Single-Variable Calculus

Learning outcomes

What learners can expect

1. Use limits to reason about local behaviour, continuity, asymptotics, and instantaneous rates.
2. Derive and compute derivatives using definitions and structural differentiation rules.
3. Use derivatives for approximation, optimization, related rates, and qualitative curve analysis.
4. Build definite integrals from accumulation and evaluate them using the Fundamental Theorem and core techniques.
5. Model area, volume, work, mass, and other distributed quantities with definite integrals.
6. Solve simple separable models, analyse equilibria, and compare analytic solutions with Euler approximations.
7. Reason about partial-sum convergence and construct Taylor polynomials with quantitative error/range-of-usefulness arguments.
8. Integrate analytic calculus, numerical approximation, accumulation, Taylor approximation, and constrained optimization in a reproducible one-variable dynamic model.