bythreedu · Math Tracks · Curriculum v1.0 · 2026

Limits, derivatives,
and the start of
the infinite.

A complete Calculus I course from limits through the Fundamental Theorem of Calculus. Built for students who want to understand calculus from the ground up — not just pass the exam. Every concept is derived, every technique is explained, and every application is set up before it is solved.

Total Lessons26at your pace
Units8progressive phases
Assignments8+problem sets
DestinationCalculus II
Ready
00Approach
Course Philosophy

The Limit Is the Foundation

Calculus is built on the limit — every definition, every theorem, every technique. This course takes limits seriously. Students who understand limits deeply don't struggle later when integration and series require them again.

Concepts Drive Technique

Most Calc I failures are conceptual, not computational. If you don't know what a derivative means, you can't set up a related rates problem. If you don't know what an integral is, you can't interpret the result. Concept first, mechanics second.

01Curriculum
Learning Path
01
Unit 1 · Weeks 1–2
Limits
3 lessons · Limit concept · Limit laws · Limits at infinity
limit notationindeterminate formslimits at infinity
+
02
Unit 2 · Weeks 3–4
Continuity and the Derivative Defined
3 lessons · Continuity · The difference quotient · Differentiability
continuity definitiondifference quotientdifferentiability
+
03
Unit 3 · Weeks 5–7
Differentiation Rules
3 lessons · Power rule · Product and quotient rules · Chain rule
power ruleproduct rulechain rule
+
04
Unit 4 · Weeks 8–9
Derivatives of Trig, Exp, and Log
3 lessons · Trig derivatives · e^x and ln(x) · Implicit differentiation
trig derivativese^x derivativeimplicit differentiation
+
05
Unit 5 · Weeks 10–12
Applications: Rates, Motion, Related Rates
3 lessons · Motion derivatives · Related rates · Linearization
position velocity accelerationrelated rates setuplinearization
+
06
Unit 6 · Weeks 13–15
Curve Sketching and Optimization
4 lessons · MVT · First and second derivative tests · Curve sketching
MVTfirst derivative testconcavity
+
07
Unit 7 · Weeks 16–18
Optimization and L'Hôpital's Rule
3 lessons · Optimization · Closed interval method · L'Hôpital
closed interval methodobjective functionL'Hôpital
+
08
Unit 8 · Weeks 19–26
Integration and Capstone
4 lessons + capstone · Antiderivatives · Riemann sums · FTC
antiderivativesRiemann sumsFTC
+
02Capstone
Simulated Final Exam

The capstone is a full-length Calc I final exam simulation. Every missed problem becomes a lesson — not just the right answer, but the reasoning that should have driven each step. The goal is to walk into Calc II without a single gap.

○
Gap Review
Two weakest units revisited before the exam simulation.
○
Timed Final Exam
Full-length, independent, same conditions as a real exam.
○
Written Corrections
Every missed problem corrected with reasoning — not just the right answer, but the decision that should have been made at each step.
○
Calculus II Readiness Review
A final session on what Calc II will demand from day one.
03Investment
Pricing Options
Location
per Session
$125
1.5 hrs · online only
Session length
  • —Flexible scheduling
  • —1-on-1 focused attention
  • —No long-term commitment

Best for trying the curriculum before committing to a plan.

Popular
per Month
$500
4 sessions · 1.5 hrs/session
Frequency
Session length
  • —Session notes after every lesson
  • —Async DM support between sessions
  • —Priority scheduling

Adjust frequency and session length above — price updates automatically.

Per Semester
$1,500
12 sessions · 1.5 hrs/session
Term length
Frequency
Session length
  • —Session notes after every lesson
  • —Async DM support between sessions
  • —Priority scheduling
  • —Student resource hub access
  • —Generated lesson review problems

The full Calculus I arc — from limits to the FTC — in one commitment.

📍
In-person available · NYC onlyMonthly and semester plans can be done in-person. Select "In-person · NYC" above to see adjusted pricing.
04Contact
Let's Talk

Starting Calc I for the first time or need a second pass? One session is enough to figure out where you are and what the path forward looks like.

What do I need to know coming in?+
Is this AP Calc AB or BC?+
Are lessons online or in-person?+
Can I switch plans later?+
What if I need to reschedule?+