Active Calculus (Boelkins)

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Adaptive
This course offers personalized support for each student.

This online user-contributed homework course comprises of algorithmic problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other user-contributed courses, add problems from the user-contributed problem repository, or write your own problems.

How to use this course

  1. Homework: Assign high quality problems with hints and personalized feedback to develop problem-solving skills.
  2. Testing: Create summative secure online quizzes and tests in minutes. 
  3. Supplementary resources: Embed videos, class notes, and applets alongside assignments.
  4. Intervention: Use rich analytics to identify and monitor at-risk students for timely intervention.
  5. Analytics: Drill down into student performance and identify problematic or difficult topics.
  6. Flipped classroom: Assign pre-class assignments. Save precious class time for discussions.
  7. Emporium classes: Use Edfinity for individual/group work for large enrollment sections in labs.

Edfinity is a full-featured homework system that supports mathematically-aware problems with algebraic input, evaluation of mathematical expressions, randomized variants, prerequisite pathways for personalized learning, collaboration, coordinated courses, flexible configuration of students’ experience, and complete customization of assignments.

Interactive, algorithmic problems
Algebraic, graphing, open response; randomized variants, hints, and tips
Adaptive learning and personalization
Each student receives personalized support
to fill learning gaps.
Corequisite course structures
Use pre-built corequisite content,
or create your own.
LMS integration and accessibility
Connect to your LMS in minutes. VPAT here.
WeBWorK-compatible
Import and author WeBWorK problems.

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Syllabus

  1. 0 Edfinity Demo
  2. Review of Prerequisites for Calculus I
  3. 1.1 How Do We Measure Velocity? (Preview)
  4. 1.1 How Do We Measure Velocity?
  5. 1.2 The Notion of a Limit (Preview)
  6. 1.2 The Notion Of A Limit
  7. 1.3 The Derivative of a Function at a Point (Preview)
  8. 1.3 The Derivative Of A Function At A Point
  9. 1.4 The Derivative Function (Preview)
  10. 1.4 The Derivative Function
  11. 1.5 Interpreting, Estimating, and Using the Derivative (Preview)
  12. 1.5 Interpreting, Estimating, And Using The Derivative
  13. 1.6 The Second Derivative (Preview)
  14. 1.6 The Second Derivative
  15. 1.7 Limits, Continuity, And Differentiability (Preview)
  16. 1.7 Limits, Continuity, And Differentiability
  17. 1.8 The Tangent Line Approximation (Preview)
  18. 1.8A The Tangent Line Approximation (no differentiation rules)
  19. 1.8B The Tangent Line Approximation (with differentiation rules)
  20. 2.1 Elementary Derivative Rules (Preview)
  21. 2.1 Elementary Derivative Rules
  22. 2.2 Sine and Cosine Functions (Preview)
  23. 2.2 The Sine And Cosine Functions
  24. 2.3 The Product and Quotient Rules (Preview)
  25. 2.3 Product And Quotient Rules
  26. 2.4 Derivatives of Other Trigonometric Functions (Preview)
  27. 2.4 Derivatives Of Other Trigonometric Functions
  28. 2.5 The Chain Rule (Preview)
  29. 2.5 The Chain Rule
  30. 2.6 Derivatives of Inverse Functions (Preview)
  31. 2.6 Derivatives Of Inverse Functions
  32. 2.7 Derivatives of Functions Given Implicitly (Preview)
  33. 2.7 Derivatives Of Functions Given Implicitly
  34. 2.8 Using Derivatives to Evaluate Limits (Preview)
  35. 2.8 Using Derivatives To Evaluate Limits
  36. 3.1 Using Derivatives to Identify Extreme Values (Preview)
  37. 3.1 Using Derivatives To Identify Extreme Values
  38. 3.2 Using Derivatives to Describe Families of Functions (Preview)
  39. 3.2 Using Derivatives To Describe Families Of Functions
  40. 3.3 Global Optimization (Preview)
  41. 3.3 Global Optimization
  42. 3.4 Applied Optimization (Preview)
  43. 3.4 Applied Optimization
  44. 3.5 Related Rates (Preview)
  45. 3.5 Related Rates
  46. 4.1 Determining Distance Traveled From Velocity (Preview)
  47. 4.1 Determining Distance Traveled from Velocity
  48. 4.2 Riemann Sums (Preview)
  49. 4.2 Riemann Sums
  50. 4.3 The Definite Integral (Preview)
  51. 4.3 The Definite Integral
  52. 4.4 The Fundamental Theorem of Calculus (Preview)
  53. 4.4 The Fundamental Theorem of Calculus
  54. Review of Prerequisites for Calculus II
  55. 5.1 Constructing Accurate Graphs of Antiderivatives (Preview)
  56. 5.1 Constructing Accurate Graphs of Antiderivatives
  57. 5.2 The Second Fundamental Theorem of Calculus (Preview)
  58. 5.2 The Second Fundamental Theorem of Calculus
  59. 5.3 Integration by Substitution (Preview)
  60. 5.3 Integration by Substitution
  61. 5.4 Integration by Parts (Preview)
  62. 5.4 Integration By Parts
  63. 5.5 Other Options for Finding Algebraic Antiderivatives (Preview)
  64. 5.5 Other Options For Finding Algebraic Antiderivatives
  65. 5.5(i) Partial Fractions (Preview)
  66. 5.5(ii) Trigonometric Integrals (Preview)
  67. 5.5(i/ii) Partial Fractions and Trigonometric Integrals
  68. 5.6 Numerical Integration (Preview)
  69. 5.6 Numerical Integration
  70. 6.1 Using Definite Integrals to Find Area and Length (Preview)
  71. 6.1 Using Definite Integrals To Find Area And Length
  72. 6.2 Using Definite Integrals to Find Volume (Preview)
  73. 6.2 Using Definite Integrals To Find Volume
  74. 6.3 Density, Mass, and Center of Mass (Preview)
  75. 6.3 Density, Mass, And Center Of Mass
  76. 6.4 Physics Applications: Work, Force, and Pressures (Preview)
  77. 6.4 Physics Applications Work Force And Pressure
  78. 6.5 Improper Integrals (Preview)
  79. 6.5 Improper Integrals
  80. 7.1 Introduction to Differential Equations (Preview)
  81. 7.1 An Introduction To Differential Equations
  82. 7.2 Qualitative Behavior of Solutions to DEs (Preview)
  83. 7.2 Qualitative Behavior Of Solutions To DEs
  84. 7.3 Euler's Method (Preview)
  85. 7.3 Eulers Method
  86. 7.4 Separable Differential Equations (Preview)
  87. 7.4 Separable Differential Equations
  88. 7.5 Modeling with Differential Equations (Preview)
  89. 7.5 Modeling With Differential Equations
  90. 7.6 Population Growth and the Logistic Equation (Preview)
  91. 7.6 Population Growth And The Logistic Equation
  92. 8.1 Sequences (Preview)
  93. 8.1 Sequences
  94. 8.2 Geometric Series (Preview)
  95. 8.2 Geometric Series
  96. 8.3 Series of Real Numbers (Preview)
  97. 8.3 Series Of Real Numbers
  98. 8.4 Alternating Series (Preview)
  99. 8.4 Alternating Series
  100. 8.5 Taylor Polynomials and Taylor Series (Preview)
  101. 8.5 Taylor Polynomials And Taylor Series
  102. 8.6 Power Series (Preview)
  103. 8.6 Power Series

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