### MS-A0211 - Differential and integral calculus 2, 26.02.2019-09.04.2019

Omfattning: 5

Tidtabel: 26.02.2019 - 09.04.2019

Kontaktuppgifter till kursens personal (gäller denna kursomgång): My name is Björn Ivarsson and I am the lecturer on the course. My office is Y326 and you can come there with any question you have about the course. You can also send me an e-mail (bjorn.ivarsson@aalto.fi).

Undervisningsperiod (är i kraft 01.08.2018-31.07.2020):

IV Spring (2018-2019)

III Spring (2019-2020)

Lärandemål (är i kraft 01.08.2018-31.07.2020):

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

Innehåll (är i kraft 01.08.2018-31.07.2020):

Functions of several variables and their derivatives, optimization of functions with several variables, double and triple integrals.

Närmare beskrivning av kursens innehåll (gäller denna kursomgång): The course book is:

- *Calculus, A Complete Course,* Adams and Essex, 8th Edition

Lecture plan:

- Lecture 1: Curves and arc length (Ch 8.2, 8.4, 11.1)
- Lecture 2: Functions of several variables, limits, continuity (Ch 12.1 - 2)
- Lecture 3: Partial derivatives (Ch 12.3 - 4)
- Lecture 4: Chain rule, Linear approximation and differentiability (Ch 12.5 - 6)
- Lecture 5: Gradient, directional derivative, implicit functions, Taylor approximation (Ch 12.6 - 9)
- Lecture 6: Optimation with or without constraints, Lagrange multipliers (Ch 13.1 - 3)
- Lecture 7: Lagrange multipliers, Method of least squares, Newton's method (Ch 13.3, 13.5, 13.7)
- Lecture 8: Double integrals, iterated integrals, generalised double integrals (Ch 14.1 - 3)
- Lecture 9: Polar coordinates, tripple integrals, change of variables (Ch 14.4 - 6)
- Lecture 10: Applications of multiple integrals (Ch 14.7)
- Lecture 11: Reserve
- Lecture 12: Reserve

Metoder, arbetssätt och bedömningsgrunder (är i kraft 01.08.2018-31.07.2020):

Lectures, exercises, midterm exams/final exam.

Arbetsmängd (är i kraft 01.08.2018-31.07.2020):

24+24 (4+4)

Ersättande prestationer (är i kraft 01.08.2018-31.07.2020):

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, MS-A0210 Mathematics 1.

Kursens webbplats (är i kraft 01.08.2018-31.07.2020):

https://mycourses.aalto.fi/course/search.php?search=MS-A0211

Förkunskaper (är i kraft 01.08.2018-31.07.2020):

MS-A00XX Matrix algebra, MS-A01XX Differential- and integral calculus 1.

Bedömningsskala (är i kraft 01.08.2018-31.07.2020):

0-5