Course
MA0 B
Term
Spring 2026
Schedule
Tue / Thu Lecture + Fri Workshop
Lessons
0
Course overview
We develop antiderivatives and definite integrals together. Starting from area and accumulation, we define the integral, connect it to derivatives through the fundamental theorem, and practice the standard computational techniques and basic applications.
- Treat the integral as accumulated change before turning it into a computational tool.
- Build fluency with antiderivatives, substitution, and the fundamental theorem.
- Apply integration to area, displacement, average value, and simple physical models.
Weekly rhythm
- Read the lesson page first and sketch the geometric picture before doing any calculations.
- Work a few definite-integral estimates by hand before using closed-form antiderivatives.
- Keep track of whether each problem is asking for an accumulation, an area, or an antiderivative.
- Attempt any challenge exercises last, once the core techniques feel automatic.
Course themes
- Riemann sums, area, and accumulation as the starting intuition.
- Definite integrals and how limits turn finite sums into continuous totals.
- Antiderivatives, the fundamental theorem of calculus, and substitution.
- Applications to area between curves, average value, displacement, and simple growth models.
Prerequisites
No prerequisites.
Course direction
The course is meant to make integration feel like one coherent idea instead of a disconnected list of tricks.
References
Outside notes, textbooks, or course pages worth keeping around.
course inspiration
MIT 18.01.2x: Calculus 1B - Integration
MIT's integration-focused course page. It emphasizes area, accumulation, techniques, and applications in the direction this course wants.
main reference
OpenStax Calculus Volume 1
A more straightforward and less proof-heavy text than Spivak, with the core definite and indefinite integral material in a standard first-calculus style.
alternate reference
Essential Calculus: Early Transcendentals by James Stewart
A more traditional calculus text with lots of worked examples and routine practice. Useful if you want a familiar classroom-style backup reference.