# Active Calculus (Boelkins)

Edfinity is supported by the National Science Foundation
This course offers personalized support for each student.

This is an online homework companion to Active Calculus. It comprises hundreds 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 catalog courses, add problems from the Edfinity problem repository, or write your own.

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.

This course was curated by Christina Safranski and the Edfinity team. Active Calculus was written by Boelkins, Austin, and Schlicker.

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

### Problem Sets

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. 1.8 The Tangent Line Approximation
19. 2.1 Elementary Derivative Rules (Preview)
20. 2.1 Elementary Derivative Rules
21. 2.2 Sine and Cosine Functions (Preview)
22. 2.2 The Sine And Cosine Functions
23. 2.3 The Product and Quotient Rules (Preview)
24. 2.3 Product And Quotient Rules
25. 2.4 Derivatives of Other Trigonometric Functions (Preview)
26. 2.4 Derivatives Of Other Trigonometric Functions
27. 2.5 The Chain Rule (Preview)
28. 2.5 The Chain Rule
29. 2.6 Derivatives of Inverse Functions (Preview)
30. 2.6 Derivatives Of Inverse Functions
31. 2.7 Derivatives of Functions Given Implicitly (Preview)
32. 2.7 Derivatives Of Functions Given Implicitly
33. 2.8 Using Derivatives to Evaluate Limits (Preview)
34. 2.8 Using Derivatives To Evaluate Limits
35. 3.1 Using Derivatives to Identify Extreme Values (Preview)
36. 3.1 Using Derivatives To Identify Extreme Values
37. 3.2 Using Derivatives to Describe Families of Functions (Preview)
38. 3.2 Using Derivatives To Describe Families Of Functions
39. 3.3 Global Optimization (Preview)
40. 3.3 Global Optimization
41. 3.4 Applied Optimization (Preview)
42. 3.4 Applied Optimization
43. 3.5 Related Rates (Preview)
44. 3.5 Related Rates
45. 4.1 Determining Distance Traveled From Velocity (Preview)
46. 4.1 Determining Distance Traveled from Velocity
47. 4.2 Riemann Sums (Preview)
48. 4.2 Riemann Sums
49. 4.3 The Definite Integral (Preview)
50. 4.3 The Definite Integral
51. 4.4 The Fundamental Theorem of Calculus (Preview)
52. 4.4 The Fundamental Theorem of Calculus
53. Review of Prerequisites for Calculus II
54. 5.1 Constructing Accurate Graphs of Antiderivatives (Preview)
55. 5.1 Constructing Accurate Graphs of Antiderivatives
56. 5.2 The Second Fundamental Theorem of Calculus (Preview)
57. 5.2 The Second Fundamental Theorem of Calculus
58. 5.3 Integration by Substitution (Preview)
59. 5.3 Integration by Substitution
60. 5.4 Integration by Parts (Preview)
61. 5.4 Integration By Parts
62. 5.5 Other Options for Finding Algebraic Antiderivatives (Preview)
63. 5.5 Other Options For Finding Algebraic Antiderivatives
64. 5.5(i) Partial Fractions (Preview)
65. 5.5(ii) Trigonometric Integrals (Preview)
66. 5.5(i/ii) Partial Fractions and Trigonometric Integrals
67. 5.6 Numerical Integration (Preview)
68. 5.6 Numerical Integration
69. 6.1 Using Definite Integrals to Find Area and Length (Preview)
70. 6.1 Using Definite Integrals To Find Area And Length
71. 6.2 Using Definite Integrals to Find Volume (Preview)
72. 6.2 Using Definite Integrals To Find Volume
73. 6.3 Density, Mass, and Center of Mass (Preview)
74. 6.3 Density, Mass, And Center Of Mass
75. 6.4 Physics Applications: Work, Force, and Pressures (Preview)
76. 6.4 Physics Applications Work Force And Pressure
77. 6.5 Improper Integrals (Preview)
78. 6.5 Improper Integrals
79. 7.1 Introduction to Differential Equations (Preview)
80. 7.1 An Introduction To Differential Equations
81. 7.2 Qualitative Behavior of Solutions to DEs (Preview)
82. 7.2 Qualitative Behavior Of Solutions To DEs
83. 7.3 Euler's Method (Preview)
84. 7.3 Eulers Method
85. 7.4 Separable Differential Equations (Preview)
86. 7.4 Separable Differential Equations
87. 7.5 Modeling with Differential Equations (Preview)
88. 7.5 Modeling With Differential Equations
89. 7.6 Population Growth and the Logistic Equation (Preview)
90. 7.6 Population Growth And The Logistic Equation
91. 8.1 Sequences (Preview)
92. 8.1 Sequences
93. 8.2 Geometric Series (Preview)
94. 8.2 Geometric Series
95. 8.3 Series of Real Numbers (Preview)
96. 8.3 Series Of Real Numbers
97. 8.4 Alternating Series (Preview)
98. 8.4 Alternating Series
99. 8.5 Taylor Polynomials and Taylor Series (Preview)
100. 8.5 Taylor Polynomials And Taylor Series
101. 8.6 Power Series (Preview)
102. 8.6 Power Series