Course
MA1 B
Term
Spring 2026
Schedule
Tue / Thu Lecture + Fri Recitation
Lessons
0
Course overview
We begin with the real number system and the definition of limits for sequences and functions, then build continuity, differentiability, and integration on top of that foundation. The second half covers indefinite and definite integrals, improper integrals, and the theory of series, finishing with power series and Taylor expansions. Every major theorem is proved, and the proofs are there to sharpen your reasoning, not to slow you down.
- Start at the foundations: the completeness of the reals, epsilon-delta limits, and continuity before any derivatives appear.
- Build the full differential and integral toolkit: mean value theorems, L'Hopital's rule, Taylor expansion, integrability, and improper integrals.
- Finish with series and power series so you can approximate, bound, and reconstruct functions from their local data.
Weekly rhythm
- Read the lesson page first and work through the examples in order.
- Open the linked alternate video only if you want a second explanation or a different pace.
- Do the exercises, then recitation or lab immediately after the notes so the ideas turn into practice.
- Attempt the homework last, without jumping straight to solutions.
Course themes
- The real numbers, completeness, and why the foundations matter for everything that follows.
- Limits of sequences and functions, continuity, and the properties of continuous functions on closed intervals.
- Derivatives, differentials, mean value theorems, L'Hopital's rule, monotonicity, convexity, and Taylor expansion.
- Indefinite and definite integrals: methods, integrability conditions, applications, and improper integrals.
- Numerical series, convergence tests, power series, and Taylor series.
Prerequisites & corequisites
No prerequisites.
- Corequisite: MCE A (Mathematical Thinking and Python)
- Corequisite: MA1 A (Applied Linear Algebra)
- Corequisite: PH1 A (Mechanics)
Course direction
The course is teaching you to handle limits, derivatives, and integrals with the precision they actually require, so that later courses in analysis and differential equations feel like a continuation, not a restart.
References
Outside notes, textbooks, or course pages worth keeping around.