Calculus
Calculus connects local change with global accumulation. The useful habit is to move between four views of the same problem: a formula, a graph, a numerical approximation, and a statement about units or meaning.
Learning Path
- Calculus Basics develops limits, derivatives, integrals, gradients, and optimization in sequence.
- Automatic Differentiation shows how programs evaluate derivatives without symbolic manipulation or finite differences.
- Calculus in SymPy provides a symbolic workflow for checking derivatives, integrals, limits, and series.
Questions to Carry Through the Branch
| Question | Main tool |
|---|---|
| What value does a function approach nearby? | limits and continuity |
| How quickly and in which direction is it changing? | derivatives and gradients |
| How much has accumulated over an interval? | definite integrals |
| Which input minimizes or maximizes an objective? | critical points and optimization |
| How can a program obtain derivatives reliably? | symbolic and automatic differentiation |
External References
- CLP Calculus Textbooks for rigorous, freely available single- and multivariable texts.
- MIT OpenCourseWare Single Variable Calculus and Multivariable Calculus for a complete course sequence.
- Paul's Online Math Notes for concise explanations and worked exercises.