Calculus for Computer Science

By the end, you can

• Explain the derivative as the limit of a secant slope and read slope-sign information off a curve.
• Apply the power rule and chain rule to compute derivatives of polynomial and composite functions.
• Define the gradient and explain why gradient descent subtracts it (not adds it) to minimize loss.
• Trace one step of gradient descent given a starting value, learning rate, and gradient formula.
• Describe what happens when the learning rate is too small or too large.
• Explain backpropagation as the chain rule run backward through a neural network's layers.
• Interpret the definite integral as accumulated area and evaluate simple integrals using the Fundamental Theorem of Calculus.
• Name four areas of CS where calculus plays a direct role: ML training, probability, optimization, and simulation.