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Calculus Foundations

Study this module after Semester 00 programming and algebra readiness, with the proof module’s function and quantifier language. It supplies the calculus needed for continuous probability and later numerical reasoning. Discrete probability can start before it. Existing module URLs remain unchanged.

Outcomes: reason about limits; differentiate composite functions; optimize with constraints; interpret integrals and their units; use substitution and parts; normalize densities; bound tails and local approximations; distinguish mathematical guarantees from numerical evidence.

Workload: 70–100 focused hours, estimated rather than learner-validated: lessons and selective source practice 44–62, lab and reused project 16–24, assessment and retention 10–14. Additional precalculus repair is conditional, normally 6–12 hours initially; repeat as needed. Full-book reading is not required. This is a focused single-variable pathway, not the whole MIT 18.01SC course, multivariable calculus, differential equations or real analysis.

Before you start​

Complete lesson 1’s domain, inverse, exponent, logarithm and radians checks. If these are unfamiliar, use the reading guide’s repair route; the Launchpad algebra gate alone does not establish trigonometry or logarithm readiness.

Learning sequence​

  1. Functions, units and prerequisite repair.
  2. Limits, continuity and existence.
  3. Derivatives from local change.
  4. Chain, product and implicit differentiation.
  5. Linearization and constrained optimization.
  6. Accumulation and the fundamental theorem.
  7. Substitution and integration by parts.
  8. Improper integrals and continuous probability.
  9. Taylor polynomials and error budgets.
  10. Numerical integration and bracketed roots.

Then complete worked examples, practice, the guided lab, project and assessment. Use the reading guide to allocate study time and choose exercises.

Progression​

Pass CAL1–CAL6 before continuous probability lessons; CAL7 completes the executable and numerical strand. All seven are required for module completion. Proceed through the probability module for modeling and statistics, which are not replaced here. Calculus is not a prerequisite for elementary discrete algorithms; follow the specific target module’s prerequisites and complete the semester gates for semester completion.

Status: authored candidate; independent mathematical review and learner pilot pending. Preserve original mistakes, corrections, help received and delayed checks.