Fourteen weeks of Calculus I
A suggested pace, with time for writing mathematics and correcting mistakes. Reading times measure exposition; exercises and proofs require additional study.
Open the continuous textbook →Before beginning, attempt the opening chapter's algebra and rate exercises. Review functions, factoring, logarithms, and radian trigonometry as needed.
Each week: read the assigned chapters, reproduce each worked example without looking, attempt every exercise before opening its solution, and write one paragraph explaining which hypotheses a theorem or model requires. Use the linked external lectures for a second explanation.
Functions, units, and limits
Domain restrictions; average rates; punctured neighborhoods; one-sided limits.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Limit calculations and proofs
Limit laws with hypotheses; factoring and conjugates; squeezing; epsilon–delta arguments.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Continuity and the derivative
Continuity, IVT and EVT; secant limits; differentiability and its consequences.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Derivative functions and rules
First-principles derivatives; domain; sum, product, and quotient rules.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Composition and elementary functions
Chain rule; trigonometric, exponential, logarithmic, and inverse derivatives.
- Chapter 9 · Composition and Trigonometric Derivatives
- Chapter 10 · Exponentials, Logarithms, and Inverses
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Constraints and related rates
Implicit differentiation; local branches; time-dependent geometric constraints.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
The mean value theorem and approximation
Rolle and MVT; monotonicity consequences; local linearization and error bounds.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Function behavior
Monotonicity, concavity, local and absolute extrema, and curve analysis.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Optimization and indeterminate forms
Constrained modeling; endpoints; justified use of L’Hôpital’s rule.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Antiderivatives and accumulation
Initial-value problems; finite sums; Riemann sums; signed area and integrability.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
The fundamental theorem of calculus
Accumulation derivatives; evaluation theorem; hypotheses and proof ideas.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Substitution and definite integrals
Change of variable; bounds; symmetry; average value.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Integral applications
Net change, area between curves, volumes, and units.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Synthesis and independent investigation
Connect local rates and accumulated change; defend assumptions and verify results.
Written work: Complete the chapter exercises and verify calculations. Retain a corrected solution and an explanation of the error for each unsuccessful attempt.
Concluding investigation
The reservoir investigation connects rates, extrema, accumulation, and physical feasibility. Submit your model, assumptions, derivations, error bounds for numerical approximations, and worked checks.
This is a study plan for a draft textbook. Independent mathematical and classroom review remain pending.