Mathematical Analysis 2

Bachelor course in Engineering Sciences 2022/23


Course led by Oliver Butterley, in collaboration with Giovanni Canestrari.

The material of the course is divided into six parts as listed below. Each part takes two weeks and is accompanied with a set of exercises. Mathematically the parts all build on each other and are intimately linked. The final weeks of the course are devoted to reviewing the material already presented.

Course content

Lecture notes are available to download. They are a collaborative work in progress, constantly updated during the course.

Part Teaching period Exercises Due date
Sequences and series of functions 26/09/22 - 07/10/22 Exercises 1 09/10/22
Differential calculus in higher dimension 10/10/22 - 21/10/22 Exercises 2 23/10/22
Extrema and other applications 24/10/22 - 04/10/22 Exercises 3 06/11/22
Curves and line integrals 07/11/22 - 18/11/22 Exercises 4 20/11/22
Multiple integrals 21/11/22 - 02/12/22 Exercises 5 04/12/22
Surfaces and surface integrals 05/12/22 - 16/12/22 Exercises 6 18/12/22

A list of core skills is available. This is not the entire content of the course, this is a list of the core skills and is provided as a convenience. To obtain top grades a full understanding of and ability to work with all the material of the course is required.


Associated to each part of the course there are 7 basic exercises and 3 extended exercises. Completing the exercises in a timely way gives a bonus towards the exam.
  • Completing the 7 basic exercises in each of the 6 exercise sets prior to the respective due dates (dates listed above) gives a 10% bonus towards the exam.
  • Completing the 7 basic exercises and the 3 extended exercises in each of the 6 exercise sets prior to the respective due dates (dates listed above) gives a 20% bonus towards the exam.
  • The bonus gained during a given year only applies to the exams taken during the same academic year.
  • Unlimited attempts (prior to the due dates) are permitted for the exercises. Anyone may ask for hints in class and you are encouraged to discuss the exercises and help each other understand the material.

Practical details

  • Join the MS Team for the course using the team code: tybz901.
  • At any point in time, during or after the course, send some feedback using this form.
  • The course is taught in Semester 1 with the following schedule:
    • Mon 14:00-14:45, 15:00-15:45 in Aula 8
    • Mon 16:00-16:45, 17:00-17:45 in Aula 8 (Tutorial - Canestrari)
    • Wed 9:30-10:15, 10:30-11:15 in Aula 8
    • Wed 16:00-16:45, 17:00-17:45 in Aula 8
  • MA2 @
  • Contact Oliver Butterley by email (
  • Course material from previous years and other instructors is available
Figure 1: Schedule

Exam rules

  • The exam consists of a 3hr, in person written test which is worth 30 points. There is no oral exam, the grade from the written exam (possibly with bonus from the exercise sets) is your final grade. A score of 31 or above is interpreted as 30 Lode.
  • The exam is passed if the final mark is at least 18/30.
  • During the year there are three exams sessions and two calls in each session. The sessions are according to the university schedule.
  • Students are permitted to attempt both calls available in a given exam session and take the highest grade of the two attempts.
  • Students are permitted to bring only the following items to their desk in the exam room:
    • Two A4 sheets of paper (writing permitted on both sides) with whatever course notes are wanted (or 4 sides of A4 or equivalent area of paper: \(0.249 m^2\)).
    • Pens and pencils.
    • An identity document.
    • A drinking bottle.
  • Paper for rough calculations will be provided in the exam room. After the exam the paper used during the exam remains in the exam room.
  • During the exam it is forbidden to communicate, using any means, with anyone except the exam invigilators.
  • Students are required to arrive at the exam room before the scheduled start of the exam.
  • Under penalty of exclusion, during written tests the use of electronic devices and applications is not allowed. Calculators are also not permitted. It is not permitted to use books and notes during the exam (except personal notes as described above).
  • A selection of past exam questions are available for practice. The exam is divided into five questions on different topics covering the course material, similar to the exams of previous years.
  • Due to cheating detected in Call IV, in the remaining calls an interview will be required to confirm a score obtained in the written exam.

Exam schedule

Winter session Call I Wednesday 25/01/2023 14:00-17:00 Aula 2. Questions and solutions
Call II Tuesday 28/02/2023 14:00-17:00 Aula 3. Questions and solutions
Summer session Call III Monday 03/07/2023 14:00-17:00. Room: Aula 3. Questions and solutions
Call IV Thursday 20/07/2023 14:00-17:00. Room: Aula 2. Questions and solutions
Autumn session Call V Thursday 31/08/2023 14:00-17:00. Room: Aula 3. Questions and answers
Call VI Thursday 21/09/2023 14:00-17:00. Room: Aula 3. Questions and answers

Lecture diary

Date Topics