## Topic outline

• ### Course homepage

An introductory video about the course.

There will be a zoom meeting every Wednesday at 12.15 (Finnish time, UTC+2). It is dedicated to questions related to the videos, materials and problems for each week.

An unofficial "pass" certificate will be given to those who solve at least 60 % of the problems. By participating in the final on-line exam on 22.2. at 13-17 o'clock you can also get an official grade (for Aalto University). In this case the weight of the exercises is 60 %, and 40 % for the exam.

• The course enrolment is open!
• The course will start January 11th 2021 and will last for approximately seven weeks.
• The course material and additional information will be updated as the course proceeds.

The main topic of the course is calculus in one variable. We cover basic concepts of sequences and series, derivative and integral, as well as the most important ordinary differential equations of degree 1 and 2.

Preliminary knowledge of derivative and integral at a high school level will be useful but not absolutely necessary.

The content of the course is the same as in the Aalto University course 'Differential and integral Calculus 1', offered to 1st year Engineering students.

All exercises are based on automatic assessment using the STACK system. Some of these use the interactive JavaScript geometry library JSXGraph, and were developed in the on-going ITEMS project co-funded by the Erasmus+ Programme of the European Union.

Contact person: Miko Karjalainen, miko.karjalainen@aalto.fi

• Meeting ID: 531 704 0428
Passcode : 708982

• ### Course materials

The materials will be added here as the course proceeds. The videos do not cover all the course material; they only contain the main definitions and some examples.

Short videos (with varying length):

1. Sequences (25:01)
2. Series (35:43; please skip blackboard cleaning from 10:00 to 13:45 :)
3. Continuity (33:09)
4. Derivative (30:11)
5. Taylor polynomials and series Part 1: Taylor (35:50), Part 2: Power series (23:24)
6. Elementary functions Part 1: Inverse (18:49); Part 2: Inverse trig. (18:58); Part 3: exp and ln (21:34)
7. The concept of area in the plane (14:22)
8. Integral Part 1: Definition (32:06); Part 2: Applications (13:12); Part 3: Improper integrals (10:58); Part 4: Methods of integration (41:51)
9. ODE of the 1st order  Part 1: Separable (24:55); Part 2: Linear (14:24)
10. ODE of the 2nd order Part 1: General theory (14:46); Part 2: Homogeneous case (18:46); Part 3: Non-homogeneous case (21:25)

• ### Exam (20.02.2021, 13.00-17.00)

#### Exam Paper and Return Box

• At the start time of the exam, the exam papers (in pdf) will be available on this page.
• The exam return box is below.
• Please read the instructions below well ahead of the actual exam.
• Before the exam date use the practice return box below to test your technology.

#### Aalto University Code of Academic Integrity

Please be reminded of the policy as can be found here: