Calculus for Machine Learning by Jon Krohn

About this course

Machine learning models do not learn by magic; they learn by measuring error and systematically reducing it. That process is calculus in action. This course connects the essential ideas of single-variable and multivariable calculus directly to how modern AI systems are trained, so the symbols on the page become tools you can recognize inside gradient descent, backpropagation, and everyday model debugging.

You will develop intuition for limits and what they reveal about behavior near a point, then translate that intuition into derivatives as rates of change and slopes of tangent lines. From there, the course builds the core differentiation rules that power optimization, showing how to move from a function to its gradient efficiently and correctly. Instead of treating formulas as isolated tricks, you learn why they work, how to choose the right rule for a given expression, and how those choices map to the way learning algorithms adjust parameters to reduce loss.

As the course advances into partial derivatives and the multivariate chain rule, you will see how training objectives depend on many parameters at once, and why the direction and sign of a gradient determine the next update step. You will also bridge the gap between theory and practice through automatic differentiation, the engine beneath libraries such as PyTorch and TensorFlow. By understanding how computation graphs represent functions and how reverse-mode differentiation scales to large models, you gain a clearer mental model of what your framework is doing when it computes gradients.

Integral calculus appears not as an abstract ending, but as a practical way to quantify accumulation and area. The course ties integration to evaluation concepts such as measuring performance across thresholds, including intuition for area under curves and numerical methods that approximate integrals when data comes in discrete points.

With frequent exercises, this course helps you become more confident reading ML papers, implementing training loops, and reasoning about optimization behavior. If you have ever used an AI library without feeling grounded in the math beneath it, this is the bridge from calculus fundamentals to machine learning competence.