Differential and Integral Calculus of One Variable (KPI, 2012–2013)
A complete source map of the KPI lecture notes and practicum for limits, continuity, differentiation, integration, Taylor approximation, and series. The two volumes provide a useful curricular spine, while independently verified definitions, hypotheses, derivations, and examples carry the GTK chapters.
This archive concatenates two department-authored course volumes in their teaching order: the 2012 lecture notes by Viktor O. Haidei and Lidiia B. Fedorova, followed by the 2013 practicum by Iryna V. Alieksieieva, Viktor O. Haidei, Oleksandr O. Dykhovychnyi, and Lidiia B. Fedorova. The resulting PDF has 300 physical pages: pp. 1–50 are the lecture volume and pp. 51–300 are the practicum.
Every physical page was read and visually inspected. The practicum's 250
native-text pages, renders, and coverage rows reconcile exactly; physical p.
76 of that original is an intentional blank. The two original SHA-256 values
are a6233124e215271a95a85a59f7500d31899b5ccfc6fc85437b8b2b087f399706
and 0be87a76fe1db698a4a395415d4211c81759d6d35179b8db01fdf4ae7398f04b.
Coverage and routing #
| Packet pages | Subject | GTK destination |
|---|---|---|
| 1–50 | limits, continuity, derivatives, integrals, sequences, and series | curricular and theoretical orientation across all four destinations |
| 51–56 | practicum front matter | source identity and course structure |
| 57–125 | sets and functions; limits, differential calculus, and integration | limits, continuity, derivatives, and integrals |
| 126 | intentional blank separator | no content |
| 127–164 | limits and continuity practice | limits and continuity |
| 165–208 | differential-calculus practice | derivatives; Taylor approximation |
| 209–241 | integration practice | derivatives and integrals |
| 242 | Greek alphabet reference | not a knowledge topic |
| 243–298 | elementary prerequisites and diagnostic exercises | elementary functions and equations |
| 299–300 | bibliography | source context only |
The packet is strongest as a progression from precise definitions to worked procedures. It repeatedly exposes the conditions that symbolic manipulation can hide: domains, one-sided behavior, monotonicity intervals, invertibility, convergence, and the distinction between a local formula and a global claim. GTK reorganizes this progression by durable concepts rather than reproducing the book's module order.
Reliability boundary #
The source is an admissible secondary course, not mathematical authority. Its mechanisms were checked against NIST DLMF, MIT OpenCourseWare, and OpenStax; GTK cites those independent sources for load-bearing statements. Printed defects include missing domain hypotheses, damaged answer mappings, incorrect remainder orders, sign and exponent errors, and a number of corrupted worked expressions. Those locations are preserved in the source audit rather than propagated into topic prose.
In particular, GTK uses a certified sign-changing bracket for bisection, retains absolute values in logarithmic antiderivatives, distinguishes a vertical tangent from a finite derivative, states implicit-function branch conditions, and derives Taylor remainders with the correct order. Printed answer keys are never treated as evidence.
Visual audit #
All diagrams, plots, tables, and long equation layouts were inspected. The practicum alone contains 288 discrete information-bearing visual items grouped into 96 ledger records. None is copied into GTK: several are bound to damaged examples or use notation that is too dense at article width. Their teaching roles are replaced by independently constructed, theme-aware diagrams for limits, accumulation, Taylor error, and the difference between sequence terms and partial sums.