Course information
Learning outcomes
After the course the student will
- know how to calculate approximations with the aid of partial derivatives
- be able to solve systems of equations with Newton s method
- know and understand the basic ideas of optimization
- be able to use Lagrange multipliers
- be able to calculate double and triple integrals
- be able to change the order of integration in double integrals
- know how to change variables in double and triple integrals
Content
Functions of several variables and their derivatives, optimization of functions with several variables, double and triple integrals.
Teacher
Ville Turunen, Jarmo Malinen
Study material
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Workload
24+24 (4+4)
Prerequisites
Recommended prerequisites: MS-A00XX Matrix algebra, MS-A01XX Differential- and integral calculus 1.
Evaluation
lectures, exercises and course exam OR exam only
Teaching time and location
The teaching time and the location of the course can be found at 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 academic year 2025-2026 is selected
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From the blue bar, click Lecture and open the Groups and teaching times tab to see the teaching time and the location of the course. Exam times can be seen by clicking Exam.
Exam instructions at the Open University
The teacher has four (4) weeks to grade the exam submissions starting from the exam date.
Further information
Equivalences to other courses: Together with the course MS-A03XX substitutes the courses Mat-1.1020, Mat-1.1220, Mat-1.1320, Mat-1.1420, Mat-1.1520, Mat-1.1620, Mat-1.1720.
Together with the course MS-A04XX Foundations of discrete mathematics or the course MS-A01XX Differential and integral calculus 1 substitutes the course Mat-1.1110.
Substitutes the courses MS-A02XX Differential and integral calculus 2.
Online learning environment for the course
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 8.12.2025 at 9.00
Registration for this course ends on 12.1.2026 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
Activating Aalto ID and Multifactor Authentication
You can activate your Aalto User ID the day after the registration and you should activate it no later than the day before the start of the course.
Instructions for activating your Aalto user ID
Once you have activated your Aalto user ID, also enable multifactor authentication. Some of Aalto University's services require multifactor authentication.
Instructions for using Multifactor Authentication
