatives and Evaluating Integrals (Exercises)
  47. 6: Using Definite Integrals
  48. 6.1: Using Definite Integrals to Find Area and Length
  49. 6.2: Using Definite Integrals to Find Volume
  50. 6.3: Density, Mass, and Center of Mass
  51. 6.4: Physics Applications - Work, Force, and Pressure
  52. 6.5: Improper Integrals
  53. 6.6: Using Definite Integrals (Exercises)
  54. 7: Differential Equations
  55. 7.1: An Introduction to Differential Equations
  56. 7.2: Qualitative Behavior of Solutions to Differential Equations
  57. 7.3: Euler's Method
  58. 7.4: Separable Differential Equations
  59. 7.5: Modeling with Differential Equations
  60. 7.6: Population Growth and the Logistic Equation
  61. 7.7: Differential Equations (Exercises)
  62. 8: Sequences and Series
  63. 8.1: Sequences
  64. 8.2: Geometric Series
  65. 8.3: Series of Real Numbers
  66. 8.4: Alternating Series
  67. 8.5: Taylor Polynomials and Taylor Series
  68. 8.6: Power Series
  69. 8.7: Sequences and Series (Exercises)
  70. 9: Multivariable and Vector Functions
  71. 9.1: Functions of Several Variables and Three Dimensional Space
  72. 9.2: Vectors
  73. 9.3: Dot Product
  74. 9.4: The Cross Product
  75. 9.5: Lines and Planes in Space
  76. 9.6: Vector-Valued Functions
  77. 9.7: Derivatives and Integrals of Vector-Valued Functions
  78. 9.8: Arc Length and Curvature
  79. 10: Derivatives of Multivariable Functions
  80. 10.1: Limits
  81. 10.2: First-Order Partial Derivatives
  82. 10.3: Second-Order Partial Derivatives
  83. 10.4: Linearization- Tangent Planes and Differentials
  84. 10.5: The Chain Rule
  85. 10.6: Directional Derivatives and the Gradient
  86. 10.7: Optimization
  87. 10.8: Constrained Optimization - Lagrange Multipliers
  88. 11: Multiple Integrals
  89. 11.1: Double Riemann Sums and Double Integrals over Rectangles
  90. 11.2: Iterated Integrals
  91. 11.3: Double Integrals over General Regions
  92. 11.4: Applications of Double Integrals
  93. 11.5: Double Integrals in Polar Coordinates
  94. 11.6: Surfaces Defined Parametrically and Surface Area
  95. 11.7: Triple Integrals
  96. 11.8: Triple Integrals in Cylindrical and Spherical Coordinates
  97. 11.9: Change of Variables
  98. 12: Appendices
  99. 12.1: A- Short Table of Integrals
  100. 12.2: B- Answers to Activities
  101. 12.3: C- Answers to Selected Exercises
  102. Back Matter
  103. Index
  104. Glossary
  105. Detailed Licensing