Mathematical Analysis 2

Bachelor course in Engineering Sciences 2019/20

  • Lectures are held: Semester 1, Mon 14:00-16:00, Wed 9:30-11:30, Fri 14:00-16:00, Aula 8.
  • Reference book: Tom M. Apostol, Calculus, Volumes 1 and 2 (2nd edition).
  • Course taught jointly by Yoh Tanimoto and Oliver Butterley.
  • Office hours with Oliver Butterley by appointment (
  • Course topics: 1. Sequences, infinite series, improper integrals; 2. Sequences and series of functions; 3. Differential calculus of scalar and vector fields; 4. Applications of differential calculus; 5. Line integrals; 6. Multiple integrals; 7. Surface integrals.
  • Course material (including past exams with solutions) by Yoh Tanimoto from 2018/19 is available.

Exam rules (2020 summer session)

  • The exam consists of a written test (using Moodle) and a compulsory oral test, both online.
  • To access the oral, a grade of at least 18/30 must be obtained on the written test. The exam is passed if the final mark is at least 18/30.
  • The written test and the oral test must take place in the same call.
  • Under penalty of exclusion, during written tests the use of electronic devices and applications except those required (MS Teams and possibly a web browser to access to the Moodle quiz) is not allowed. It is not permitted to use books and notes.
  • It is necessary to have a webcam and a microphone to take the test.

A simulation of the written test is available.

Exam schedule

Winter session Call I Written 24/01/20, 9:30-12:30 (aula C6) Oral 29/01/20, 9:30-18:00 (aula C12) Solutions
Call II Written 11/02/20, 9:30-12:30 (aula C6) Oral 18/02/20, 9.30-18:00 (aula C12) Solutions
Summer session Call III Written 30/06/20 Oral 03/07/20 Solutions
Call IV Written 14/07/20 Oral 17/07/20 Solutions
Autumn session Call V Written 31/08/20, 9:30-12:30 Oral 31/08/20, 13:30 Solutions
Call VI Written 15/09/20, 9:30-12:30 Oral 15/09/20, 13:30 Solutions

Lecture schedule

Date Topics Instructor Reference Exercises