
BM30A3300 Lämpö ja sähkö - Luento-opetus 16.1.2023-3.3.2023
Lämpö-osuus: Lämpöopin fysikaaliset perusteet, termodynamiikan pääsäännöt sekä termodynaamiset laitteet ja kiertoprosessit. Aineen lämpölaajeneminen ja lämmönsiirron mekanismit.
Sähkö-osuus: Sähköstatiikka (sähköinen voima, sähkökenttä, sähkökentän potentiaali), tasavirtapiirit, magnetismi (magneettinen voima, magneettikenttä), sähkömagneettinen induktio, muuttuvat virrat tasavirtapiirissä, vaihtovirtapiirien perusteet.
- Responsible teacher: Kirsi Ikonen
- Responsible teacher: Ahti Karjalainen

BM30A3200 Mekaniikka ja aaltoliike - Luento-opetus 5.9.2022-16.12.2022
Mekaniikka-osuus: Etenevän ja pyörimisliikkeen perusteet, Newtonin lait, säilymislait (energia, liikemäärä ja liikemäärämomentti).
Aaltoliike-osuus: Mekaaniset värähtelyt (harmoninen, vaimeneva, pakotettu), harmoninen aalto, mekaaniset ja sähkömagneettiset aallot, interferenssi, diffraktio, polarisaatio.
- Responsible teacher: Kirsi Ikonen
- Responsible teacher: Ahti Karjalainen

BM30A2200 Semiconductor and Superconductor Physics - Luento-opetus 5.9.2022-16.12.2022
Semiconductors: bonds, crystals, defects and defect states, doping, mechanical structure, band structure, transport, recombination, external fields, light-to-electricity conversion, electricity-to-light conversion, examples of different semiconductor materials and their properties, basics of diodes and some other most important components.
Superconductors: basic properties of superconductivity, London equations, thermodynamics of the superconducting transition, intermediate state, coherence length, current in superconductor, thin films, BCS-theory, type-II superconductors, high-Tc superconductors, and some applications of superconductivity.
- Responsible teacher: Panja Luukka
- Teacher: Mihaela Bezak

BM30A1701 Physics of Semiconductor Devices - Luento-opetus 16.1.2023-28.4.2023
Structure, operation and physics of semiconductor devices.
- Responsible teacher: Panja Luukka
- Teacher: Mihaela Bezak
- Teacher: Mihaela Bezak

BM30A1600 Microelectronics - Luento-opetus 5.9.2022-21.10.2022
We study classical Microelectronics based on Silicon technology by considering p-n junctions, diodes, and transistors (bipolar junctions and MOSFET). The course includes also computations and simulations performed in MATLAB. These tasks help to visualize the working principle of devices and allow a better understanding of the lectures. We will also discuss the Moore's law and beyond.
- Responsible teacher: Bernardo Barbiellini
- Teacher: Veenavee Kothalawala

BM30A0601 Optoelectronics - Luento-opetus 5.9.2022-21.10.2022
The course begins by summarizing Maxwell equations for the electromagnetic field and the wave equations. Then the lectures discuss optical planar waveguides, linear optical fibres, propagation of linear pulses, LEDs, LASERs, detectors and photovoltaic devices. Some exercises with MATLAB will be given so that students can start their own numerical experiments.
- Responsible teacher: Bernardo Barbiellini
- Teacher: Veenavee Kothalawala

BM30A0312 Fysiikan laboratoriotyöt - Laboratoriotyöskentely 13.3.2023-28.4.2023
Tieteellinen mittaustekniikka, tulostenkäsittely ja raportin teko.
- Responsible teacher: Kirsi Ikonen
- Responsible teacher: Erik Vartiainen
- Teacher: Juha Parviainen

BM20A8100 Integraalilaskenta - Luento-opetus 13.3.2023-28.4.2023
Yhden muuttujan funktion integraalilaskentaa sovelluksineen: differentiaalien soveltaminen, pyörähdyskappaleet, käyrän pituus, parametriset käyrät ja integraalilaskenta, osittaisintegrointi. Sovellusesimerkkejä useilta tekniikan aloilta. Kaksinkertaiset ja kolminkertaiset integraalit. Funktion parillisuus, parittomuus ja jaksollisuus. Kurssin aiheiden käsittely MATLABilla sekä funktiotiedoston luominen.
- Responsible teacher: Juho Virpiranta
- Teacher: Simo Heiliö
- Teacher: Esko Makkonen
- Teacher: Jouni Sampo
- Teacher: Akseli Suutari

BM20A8000 Differentiaaliyhtälöt - Luento-opetus 16.1.2023-3.3.2023
Kompleksiluvut: peruslaskutoimitukset, kompleksitaso, Eulerin kaava. Differentiaaliyhtälöt: 1. kertaluvun differentiaaliyhtälöt. 2. kertaluvun lineaariset differentiaaliyhtälöt, differentiaaliyhtälöryhmät. Matriisin ominaisarvot ja -vektorit. Differentiaaliyhtälöiden ja -yhtälöryhmien ratkaiseminen MATLABilla numeerisesti ja symbolisesti.
- Responsible teacher: Juho Virpiranta
- Teacher: Simo Heiliö
- Teacher: Esko Makkonen
- Teacher: Esko Makkonen
- Teacher: Juha Parviainen

BM20A7900 Differentiaalilaskenta - Luento-opetus 31.10.2022-16.12.2022
Yhden muuttujan funktion raja-arvot, korkeamman dertaluvun derivaatat, lineaarinen approksimaatio ja virhearviot, Taylorin polynomit sekä implisiittinen derivointi. Usean muuttujan funktion raja-arvot ja ääriarvot, myös rajoitteilla. Ketjusääntö, gradientti ja suunnattu derivaatta. Pienimmän neliösumman menetelmä. MATLABin soveltaminen kurssin aiheisiin sekä ohjelmoinnin ehto- ja toistorakenteiden hallitseminen.
- Responsible teacher: Juho Virpiranta
- Teacher: Simo Heiliö
- Teacher: Esko Makkonen

BM20A7800 Yliopistomatematiikan perusteet - Luento-opetus 5.9.2022-21.10.2022
Perusteet funktioista, derivaatasta, integraalista, vektoreista ja matriisilaskennasta sekä MATLABin käytöstä.
- Responsible teacher: Juho Virpiranta
- Teacher: Simo Heiliö
- Teacher: Esko Makkonen
- Teacher: Lassi Roininen

BM20A7600 Numerical Methods II - Luento-opetus 31.10.2022-16.12.2022
Basics of partial differential equations
Modeling with PDEs
The stationary diffusion–advection–reaction equation
Existence and uniqueness of weak solutions
Construction of the finite element method
Meshes
Test and trial functions
Transformation of finite elements
Obtaining the system of linear equations
Direct methods for sparse linear systems of equations
LU decomposition without pivoting
Data structures
Bandwidth reduction
Iterative methods for systems of linear equations
Linear stationary iterative methods
Gradient and conjugate gradient methods
Preconditioned conjugate gradient method
- Responsible teacher: Andreas Rupp
- Teacher: Hanz Cheng
- Teacher: Aleksi Salo

BM20A7501 Seminar on Computational Engineering - Luento-opetus 5.9.2022-28.4.2023
This is a research seminar mainly intended for research purposes. Final year MSc and PhD students can obtain credits from this course through study diary. For details on the study, you should contact the lecturers.
- Responsible teacher: Lassi Roininen
- Responsible teacher: Andreas Rupp

BM20A7400 Introduction to Inverse Problems - Luento-opetus 31.10.2022-16.12.2022
Inverse problems appear in several fields, including medical imaging, image processing, mathematical finance, astronomy, geophysics, nondestructive material testing and sub-surface prospecting. Typical inverse problems arise from asking simple questions "backwards". For instance, the simple question might be "If we know precisely the structure of the inner organs of a patient, what kind of X-ray images would we get from her?" The same question backwards is "Given a set of X-ray images of a patient, what is the three-dimensional structure of her inner organs?" This is the inverse problem of Computerized Tomography, or CT imaging.
Usually the inverse problem is more difficult than the simple question that it reverses. Successful solution of inverse problems requires specially designed algorithms that can tolerate errors in measured data.
- Responsible teacher: Tapio Helin
- Teacher: Rodrigo Rojo Garcia
- Teacher: Aleksi Salo

BM20A7300 Functional Analysis - Luento-opetus 5.9.2022-21.10.2022
Functional analysis is a classical field of mathematics, which aims to describe general vector spaces (e.g. function spaces or graphs) and mappings defined on these spaces, and aims to characterize their relationships and properties. Functional analysis offers tools for deeper understanding of many mathematical phenomena such as Fourier transform or numerical analysis. The topic of functional analysis is contemporary, since the data masses studied in modern science are often vast and high-dimensional. It is necessary to understand how different mappings between such data sets scale as the size or the dimension of the data increases. The contents of this course are mostly theoretical and exercises emphasise being able to prove mathematical statements.
- Responsible teacher: Tapio Helin
- Teacher: Rodrigo Rojo Garcia

BM20A7200 Bayesian Continuous-Parameter Estimation - Luento-opetus 5.9.2022-21.10.2022
This is a research level course mainly intended to final year MSc students and PhD students. The exact content is always agreed with the students. Topics include, but are not limited to, connections between deep Gaussian processes, deep neural networks and stochastic differential equations; implementation needed sampling methods with MCMC, variational Bayes or optimisation as needed; mixture of Gaussian process experts; high-performance computing and random field models for Bayesian inversion.
- Responsible teacher: Lassi Roininen
- Teacher: Teemu Hannu Tapani Härkönen
- Teacher: Tomas Soto

BM20A7101 Tilastollisten menetelmien jatkokurssi - Luento-opetus 31.10.2022-16.12.2022
Tilastollinen päätelmä: jakaumien testaaminen, hypoteesitestaus, kaksi tai useampi näytetestiä. Parilliset testit. Ei-parametriset testit. Varianssianalyysin perusteet, aikasarja-analyysi ja ueamman taustamuuttujan regressiomalleja. Johdatus epälineaariseen regressioon. Johdanto tekijäanalyysiin.
- Responsible teacher: Matylda Jablonska-Sabuka

BM20A6400 Laskennallisen tekniikan työkurssi - Luento-opetus 31.10.2022-16.12.2022
Kurssilla ei käsitellä uusia menetelmiä vaan sovelletaan aiemmin opittuja lakennallisen tekniikan menetelmiä käytännön ongelmien ratkaisemiseen.
- Responsible teacher: Matylda Jablonska-Sabuka
- Teacher: Tapio Helin

BM20A5200 Modelling Workshop and Summer School - Conference studies 5.9.2022-16.12.2022
Students are expected to analyze the problem, formulate mathematical models, evaluate and select appropriate theoretical and numeric methods and derive solutions. Lectures presenting the problems and required methods will be delivered.
- Responsible teacher: Lassi Roininen
- Teacher: Michael Boy
- Teacher: Teemu Härkönen
- Teacher: Martin Simon
- Teacher: Tomas Soto
- Teacher: Jarkko Suuronen

BM20A4702 Modelling with Partial Differential Equations - Luento-opetus 16.1.2023-3.3.2023
Introduction to PDE models and their applications;
Finite difference method (FDM);
Numerical discretization of PDE;
Temporal and spatial discretization schemes;
Method of Lines for PDEs;
Matlab implementation of PDE models based on FDM and MOL;
Properties of numerical modelling;
System of PDEs;
Solution of Nonlinear PDEs
- Responsible teacher: Ashvinkumar Chaudhari
- Responsible teacher: Andreas Rupp
- Teacher: Duc-Lam Duong
- Teacher: Fabian Schneider