01
The accumulation function
Sweep across a curve and watch the area-so-far become a new function, the heart of the Fundamental Theorem.
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All courses
MTH 264
Calculus II
Continues the study of calculus of algebraic and transcendental functions including rectangular, polar, and parametric graphing, indefinite and definite integrals, methods of integration, and power series along with applications.
How this course is taught: Taught in person. This page has selected videos, demos, the book, and free resources.
How to use this page
- This is an in-person class, so the main teaching happens in the room. Use this page to review and catch up.
- Experiment with the interactive demos to picture the integrals and series we cover.
- Read and practice from the free OpenStax book, and lean on the recommended resources below when you are stuck.
Practice problems: OpenStax Calculus Volume 2 and Paul's Online Math Notes (in the resources below) both have worked exercises with solutions.
MTH 264 is taught in person, so the lectures happen in class. These are a few recordings I have made for review and for catching up. The recommended resources further down cover the rest of the course.
Videos
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Course outline
What we cover, and where to read it
The free, peer-reviewed OpenStax Calculus Volume 2 lines up well with MTH 264. Each unit below links to the matching chapter so you can read alongside class.
Unit 1 · Chapter 3
Techniques of Integration
- Integration by parts
- Trigonometric integrals and substitution
- Partial fractions
- Numerical integration and improper integrals
Unit 2 · Chapter 2
Applications of Integration
- Area between curves
- Volumes of solids of revolution
- Arc length and surface area
- Work and other physical applications
Unit 3 · Chapter 5
Sequences & Series
- Sequences and series of numbers
- The divergence, integral, and comparison tests
- Alternating series and absolute convergence
- Ratio and root tests
Unit 4 · Chapter 6
Power & Taylor Series
- Power series and their convergence
- Properties of power series
- Taylor and Maclaurin series
- Working with Taylor series
Unit 5 · Chapter 7
Parametric Equations & Polar Coordinates
- Parametric equations and their calculus
- Polar coordinates and polar graphs
- Area and arc length in polar coordinates
Official grades, submissions, and course announcements live in Canvas. This site hosts public course materials, explanations, examples, and study resources.
If you are stuck, start here
Recommended free resources
Every one of these is free, and I picked each for a different job. Use the one that matches what you need right now.
Full lectures
Professor Leonard
Long, complete Calculus II lectures. The closest thing to sitting through a class again, start to finish.
YouTubeNotes & practice
Paul's Online Math Notes
Clear written notes for every Calc II topic, with practice problems and full worked solutions. Great for homework.
Lamar UniversityWorked examples
The Organic Chemistry Tutor
A huge library of short, worked Calc II problems. Best when you want to see one more example of a specific type.
YouTubeGuided practice
Khan Academy
Structured practice with instant feedback and progress tracking. Good for drilling skills until they stick.
Integral CalculusIntuition
3Blue1Brown: Essence of Calculus
Beautiful visual explanations of why calculus works. Best for understanding ideas like series and Taylor approximations.
YouTubeGo deeper
MIT OpenCourseWare
A full university calculus course with notes, problem sets, and exams, for when you want more depth and rigor.
18.01 Single VariableWhere to go by topic
| If you are working on… | Try first | Then |
|---|---|---|
| Integration techniques (parts, trig, partial fractions) | Paul's Online Math Notes | The Organic Chemistry Tutor |
| Volumes, arc length, work | Professor Leonard | Khan Academy |
| Series and convergence tests | Paul's Online Math Notes | Professor Leonard |
| Why Taylor series work | 3Blue1Brown | OpenStax Volume 2, Ch. 6 |
| Parametric & polar | The Organic Chemistry Tutor | OpenStax Volume 2, Ch. 7 |
Interactive demos
Explore the ideas, hands on
Integration and infinite series are full of pictures a flat page cannot show: areas accumulating, solids forming, partial sums marching to a limit. Each tool walks through the idea, then hands you the controls. Nothing here is graded, so experiment freely. Not sure how to study this? See Study Strategies. Back to the lessons
Integration
02
Solids of revolution
Spin a region into a 3D solid and slice it into disks, washers, or shells.
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03
Average value of a function
Find the single flat height whose rectangle has the same area as the curve.
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04
Arc length
Approximate a curve with tiny straight segments and watch their total approach the true length.
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05
Work: pumping a tank
Lift each layer of water a different distance and sum the work into an integral.
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06
u-substitution as re-scaling
See substitution stretch the x-axis so a messy integral becomes one you recognize.
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07
Improper integrals
Watch an area that runs to infinity yet can still add up to a finite number.
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Sequences & Series
08
Partial sums: converge or diverge
Watch running totals settle to a limit, or climb forever, the core question of every series.
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09
A geometric series fills a whole
Add 1/2 + 1/4 + 1/8 + ... by filling a square, and see the infinite sum reach exactly 1.
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10
Taylor series, term by term
Add polynomial terms and watch them hug sin x, cos x, or eˣ over a widening interval.
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11
The integral test
Lay the series' terms as bars beside a curve and let the area decide convergence.
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12
Alternating series
See the totals zigzag inward to the limit, with an error no bigger than the next term.
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13
Interval of convergence
Plug different x into a power series and find the band where it converges.
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14
The p-series boundary
Slide the exponent p and watch convergence flip exactly at p = 1.
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Turn it in
Your practice report
Every quick check above feeds this report: what you got right on the first try, and what you got right eventually. Download it and upload it to Canvas.
MTH practice report · bryantclass.com