Free module · Calculus & mathematical models
Differential Calculus: Limits & Derivatives
Understand change, then learn the rules for measuring it. No finance background is needed.
functions · limits · slopes · chain rule · optimisation
The building blocks
- First calculate outputs.
- Then compare two outputs.
- A slope is output change divided by input change.
- Compute a finite change and slope
- Take a limit and apply derivative rules
- Use curvature and optimization
Lessons in this module
- Start with a straight line: input, output and slope
- Functions, limits and continuity
- The derivative: from an average slope to an instantaneous rate
- Core derivative rules: constants, powers and sums
- Derivative rules: powers, products, quotients and compositions
- Second derivatives, Taylor expansions and numerical error
- Stationary points, optimisation and Newton’s method
Practice and apply
- Build a tangent and check its error — For f(x)=x³ at x=2, estimate f(2.1) using first and second derivatives.
- Evaluate a function — For f(x)=2x+1, calculate f(4).
- Constant slope — Find the derivative of f(x)=9.
Work through the practice exercises · Quant development tools