### Course home page

**Teachers: **

Ragnar Freij-Hollanti, Lectures and responsible teacher

Aapo Pajala, H01

Anton Vavilov, H02

Olga Kuznetsova, H03 and main assistant

Aleksi Sundell, H04

**Schedule**, including references to sections in Stewart (S), Guichard and friends (G), and slides (sl):

Observe that the slides are highly incomplete, and only serve as memory notes The slides will only be uploaded **after** each lecture. The schedule is subject to changes as the course progresses.

**9.9.** Lecture 1: Sequences and their limits (S: 11.1) (G: 11.1) (sl: 1-27)

**11.9.** Lecture 2: Series and convergence tests (S: 11.2,4-5) (G: 11.2,4-6) (sl: 28-61)

**16.9.** Lecture 3: Standard functions and continuity (S: 11.6, 2.4-5) (G: 11.7, 2.3) (sl: 62-89)

**18.9.** Lecture 4: Derivatives and how to compute them (S: 2.7-8, 3.1) (G: 2.1-4, 3.1-3, 4.1,3,6) (sl: 90-112)

**23.9.** Lecture 5: Standard derivatives and the chain rule (S: 3.2-6) (G: 3.4-5, 4.2,4,5,7) (sl: 113-142)

**25.9.** Lecture 6: Extreme values and asymptotes (S: 4.1-3,7) (G: 5.1-5, 6.1) (sl: 143-171)

**30.9.** Lecture 7: Taylor polynomials and power series (S: 4.8, 11.8-9) (G: 6.3-4, 11.10) (sl: 172-201)

**2.10.** Lecture 8: Integrals and the fundamental theorem of calculus (S: 11.10-11, 5.1-3) (G:11.9,11, 7.1-2)** **(sl: 202-225)

**7.10.** Lecture 9: Variable substitution and partial fractions (S: 5.3,5, 7.4) (G: 7.2-3, 8.1,5) (sl: 226-247)

**10.10.** Lecture 10: Integration by parts and unbounded integrals (S: 5.4, 7.1-3) (G: 8.2,4) (sl: 248-270)

**14.10.** Lecture 11: First order differential equations: separable and linear (S: 9.1,3-5) (G: 17:1-3) (sl: 271-293)

**16.10.** Lecture 12: Second order differential equations and repetition (S: 17.1-3) (G: 17:5-7) (sl: 294-328)

(S) James Stewart

Calculus: Early transcendentals, 7th edition

(I will use the and refer to chapter numbers in the 7th edition, but all editions are pretty much the same)

(G) David Guichard and friends

Single variable calculus: Early transcendentals

PDF (Entire book): https://www.whitman.edu/mathematics/calculus/calculus.pdf

HTML and Chapter-by chapter: https://www.whitman.edu/mathematics/calculus_online

There will be five homework sets during the course, due on Sunday evenings 22.9., 29.9., 6.10., 13.10., 20.10.. They should be handed in under Assignments on the course homepage. You are allowed and encouraged
to discuss the homework problems with your fellow students, but every student
should write down their own solutions. It is encouraged to solve **many** of
the “additional exercises”, and other exercises that you find in the
textbook or elsewhere, in addition to the homework problems.

Under Materials, I will update slides immediately **after** each lecture, and "exploratory problems" a few days **before** each lecture. The purpose of the exploratory problems is that you should look at them and ideally discuss them with your fellow students before the lecture. They are more theoretical in nature than the homework problems and additional problems, and will help you to think of important concepts and ideas before they are introduced formally in class.