Skip to content

Calculus I

Book Contents Navigation

Book Contents
  1. Faculty Resources
    1. Teaching Resources

    2. Evidence-Based Teaching Practices

  2. Course Resources
    1. Appendix A: Table of Integrals

    2. Glossary of Terms

    3. Students: Additional Lumen Resources

    4. Appendix B: Table of Derivatives

    5. Appendix C: Precalculus Formulas

  3. Basic Functions and Graphs
    1. Basic Functions and Graphs: Cheat Sheet

    2. Basic Functions and Graphs: Background You’ll Need 1

    3. Basic Functions and Graphs: Background You’ll Need 2

    4. Review of Functions: Learn It 1

    5. Review of Functions: Learn It 2

    6. Review of Functions: Learn It 3

    7. Review of Functions: Learn it 4

    8. Review of Functions: Learn it 5

    9. Review of Functions: Apply It

    10. Review of Functions: Fresh Take

    11. Basic Classes of Functions: Learn It 1

    12. Basic Classes of Functions: Learn It 2

    13. Basic Classes of Functions: Learn It 3

    14. Basic Classes of Functions: Learn It 4

    15. Basic Classes of Functions: Learn It 5

    16. Basic Classes of Functions: Learn It 6

    17. Basic Classes of Functions: Apply It

    18. Basic Classes of Functions: Fresh Take

    19. Basic Functions and Graphs: Get Stronger

    20. Basic Functions and Graphs: Get Stronger Answer Key

  4. More Basic Functions and Graphs
    1. More Basic Functions and Graphs: Cheat Sheet

    2. More Basic Functions and Graphs: Background You’ll Need 1

    3. More Basic Functions and Graphs: Background You’ll Need 2

    4. More Basic Functions and Graphs: Background You’ll Need 3

    5. Trigonometric Functions: Learn It 1

    6. Trigonometric Functions: Learn It 2

    7. Trigonometric Functions: Learn It 3

    8. Trigonometric Functions: Learn It 4

    9. Trigonometric Functions: Apply It

    10. Trigonometric Functions: Fresh Take

    11. Inverse Functions: Learn It 1

    12. Inverse Functions: Learn It 2

    13. Inverse Functions: Learn It 3

    14. Inverse Functions: Learn It 4

    15. Inverse Functions: Apply It

    16. Inverse Functions: Fresh Take

    17. Exponential and Logarithmic Functions: Learn It 1

    18. Exponential and Logarithmic Functions: Learn It 2

    19. Exponential and Logarithmic Functions: Learn It 3

    20. Exponential and Logarithmic Functions: Learn It 4

    21. Exponential and Logarithmic Functions: Learn It 5

    22. Exponential and Logarithmic Functions: Apply It

    23. Exponential and Logarithmic Functions: Fresh Take

    24. More Basic Functions and Graphs: Get Stronger

    25. More Basic Functions and Graphs: Get Stronger Answer Key

  5. Understanding Limits
    1. Understanding Limits: Cheat Sheet

    2. Understanding Limits: Background You’ll Need 1

    3. Understanding Limits: Background You’ll Need 2

    4. Understanding Limits: Background You’ll Need 3

    5. A Preview of Calculus: Learn It 1

    6. A Preview of Calculus: Learn It 2

    7. A Preview of Calculus: Learn It 3

    8. A Preview of Calculus: Learn It 4

    9. A Preview of Calculus: Apply It

    10. A Preview of Calculus: Fresh Take

    11. Introduction to the Limit of a Function: Learn It 1

    12. Introduction to the Limit of a Function: Learn It 2

    13. Introduction to the Limit of a Function: Learn It 3

    14. Introduction to the Limit of a Function: Learn It 4

    15. Introduction to the Limit of a Function: Apply It

    16. Introduction to the Limit of a Function: Fresh Take

    17. Understanding Limits: Get Stronger

    18. Understanding Limits: Get Stronger Answer Key

  6. Limits and Continuity
    1. Limits and Continuity: Cheat Sheet

    2. Limits and Continuity: Background You'll Need 1

    3. Limits and Continuity: Background You'll Need 2

    4. The Limit Laws: Learn It 1

    5. The Limit Laws: Learn It 2

    6. The Limit Laws: Learn It 3

    7. The Limit Laws: Learn It 4

    8. The Limit Laws: Apply It

    9. The Limit Laws: Fresh Take

    10. Continuity: Learn It 1

    11. Continuity: Learn It 2

    12. Continuity: Learn It 3

    13. Continuity: Learn It 4

    14. Continuity: Apply It

    15. Continuity: Fresh Take

    16. The Precise Definition of a Limit: Learn It 1

    17. The Precise Definition of a Limit: Learn It 2

    18. The Precise Definition of a Limit: Learn It 3

    19. The Precise Definition of a Limit: Apply It

    20. The Precise Definition of a Limit: Fresh Take

    21. Limits and Continuity: Get Stronger

    22. Limits and Continuity: Get Stronger Answer Key

  7. Introduction to Derivatives
    1. Introduction to Derivatives: Cheat Sheet

    2. Introduction to Derivatives: Background You'll Need 1

    3. Introduction to Derivatives: Background You'll Need 2

    4. Defining the Derivative: Learn It 1

    5. Defining the Derivative: Learn It 2

    6. Defining the Derivative: Learn It 3

    7. Defining the Derivative: Apply It

    8. Defining the Derivative: Fresh Take

    9. The Derivative as a Function: Learn It 1

    10. The Derivative as a Function: Learn It 2

    11. The Derivative as a Function: Learn It 3

    12. The Derivative as a Function: Learn It 4

    13. The Derivative as a Function: Apply It

    14. The Derivative as a Function: Fresh Take

    15. Differentiation Rules: Learn It 1

    16. Differentiation Rules: Learn It 2

    17. Differentiation Rules: Learn It 3

    18. Differentiation Rules: Learn It 4

    19. Differentiation Rules: Learn It 5

    20. Differentiation Rules: Apply It

    21. Differentiation Rules: Fresh Take

    22. Derivatives as Rates of Change: Learn It 1

    23. Derivatives as Rates of Change: Learn It 2

    24. Derivatives as Rates of Change: Learn It 3

    25. Derivatives as Rates of Change: Learn It 4

    26. Derivatives as Rates of Change: Apply It

    27. Derivatives as Rates of Change: Fresh Take

    28. Introduction to Derivatives: Get Stronger

    29. Introduction to Derivatives: Get Stronger Answer Key

  8. Techniques for Differentiation
    1. Techniques for Differentiation: Cheat Sheet

    2. Techniques for Differentiation: Background You'll Need 1

    3. Techniques for Differentiation: Background You'll Need 2

    4. Derivatives of Trigonometric Functions: Learn It 1

    5. Derivatives of Trigonometric Functions: Learn It 2

    6. Derivatives of Trigonometric Functions: Learn It 3

    7. Derivatives of Trigonometric Functions: Apply It

    8. Derivatives of Trigonometric Functions: Fresh Take

    9. The Chain Rule: Learn It 1

    10. The Chain Rule: Learn It 2

    11. The Chain Rule: Learn It 3

    12. The Chain Rule: Learn It 4

    13. The Chain Rule: Apply It

    14. The Chain Rule: Fresh Take

    15. Derivatives of Inverse Functions: Learn It 1

    16. Derivatives of Inverse Functions: Learn It 2

    17. Derivatives of Inverse Functions: Apply It

    18. Derivatives of Inverse Functions: Fresh Take

    19. Implicit Differentiation: Learn It 1

    20. Implicit Differentiation: Learn It 2

    21. Implicit Differentiation: Apply It

    22. Implicit Differentiation: Fresh Take

    23. Derivatives of Exponential and Logarithmic Functions: Learn It 1

    24. Derivatives of Exponential and Logarithmic Functions: Learn It 2

    25. Derivatives of Exponential and Logarithmic Functions: Learn It 3

    26. Derivatives of Exponential and Logarithmic Functions: Apply It

    27. Derivatives of Exponential and Logarithmic Functions: Fresh Take

    28. Techniques for Differentiation: Get Stronger

    29. Techniques for Differentiation: Get Stronger Answer Key

  9. Analytical Applications of Derivatives
    1. Analytical Applications of Derivatives: Cheat Sheet

    2. Analytical Applications of Derivatives: Background You'll Need 1

    3. Analytical Applications of Derivatives: Background You'll Need 2

    4. Analytical Applications of Derivatives: Background You'll Need 3

    5. Introduction to Related Rates

    6. Related Rates: Learn It 1

    7. Related Rates: Learn It 2

    8. Related Rates: Apply It

    9. Related Rates: Fresh Take

    10. Linear Approximations and Differentials: Learn It 1

    11. Linear Approximations and Differentials: Learn It 2

    12. Linear Approximations and Differentials: Learn It 3

    13. Linear Approximations and Differentials: Apply It

    14. Linear Approximations and Differentials: Fresh Take

    15. Maxima and Minima: Learn It 1

    16. Maxima and Minima: Learn It 2

    17. Maxima and Minima: Learn It 3

    18. Maxima and Minima: Apply It

    19. Maxima and Minima: Fresh Take

    20. The Mean Value Theorem: Learn It 1

    21. The Mean Value Theorem: Learn It 2

    22. The Mean Value Theorem: Learn It 3

    23. The Mean Value Theorem: Apply It

    24. The Mean Value Theorem: Fresh Take

    25. Derivatives and the Shape of a Graph: Learn It 1

    26. Derivatives and the Shape of a Graph: Learn It 2

    27. Derivatives and the Shape of a Graph: Learn It 3

    28. Derivatives and the Shape of a Graph: Apply It

    29. Derivatives and the Shape of a Graph: Fresh Take

    30. Analytical Applications of Derivatives: Get Stronger

    31. Analytical Applications of Derivatives: Get Stronger Answer Key

  10. Contextual Applications of Derivatives
    1. Contextual Applications of Derivatives: Cheat Sheet

    2. Contextual Applications of Derivatives: Background You'll Need 1

    3. Contextual Applications of Derivatives: Background You'll Need 2

    4. Contextual Applications of Derivatives: Background You'll Need 3

    5. Limits at Infinity and Asymptotes: Learn It 1

    6. Limits at Infinity and Asymptotes: Learn It 2

    7. Limits at Infinity and Asymptotes: Learn It 3

    8. Limits at Infinity and Asymptotes: Learn It 4

    9. Limits at Infinity and Asymptotes: Learn It 5

    10. Limits at Infinity and Asymptotes: Learn It 6

    11. Limits at Infinity and Asymptotes: Apply It

    12. Limits at Infinity and Asymptotes: Fresh Take

    13. Applied Optimization Problems: Learn It 1

    14. Applied Optimization Problems: Learn It 2

    15. Applied Optimization Problems: Apply It

    16. Applied Optimization Problems: Fresh Take

    17. L’Hôpital’s Rule: Learn It 1

    18. L’Hôpital’s Rule: Learn It 2

    19. L’Hôpital’s Rule: Learn It 3

    20. L’Hôpital’s Rule: Learn It 4

    21. L’Hôpital’s Rule: Apply It

    22. L’Hôpital’s Rule: Fresh Take

    23. Newton’s Method: Learn It 1

    24. Newton’s Method: Learn It 2

    25. Newton’s Method: Learn It 3

    26. Newton’s Method: Apply It

    27. Newton’s Method: Fresh Take

    28. Antiderivatives: Learn It 1

    29. Antiderivatives: Learn It 2

    30. Antiderivatives: Learn It 3

    31. Antiderivatives: Apply It

    32. Antiderivatives: Fresh Take

    33. Contextual Applications of Derivatives: Get Stronger

    34. Contextual Applications of Derivatives: Get Stronger Answer Key

  11. Introduction to Integration
    1. Introduction to Integration: Cheat Sheet

    2. Introduction to Integration: Background You'll Need 1

    3. Introduction to Integration: Background You'll Need 2

    4. Introduction to Integration: Background You'll Need 3

    5. Approximating Areas: Learn It 1

    6. Approximating Areas: Learn It 2

    7. Approximating Areas: Learn It 3

    8. Approximating Areas: Apply It

    9. Approximating Areas: Fresh Take

    10. The Definite Integral: Learn It 1

    11. The Definite Integral: Learn It 2

    12. The Definite Integral: Learn It 3

    13. The Definite Integral: Learn It 4

    14. The Definite Integral: Apply It

    15. The Definite Integral: Fresh Take

    16. The Fundamental Theorem of Calculus: Learn It 1

    17. The Fundamental Theorem of Calculus: Learn It 2

    18. The Fundamental Theorem of Calculus: Learn It 3

    19. The Fundamental Theorem of Calculus: Apply It

    20. The Fundamental Theorem of Calculus: Fresh Take

    21. Integration Formulas and the Net Change Theorem: Learn It 1

    22. Integration Formulas and the Net Change Theorem: Learn It 2

    23. Integration Formulas and the Net Change Theorem: Learn It 3

    24. Integration Formulas and the Net Change Theorem: Apply It

    25. Integration Formulas and the Net Change Theorem: Fresh Take

    26. Introduction to Integration: Get Stronger

    27. Introduction to Integration: Get Stronger Answer Key

  12. Techniques for Integration
    1. Techniques for Integration: Cheat Sheet

    2. Techniques for Integration: Background You'll Need 1

    3. Techniques for Integration: Background You'll Need 2

    4. Techniques for Integration: Background You'll Need 3

    5. Integration using Substitution: Learn It 1

    6. Integration using Substitution: Learn It 2

    7. Integration using Substitution: Apply It

    8. Integration using Substitution: Fresh Take

    9. Integrals Involving Exponential and Logarithmic Functions: Learn It 1

    10. Integrals Involving Exponential and Logarithmic Functions: Learn It 2

    11. Integrals Involving Exponential and Logarithmic Functions: Apply It

    12. Integrals Involving Exponential and Logarithmic Functions: Fresh Take

    13. Integrals Resulting in Inverse Trigonometric Functions: Learn It 1

    14. Integrals Resulting in Inverse Trigonometric Functions: Learn It 2

    15. Integrals Resulting in Inverse Trigonometric Functions: Apply It

    16. Integrals Resulting in Inverse Trigonometric Functions: Fresh Take

    17. Approximating Integrals: Learn It 1

    18. Approximating Integrals: Apply It

    19. Approximating Integrals: Fresh Take

    20. Techniques for Integration: Get Stronger

    21. Techniques for Integration: Get Stronger Answer Key

  13. Applications of Integration
    1. Applications of Integration: Cheat Sheet

    2. Applications of Integration: Background You'll Need 1

    3. Applications of Integration: Background You'll Need 2

    4. Applications of Integration: Background You'll Need 3

    5. Areas Between Curves: Learn It 1

    6. Areas Between Curves: Learn It 2

    7. Areas Between Curves: Learn It 3

    8. Areas Between Curves: Apply It

    9. Areas Between Curves: Fresh Take

    10. Determining Volumes by Slicing: Learn It 1

    11. Determining Volumes by Slicing: Learn It 2

    12. Determining Volumes by Slicing: Learn It 3

    13. Determining Volumes by Slicing: Learn It 4

    14. Determining Volumes by Slicing: Apply It

    15. Determining Volumes by Slicing: Fresh Take

    16. Volumes of Revolution: Cylindrical Shells: Learn It 1

    17. Volumes of Revolution: Cylindrical Shells: Learn It 2

    18. Volumes of Revolution: Cylindrical Shells: Learn It 3

    19. Volumes of Revolution: Cylindrical Shells: Apply It

    20. Volumes of Revolution: Cylindrical Shells: Fresh Take

    21. Arc Length of a Curve and Surface Area: Learn It 1

    22. Arc Length of a Curve and Surface Area: Learn It 2

    23. Arc Length of a Curve and Surface Area: Learn It 3

    24. Arc Length of a Curve and Surface Area: Apply It

    25. Arc Length of a Curve and Surface Area: Fresh Take

    26. Applications of Integration: Get Stronger

    27. Applications of Integration: Get Stronger Answer Key

  14. Physical Applications of Integration
    1. Physical Applications of Integration: Cheat Sheet

    2. Physical Applications of Integration: Background You'll Need 1

    3. Physical Applications of Integration: Background You'll Need 2

    4. Physical Applications of Integration: Background You'll Need 3

    5. Physical Applications: Learn It 1

    6. Physical Applications: Learn It 2

    7. Physical Applications: Learn It 3

    8. Physical Applications: Learn It 4

    9. Physical Applications: Learn It 5

    10. Physical Applications: Apply It

    11. Physical Applications: Fresh Take

    12. Moments and Centers of Mass: Learn It 1

    13. Moments and Centers of Mass: Learn It 2

    14. Moments and Centers of Mass: Learn It 3

    15. Moments and Centers of Mass: Learn It 4

    16. Moments and Centers of Mass: Apply It

    17. Moments and Centers of Mass: Fresh Take

    18. Physical Applications of Integration: Get Stronger

    19. Physical Applications of Integration: Get Stronger Answer Key

  15. Integration of Exponential, Logarithmic, and Hyperbolic Functions
    1. Integration of Exponential, Logarithmic, and Hyperbolic Functions: Cheat Sheet

    2. Integration of Exponential, Logarithmic, and Hyperbolic Functions: Background You'll Need 1

    3. Integration of Exponential, Logarithmic, and Hyperbolic Functions: Background You'll Need 2

    4. Integration of Exponential, Logarithmic, and Hyperbolic Functions: Background You'll Need 3

    5. Integrals, Exponential Functions, and Logarithms: Learn It 1

    6. Integrals, Exponential Functions, and Logarithms: Learn It 2

    7. Integrals, Exponential Functions, and Logarithms: Learn It 3

    8. Integrals, Exponential Functions, and Logarithms: Apply It

    9. Integrals, Exponential Functions, and Logarithms: Fresh Take

    10. Exponential Growth and Decay: Learn It 1

    11. Exponential Growth and Decay: Learn It 2

    12. Exponential Growth and Decay: Apply It

    13. Exponential Growth and Decay: Fresh Take

    14. Calculus of the Hyperbolic Functions: Learn It 1

    15. Calculus of the Hyperbolic Functions: Learn It 2

    16. Calculus of the Hyperbolic Functions: Learn It 3

    17. Calculus of the Hyperbolic Functions: Apply It

    18. Calculus of the Hyperbolic Functions: Fresh Take

    19. Integration of Exponential, Logarithmic, and Hyperbolic Functions: Get Stronger

    20. Integration of Exponential, Logarithmic, and Hyperbolic Functions: Get Stronger Answer Key

Students: Additional Lumen Resources

A student using a magnifying glass to get a closer look at the details in a data visualization.Welcome, students!

Here, you’ll find links to resources to support your learning in this course.

——————————————————

Alphabetical Glossary

Cheat Sheets

Essential concepts, study tips and a glossary for each module.

Basic Functions and Graphs
More Basic Functions and Graphs
Understanding Limits
Limits and Continuity
Introduction to Derivatives
Techniques for Differentiation
Analytical Applications of Derivatives
Contextual Applications of Derivatives
Introduction to Integration
Techniques for Integration
Applications of Integration
Physical Applications of Integration
Integration of Exponential, Logarithmic, and Hyperbolic Functions

Appendices

Appendix A: Table of Integrals
Appendix B: Table of Derivatives
Appendix C: Precalculus Formulas

Helpful Links

Links to external websites if you need some additional review of any concepts.

https://www.wolframalpha.com/

https://www.khanacademy.org/math

https://www.purplemath.com/

https://www.minutemathtutor.com/

http://patrickjmt.com/

http://www.mathispower4u.com/

Graphing Calculators

Links to online graphing calculators that may be helpful to use during this course.

https://www.desmos.com/calculator

https://www.meta-calculator.com/

https://www.geogebra.org/graphing?lang=en

https://www.graphcalc.com/online-graphing-calculator/

https://www.numworks.com/simulator/

Previous/next navigation

Previous: Glossary of Terms
Next: Appendix B: Table of Derivatives