bythreedu · Math Tracks · Curriculum v1.0 · 2026

Integration techniques,
series, and the mathematics
of convergence.

A complete Calculus II course covering integration techniques, improper integrals, geometric applications, sequences and series, power series, Taylor series, and an introduction to parametric and polar. Built for students who finished Calc I and are ready to go deeper.

Total Lessons19at your pace
Units6progressive phases
Assignments6+problem sets
DestinationCalculus III
Ready
00Approach
Course Philosophy

Techniques Are Tools, Not Tricks

Every integration technique in this course is derived before it is applied. U-substitution comes from the chain rule. Integration by parts comes from the product rule. Understanding the origin of each method is what lets you choose the right one.

Series Require Real Understanding

The convergence tests are not a flowchart to follow — they are theorems with conditions. This course builds intuition for why series converge or diverge before introducing formal tests, so you understand what each test is actually measuring.

01Curriculum
Learning Path
01
Unit 1 · Weeks 1–3
Integration Techniques
4 lessons · U-substitution · Integration by parts · Trig integrals · Partial fractions
u-substitutionintegration by partspartial fractions
+
02
Unit 2 · Weeks 4–5
Improper Integrals and Applications
3 lessons · Improper integrals · Area between curves · Arc length
improper integralsconvergencearea between curves
+
03
Unit 3 · Weeks 6–8
Volumes of Solids
3 lessons · Disk and washer · Shell method · Method selection
disk methodwasher methodshell method
+
04
Unit 4 · Weeks 9–11
Sequences and Series
3 lessons · Sequences · Series convergence · Convergence tests
convergence testsgeometric seriesp-series
+
05
Unit 5 · Weeks 12–14
Power Series and Taylor Series
3 lessons · Power series · Taylor series · Applications
radius of convergenceTaylor seriesMaclaurin series
+
06
Unit 6 · Weeks 15–18
Parametric, Polar, and Capstone
3 lessons + capstone · Parametric equations · Polar coordinates · Conic sections
parametric derivativespolar areaconic sections in polar
+
02Capstone
Simulated Final Exam

The capstone is a full-length Calc II 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 III 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.
○
Calculus III Readiness Review
A final session on what multivariable calculus 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
$2,000
16 sessions · 1.5 hrs/session
Term length
Frequency
Session length
  • —All 6 units — full course arc
  • —Session notes after every lesson
  • —Capstone simulated final + written corrections
  • —Calculus III readiness review at completion

The full Calculus II arc — from integration techniques to Taylor series — 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

Finished Calc I and ready to keep going? One session is enough to see where you are and map out the path forward.

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