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Selective reading and prerequisite repair

Use the local lessons first, then read the named source sections and solve problems. External reading supplements the original local teaching. No book purchase or conversion is required.

Precalculus repair — conditional​

In OpenStax Calculus Volume 1, use the contents to study sections 1.1 functions, 1.2 basic classes, 1.3 trigonometric functions, 1.4 inverse functions and 1.5 exponential/logarithmic functions. Concentrate on domains, composition, graph shape, radians, inverse restrictions and solving exponential equations. Initially allow 6–12 hours beyond the core. Recheck on changed examples; unfamiliarity may require a longer precalculus course.

Core reading and problem selection — 44–62 hours including local lessons​

  1. Functions and limits: 8–12 hours. Volume 1 sections 1.1–1.5 as review, then 2.2–2.5 for limits, limit laws, continuity and a first precise definition. Solve 6 problems: two algebraic limits, two one-sided/continuity cases, one domain restriction, one linear epsilon-delta argument.
  2. Derivatives and applications: 12–16 hours. Volume 1 sections 3.1–3.6, 3.8–3.9, 4.2, 4.6 and 4.8. Solve 10 problems covering definition, product, quotient, chain, implicit differentiation, logs, trigonometry, linearization and two constrained extrema. Include endpoints and a nondifferentiable case.
  3. Accumulation and integration: 10–14 hours. Volume 1 sections 5.1–5.5; Volume 2 section 3.1 for integration by parts. Solve 8 problems: a Riemann sum, signed area, units, both fundamental theorem directions, two substitutions and one parts calculation.
  4. Tails and density: 6–8 hours. Volume 2 section 3.7. Solve 4 problems: one convergent tail, one divergent integral, one density normalization and one expectation. Use the local density exercises where the source lacks a probability prompt.
  5. Approximation and numerical guarantees: 8–12 hours. Volume 2 sections 3.6 and 6.3, selecting trapezoids and finite Taylor remainder bounds. Solve 4 problems: two polynomial/error bounds, one quadrature bound, one bisection iteration budget. Infinite series tests and Simpson’s rule are optional.

Select source end-of-section problems matching these descriptions, record their section/number and URL, and prefer problems with answers for self-checking. Spread choices across topics; do not select only routine substitutions. If a prompt requires an omitted technique, replace it and record why. This is a 32-problem minimum practice contract, not a reading-completion gate; use the local assessment to demonstrate independent transfer. Extra attempts belong within these estimates when possible; record actual times.

Alternative explanations​

MIT 18.01SC Single Variable Calculus offers lectures, problems and exams. Use Units 1–2 for differentiation, Unit 3 for accumulation, Unit 4 Part B for parts, and Unit 5 for improper integrals/Taylor. In Unit 3 Part C, sessions 60–65 connect averages, probability and numerical integration. These are optional alternative explanations, not an additional full course assignment.

Stop reading when you can solve and explain the changed problem. Keep source links and your own notes rather than copying chapters into the curriculum.