Course
MA0 A
Term
Spring 2026
Schedule
Mon / Wed Lecture + Fri Workshop
Lessons
2
Course overview
We begin with functions, graphs, and the idea of limit, then define the derivative as a rate of change and a slope. The course builds the standard differentiation rules, tangent-line approximations, curve sketching, and first applications to motion and optimization without assuming prior calculus.
- Build the derivative from limits instead of starting with a bag of formulas.
- Learn the product, quotient, and chain rules well enough to use them fluently.
- Apply differentiation to motion, extrema, and local approximation.
Weekly rhythm
- Read the lesson page first and work through the examples in order.
- Work the practice problems immediately after the notes while the algebra is still fresh.
- Use graphs and small tables of values to sanity-check each symbolic computation.
- Attempt any challenge exercises last, once the core techniques feel automatic.
Course themes
- Functions, graphs, domains, ranges, and the language of mathematical models.
- Limits and continuity as the bridge from algebra to calculus.
- Derivative rules, implicit differentiation, and tangent-line approximation.
- Applications to velocity, optimization, monotonicity, and concavity.
Prerequisites
No prerequisites.
Course direction
The course is meant to remove the mystery from differentiation so later courses can assume fluency instead of rushing the foundations.
References
Outside notes, textbooks, or course pages worth keeping around.
course inspiration
MIT 18.01.1x: Calculus 1A - Differentiation
MIT's differentiation-focused course page. Good fit for the tone of this class: computational, geometric, and application-aware without turning into analysis.
main reference
OpenStax Calculus Volume 1
A more standard first-course text than Spivak: clearer, lighter on proofs, and better aligned with an A-level-to-early-university transition.
alternate reference
Essential Calculus: Early Transcendentals by James Stewart
A more traditional calculus text with lots of worked examples and routine practice. Useful if you want a familiar classroom-style backup reference.