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

1. Calculus Basics develops limits, derivatives, integrals, gradients, and optimization in sequence.
2. Automatic Differentiation shows how programs evaluate derivatives without symbolic manipulation or finite differences.
3. 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.

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