Course information
Learning outcomes
After the course the student will be able to
- evaluate multiple integrals in cartesian, cylindrical and spherical coordinates,
- analyze the properties of vector fields,
- evaluate line and surface integrals of vector fields,
- calculate the gradient, divergence and curl, and knows what they represent,
- explain the idea of Gauss and Stokes theorems, and apply them in calculations.
Content
Change of variables in multiple integrals, integration in cylindrical and spherical coordinates, vector fields, line and surface integrals, gradient, divergence, curl, Gauss s, Green s and Stokes theorems.
Teacher
Björn Ivarsson
Study material
-
Workload
24+24 (4+4)
Prerequisites
Recommended prerequisites:
MS-A02XX Differential and integral calculus 2.
Evaluation
lectures, exercises and course exam OR exam
Teaching time and location
The teaching time and the location of the course can be found in the Sisu information system.
- The link leads to Completion methods tab of the course page
- From the top of the page (Version drop-down menu), check that the academic year 2026-2027 is selected
- From the blue bar, choose the right teaching and open the Groups and study events tab to see the teaching time and location of the course. To see exam times, click Exam.
Exam instructions at the Open University
The teacher has four (4) weeks to grade the exam submissions starting from the exam date.
Other information
Equivalences to other courses:
Together with the course MS-A02XX substitutes the courses Mat-1.1020, Mat-1.1220, Mat-1.1320, Mat-1.1420, Mat-1.1520, Mat-1.1620, Mat-1.1720.
Substitutes the courses MS-A03XX Differential and integral calculus 3.
Online learning environment for the course
The MyCourses online learning environment is a tool for both students and teachers for communication and managing everyday course work. You need an Aalto User ID to log in to the course's MyCourses workspace and participate in teaching.
Digital workspace of the course:
MyCourses
More details on completing the course will be available at MyCourses closer to the start of the course.
Registration and course fee
Registration for Open University courses is done via the link below:
Course registration
Registration for this course starts on 1.2.2027 at 9.00
Registration for this course ends on 8.3.2027 at 23.59
It is not possible to register before the registration period has started or after it has ended.
The number of participants is limited to 5.
This course is organized by the Aalto University School of Science.
The course fee is paid upon registration for each course at a time and it is binding. Familiarize yourself with registration and payment rules as well as other guidelines for students:
Registration, payments and rules
