Interactive pages that follow the chapter order and teaching pace of The Calculus Lifesaver — not a translation dump, not an outline placeholder. Explanations, examples, and drills are original. Every chapter has a figure you can drive, plus worked examples.
Built for HKUST(GZ) BEng(AI): get single-variable calculus standing, then plug into the year plan’s probability, optimization, and stochastic processes.
Read it against Banner’s book. Do not treat it as a replacement. The book owns detail and drill volume. These pages own the geometric intuition of each chapter, made draggable — when you stall, open the matching chapter, read the one-line takeaway, and use the lab.
The 10 chapters marked must are the skeleton: limits, continuity/differentiability, differentiation, exp/log, optimization, definite integrals, FTC, series, Taylor, ODEs. Chapters marked “drill” are Banner’s How-to chapters — you may go fast, but do not skip them empty; they are craft, not new ideas.
Copyright, one line
This course tracks the book’s table of contents and pace. It does not excerpt Banner’s prose or the Chinese translation. You may say “see Chapter X”; you may not treat this as an ebook of the book.
Every chapter is built the same way
The whole course was rearranged as intuition first, formalization second. Open any chapter and the order is identical:
Slot
What it answers
In plain words
The one sentence of the chapter. First, before definitions.
One figure
The core of the chapter drawn as one picture.
Key words
3–5 new terms, each with a two-to-four-word hook.
Full recap (folded)
The dense bullet list, for review; skip on first read.
Common deaths
Right after a concept: how most people get this wrong, and the correct move.
Lab + watch list
Three questions to answer yourself before you drag.
AI hook
Always the section before the examples. Answers “what does this have to do with what I build?”
Example · Think 30 seconds
A prompt between stem and solution. Think first.
Drills / terms / Banner
Five-tier exercises, EN/ZH glossary, section map to the book.
How this stacks with school and the year plan
Q1 school has UFUG1105 Honors Calculus I (single-variable). The year plan already said: self-study does not redo calculus — this course is the interactive companion to the school class, not a parallel course. What you must add yourself in Q2 is 18.02 multivariable (gradient / Jacobian / Lagrange). That is the next layer; it is not in Banner.
Route AWalk the whole book (recommended, ~10–14 weeks)
Chapter 1 → 30 in order. Use the drill chapters (4 / 6 / 18–19 / 21 / 23 / 25–26) on problem Saturdays; on weekdays drag the must-chapter labs first.
Route BSkeleton only (~4 weeks, pairs with Honors Calc I)
1 functions → 3 limits → 5 continuity / differentiability → 6 differentiation → 9 exp / log → 13 optimization / linearization → 15–16 integrals → 17 FTC → 22 series → 24 Taylor → 30 ODEs. Wherever the school class is, open that page as the lab bench.
Route CWarm-up for probability / optimization (~10 days) 5 definition of the derivative (later gradients are the high-dimensional version) → 9 $e^x$ and $\ln$ (parts of cross-entropy and softmax) → 13 linearization and extrema (1-D prototype of gradient descent) → 16–17 definite integrals and FTC (continuous expectation $\mathbb{E}[X]=\int x f(x)\,dx$) → 22 series (intuition for characteristic / generating functions) → 24 Taylor (any local quadratic model) → 30 ODEs (deterministic precursor of stochastic calculus).
Chapters 22 / 24 / 30 are reusable parts: series, local polynomials, ODEs. Revisit when you need them; do not re-grind the book.
Relation to the 18.06 course
Visual language, navigation, one-page-per-lecture, folded answers — the same skin. Linear algebra is done (34 lectures). Calculus is the next public artifact.
04关于目录的声明
诚实标注
章名中英对照来自 Banner, The Calculus Lifesaver（Princeton, 2007）目录，以及人民邮电《普林斯顿微积分读本（修订版）》中译目录。附录 A「极限及其证明」、附录 B「估算积分」按原书附录收录。若你手上的版本分节编号有出入，以纸书目录为准，本课按章对齐。
04A note on the table of contents
Labeled honestly
Chinese/English chapter names follow Banner, The Calculus Lifesaver (Princeton, 2007), and the Posts & Telecom Chinese edition. Appendix A “Limits and Proofs” and Appendix B “Estimating Integrals” follow the book’s appendices. If your print edition numbers sections differently, the paper TOC wins; this course aligns by chapter.