Intuitive Learning

Understand calculus through mathematical reasoning and hands-on exploration using Python.

Active Engagement

Work through exercises, visualize concepts, and use Python libraries like NumPy and SymPy to build intuition and technical fluency.

Comprehensive Approach

No prior coding experience needed. Includes a Python tutorial for beginners and integrates symbolic math and coding for experienced learners.

About the Course

At its heart, calculus is about change. Life is full of change, and calculus is the language that humans developed (invented or discovered -- that's an ongoing debate!) to understand how physical, biological, and abstract systems change. Calculus is more than just some equations you have to memorize; it's a way of looking at the world and trying to understand how the tiniest infinitesimal changes can lead to gigantic complexity bigger than the imagination. You can learn it the way most people do -- by watching someone else scratch on a chalkboard while you furiously take notes and try to decipher their sloppy handwriting, all the while having a little voice in your head telling you that you don't get it because you're not smart enough.  Or you can try a different approach. I follow the maxim "you can learn a lot of math with a bit of coding." In this course, you will use Python to help you learn concepts, proofs, visualizations, and algorithms in calculus. This course is designed for anyone who wants to understand the beauty and power of calculus—whether you’re a student, coder, data scientist, or simply curious about the math that underlies modern technology. 

Meet Your Instructor

I am a full-time educator and writer, and former professor of neuroscience. I "retired" from my tenured job so I could focus my time and energy creating high-quality educational material just for you. I have 20 years of experience teaching coding, data analysis, signal processing, statistics, and math. I've taught undergraduate students, PhD candidates, postdoctoral researchers, and full professors. I have taught in "traditional" university courses, special week-long intensive courses, and Nobel prize-winning research labs. So trust me when I say that that you've come to the right place to maximize your learning from an instructor who has spent two decades refining and perfecting his teaching style. Over 300,000 students have watched over 50,000,000 minutes of my courses. Come find out why!

Course Curriculum

12 Chapters · 143 Lessons

  1. 1

    Introductions

    1. Prerequisites and how to rock this course Free preview
    2. Gradient fields forever (hands-on activity) Free preview
  2. 2

    Download all course materials!

    1. (Included in full purchase)

      IMPORTANT: Downloading and using the code

    2. (Included in full purchase)

      My policy on sharing code

  3. 3

    Functions

    1. (Included in full purchase)

      Section summary and goals

    2. (Included in full purchase)

      Terminology in math vs. coding

    3. (Included in full purchase)

      What is a "function"?

    4. (Included in full purchase)

      Domain and range of a function

    5. (Included in full purchase)

      Linear and nonlinear functions

    6. (Included in full purchase)

      CodeChallenge: math in python, part 1

    7. (Included in full purchase)

      CodeChallenge: math in python, part 2

    8. (Included in full purchase)

      Polynomial functions

    9. (Included in full purchase)

      CodeChallenge: polynomials, part 1

    10. (Included in full purchase)

      CodeChallenge: polynomials, part 2

    11. (Included in full purchase)

      Transcendental functions

    12. (Included in full purchase)

      Exponential and log functions

    13. (Included in full purchase)

      CodeChallenge: exp and log, part 1

    14. (Included in full purchase)

      CodeChallenge: exp and log, part 2

    15. (Included in full purchase)

      CodeChallenge: Power and log rules, part 1

    16. (Included in full purchase)

      CodeChallenge: Power and log rules, part 2

    17. (Included in full purchase)

      Trigonometric functions

    18. (Included in full purchase)

      CodeChallenge: trigonometry

    19. (Included in full purchase)

      Piecewise functions

    20. (Included in full purchase)

      CodeChallenge: piecewise functions, part 1

    21. (Included in full purchase)

      CodeChallenge: piecewise functions, part 1

    22. (Included in full purchase)

      Continuous and discontinuous functions

    23. (Included in full purchase)

      CodeChallenge: discontinuities, part 1

    24. (Included in full purchase)

      CodeChallenge: discontinuities, part 1

    25. (Included in full purchase)

      Intermediate value theorem

    26. (Included in full purchase)

      Composite functions

    27. (Included in full purchase)

      Inverse functions

    28. (Included in full purchase)

      CodeChallenge: Composite and inverse, part 1

    29. (Included in full purchase)

      CodeChallenge: Composite and inverse, part 1

    30. (Included in full purchase)

      Function symmetry (even and odd)

    31. (Included in full purchase)

      Sketching functions by hand

    32. (Included in full purchase)

      CodeChallenge: Infinite functions to sketch, part 1

    33. (Included in full purchase)

      CodeChallenge: Infinite functions to sketch, part 2

  4. 4

    Tangent: Levels of understanding

    1. (Included in full purchase)

      What does it mean to "understand math"?

    2. (Included in full purchase)

      Timescales of discovering vs. learning math

  5. 5

    Limits

    1. (Included in full purchase)

      Section summary and goals

    2. (Included in full purchase)

      Limits in geometry and algebra

    3. (Included in full purchase)

      CodeChallenge: Limits via Zeno's paradox

    4. (Included in full purchase)

      "Easy" limits by plugging in or factoring

    5. (Included in full purchase)

      One-sided limits and infinities

    6. (Included in full purchase)

      CodeChallenge: limits in numpy & sympy, part 1

    7. (Included in full purchase)

      CodeChallenge: limits in numpy & sympy, part 2

    8. (Included in full purchase)

      CodeChallenge: properties of limits, part 1

    9. (Included in full purchase)

      CodeChallenge: properties of limits, part 2

    10. (Included in full purchase)

      Continuity and discontinuities, revisited

    11. (Included in full purchase)

      CodeChallenge: Limits at discontinuities, part 1

    12. (Included in full purchase)

      CodeChallenge: Limits at discontinuities, part 2

    13. (Included in full purchase)

      Limits of trig functions, part 1

    14. (Included in full purchase)

      CodeChallenge: Confirm the trig limits

    15. (Included in full purchase)

      Squeeze theorem

    16. (Included in full purchase)

      Limits of trig functions, part 2

    17. (Included in full purchase)

      CodeChallenge: Trig limits in sympy, part 1

    18. (Included in full purchase)

      CodeChallenge: Trig limits in sympy, part 2

    19. (Included in full purchase)

      Limited limits possibilities

    20. (Included in full purchase)

      What the ?$%# is an "infinitesimal"??

    21. (Included in full purchase)

      Sketching functions by hand, part 2

    22. (Included in full purchase)

      CodeChallenge: Infinite limits exercises, part 1

    23. (Included in full purchase)

      CodeChallenge: Infinite limits exercises, part 2

  6. 6

    Tangent: Accountability in online learning

    1. (Included in full purchase)

      The pros and cons of self-directed learning

    2. (Included in full purchase)

      Suggestions for learning accountability

  7. 7

    Differentiation fundamentals

    1. (Included in full purchase)

      Section summary and goals

    2. (Included in full purchase)

      Slope of a line

    3. (Included in full purchase)

      CodeChallenge: Global and local slopes

    4. (Included in full purchase)

      Formal definition of the derivative

    5. (Included in full purchase)

      Derivative of a constant is 0 (proof)

    6. (Included in full purchase)

      Various notations of the derivative

    7. (Included in full purchase)

      CodeChallenge: derivatives in sympy

    8. (Included in full purchase)

      Interpreting derivatives plots

    9. (Included in full purchase)

      CodeChallenge: Linearity of differentiation

    10. (Included in full purchase)

      Derivatives of polynomials

    11. (Included in full purchase)

      Derivatives of cosine and sine

    12. (Included in full purchase)

      CodeChallenge: trig derivatives

    13. (Included in full purchase)

      Derivatives of absolute value and square root

    14. (Included in full purchase)

      Derivatives of log and exp

    15. (Included in full purchase)

      Critical points: Definition and applications

    16. (Included in full purchase)

      Finding critical points

    17. (Included in full purchase)

      CodeChallenge: Critical points in Python, part 1

    18. (Included in full purchase)

      CodeChallenge: Critical points in Python, part 2

    19. (Included in full purchase)

      CodeChallenge: Infinite derivatives exercises

  8. 8

    Tangent: Where does math come from?

    1. (Included in full purchase)

      Is math discovered or invented?

  9. 9

    Differentiation rules and theorems

    1. (Included in full purchase)

      Section summary and goals

    2. (Included in full purchase)

      Linearity of differentiation (proof)

    3. (Included in full purchase)

      Theorem: Differentiability implies continuity

    4. (Included in full purchase)

      Product rule

    5. (Included in full purchase)

      Chain rule

    6. (Included in full purchase)

      Quotient rule

    7. (Included in full purchase)

      CodeChallenge: product and quotient rules

    8. (Included in full purchase)

      CodeChallenge: chain rule

    9. (Included in full purchase)

      Implicit differentiation

    10. (Included in full purchase)

      Implicit differentiation proofs (log, exp, power)

    11. (Included in full purchase)

      CodeChallenge: implicit differentiation, part 1

    12. (Included in full purchase)

      CodeChallenge: implicit differentiation, part 2

    13. (Included in full purchase)

      CodeChallenge: derivative of c^x and x^x

    14. (Included in full purchase)

      Higher-order derivatives

    15. (Included in full purchase)

      CodeChallenge: Derivatives of derivatives... (part 1)

    16. (Included in full purchase)

      CodeChallenge: Derivatives of derivatives... (part 2)

    17. (Included in full purchase)

      L'Hospital's Rule for indeterminant limits

    18. (Included in full purchase)

      Rolle's Theorem

    19. (Included in full purchase)

      Mean value theorem

    20. (Included in full purchase)

      CodeChallenge: Implement the MVT algorithm

    21. (Included in full purchase)

      CodeChallenge: Use the MVT to explore functions

    22. (Included in full purchase)

      CodeChallenge: numerical approximations to MVT

    23. (Included in full purchase)

      CodeChallenge: More differentiation exercises, part 1

    24. (Included in full purchase)

      CodeChallenge: More differentiation exercises, part 1

  10. 10

    Applications

    1. (Included in full purchase)

      Section summary and goals

    2. (Included in full purchase)

      Racing functions to infinity and beyond!

    3. (Included in full purchase)

      The second derivative test

    4. (Included in full purchase)

      Code challenge: The second derivative test, part 1

    5. (Included in full purchase)

      Code challenge: The second derivative test, part 2

    6. (Included in full purchase)

      Linear approximations

    7. (Included in full purchase)

      CodeChallenge: linear approximations, part 1

    8. (Included in full purchase)

      CodeChallenge: linear approximations, part 2

    9. (Included in full purchase)

      Newton's method for finding roots

    10. (Included in full purchase)

      CodeChallenge: Newt's roots, part 1

    11. (Included in full purchase)

      CodeChallenge: Newt's roots, part 2

    12. (Included in full purchase)

      Solving simple optimization problems

    13. (Included in full purchase)

      Optimize for surface area

    14. (Included in full purchase)

      Optimize for volume

    15. (Included in full purchase)

      CodeChallenge: the farmer and Qbert

    16. (Included in full purchase)

      Gradient descent

    17. (Included in full purchase)

      CodeChallenge: Gradient descent in numpy

    18. (Included in full purchase)

      CodeChallenge: Gradient descent using sympy

  11. 11

    Tangent: The joys and challenges of learning

    1. (Included in full purchase)

      Embrace difficulties

  12. 12

    Multivariable differentiation

    1. (Included in full purchase)

      Section summary and goals

    2. (Included in full purchase)

      2D functions

    3. (Included in full purchase)

      CodeChallenge: Fun with 2D functions (numpy), part 1

    4. (Included in full purchase)

      CodeChallenge: Fun with 2D functions (numpy), part 2

    5. (Included in full purchase)

      CodeChallenge: 2D functions in sympy

    6. (Included in full purchase)

      Partial derivatives

    7. (Included in full purchase)

      CodeChallenge: Partial derivatives

    8. (Included in full purchase)

      Higher-order partial derivatives

    9. (Included in full purchase)

      CodeChallenge: Higher-order partial derivatives

    10. (Included in full purchase)

      CodeChallenge: Complete partial exercises

    11. (Included in full purchase)

      Gradients and gradient fields

    12. (Included in full purchase)

      CodeChallenge: Gradient fields, part 1

    13. (Included in full purchase)

      CodeChallenge: Gradient fields, part 2

    14. (Included in full purchase)

      Gradient descent in 2D

    15. (Included in full purchase)

      CodeChallenge: 2D gradient descent, part 1

    16. (Included in full purchase)

      CodeChallenge: 2D gradient descent, part 2

Ready to master calculus with Python?

Explore the structure behind change and complexity with hands-on learning and Python coding

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