MATH 110 — Calculus I

Mathematics & Science · 4 units · Semester 1 · Required core — everyone takes it

Overview

Calculus is the mathematics of motion, and you already know the motion. Every drop-in, racing line, and fading swell is a curve; the derivative is what it feels like at exactly this instant. At SDIT every concept arrives physical before formal — you see it move, then you name it, then you compute with it. The notation is the last step, never the first.

Taught as The Mathematics of Motion: ramp transitions, swell decay, the moment a turn is tightest. By the time limits and derivatives appear as symbols, they’re descriptions of things you’ve watched happen — which is the only way the symbols ever meant anything to anyone.

One day a week, about ten minutes a sitting, with problems that start in the world and end on the page. AI tools stay open for exploration; your own unassisted command of the material is examined, because the degree certifies you, not your tools.

The Two Registers

• Catalog register: Differential calculus — limits, derivatives, optimization, with applications. Transfer-legible Calculus I.
• Teaching frame: The Mathematics of Motion — every concept physical before formal: the drop-in, the racing line, the fading swell, finally explained.

Learning Outcomes

By the end of this course you can:

1. Evaluate limits and compute derivatives of polynomial, trigonometric, exponential, and composed functions. → Craft
2. Model position, velocity, and acceleration from real motion, and interpret a derivative physically before symbolically. → Judgment
3. Solve optimization and related-rates problems drawn from physical situations, and defend the setup, not just the answer. → Judgment · Craft
4. Move fluently between graphical, numerical, and symbolic representations of the same behavior. → Breadth of Mind
5. Demonstrate the above unassisted, in periodic written examinations. → Command of Intelligence

Each outcome maps to the five institutional outcomes (Judgment, Command of Intelligence, Craft, Articulation, Breadth of Mind) — the assessment spine of the degree and its accreditation evidence file.

The Made Thing

A motion study: a real moving thing — a ride, a wave, a thrown object, a song’s envelope — measured, modeled, and explained in the language of derivatives, presented with the data and the mathematics side by side.

How You’re Assessed

• Weekly problem sets — AI tools open; what’s graded is your setup, your verification, and your explanation.
• The motion study, presented and defended.
• Unassisted written examinations — limits, derivatives, and modeling with the tools closed. AI-native, not AI-dependent.
• Everything lands in your portfolio, reviewed against the five outcomes at the end-of-year gate.

The Daily Path

One session per course day — each one built to look easy and pull you in: one thing to experience, one idea, one question to carry. The schedule below is generated from the course’s own day files.

Day 01 — Zoom In Until It’s Straight

Ten minutes. One video, one trick, one question. No equations today.

Begin Day 01 →

Day 02 — coming soon

Being written — publishes with Week 2. All five courses advance together, week by week.

Day 03 — coming soon

Being written — publishes with Week 3. All five courses advance together, week by week.

Day 04 — coming soon

Being written — publishes with Week 4. All five courses advance together, week by week.

Day 05 — coming soon

Being written — publishes with Week 5. All five courses advance together, week by week.

Day 06 — coming soon

Being written — publishes with Week 6. All five courses advance together, week by week.

Day 07 — coming soon

Being written — publishes with Week 7. All five courses advance together, week by week.

Day 08 — coming soon

Being written — publishes with Week 8. All five courses advance together, week by week.

Day 09 — coming soon

Being written — publishes with Week 9. All five courses advance together, week by week.

Day 10 — coming soon

Being written — publishes with Week 10. All five courses advance together, week by week.

Day 11 — coming soon

Being written — publishes with Week 11. All five courses advance together, week by week.

Day 12 — coming soon

Being written — publishes with Week 12. All five courses advance together, week by week.

Day 13 — coming soon

Being written — publishes with Week 13. All five courses advance together, week by week.

Day 14 — coming soon

Being written — publishes with Week 14. All five courses advance together, week by week.

Day 15 — coming soon

Being written — publishes with Week 15. All five courses advance together, week by week.

Every course here is built to one standard: it ends in a made thing you can show, and it ships day by day.