## Online Teaching Materials

Here you can find a collection of the teaching materials I have produced. If you have any comments or suggestions regarding the materials, I am always happy to hear your thoughts. You are also free to use the materials in your own teaching, and if you do use them, I'd be very interested in hearing about it!

### Online course on "Partial Differential Equations in Mathematical Modeling"

The following online course material was developed as a one-week study module for a Finnish-Chinese online course on mathematical modeling. The online module was first implemented in October 2017.#### Course material:

**Lecture notes:**"Partial Differential Equations in Mathematical Modeling", Lassi Paunonen, 2017.

**Matlab code:**Matlab demonstration files (m-files)

**Video lectures:**Video lecture series (YouTube playlist, 6 videos, roughly 60min):

### Online course "Introduction to Functional Analysis"

The following course material was developed for the online implementation of the 7-week course Introduction to Functional Analysis at Tampere University in January-February 2021. The course material consists of a series of 19 video lectures (each with 10-20 minute duration and available in Youtube) and complete lectures notes.The main topics of the course are the following:

**•**Vector spaces, normed spaces, and Banach spaces

**•**Linear operators on Banach spaces

**•**The Hahn-Banach Theorem and dual spaces

**•**Inner product spaces and Hilbert spaces

**•**The Riesz Representation Theorem and adjoint operators

**•**Orthonormal bases on Hilbert spaces

**•**Spectral theory of linear operators

**•**Spectral properties of self-adjoint and compact operators

#### Course material:

**Lecture notes:**"Introduction to Functional Analysis" by Lassi Paunonen, 2023.

**Video lectures:**Complete video lectures (Youtube playlist, 19 videos):

**Slides:**Video lecture slides (zip file of PDF slides)

### Course "Advanced Functional Analysis" (2020, 2022)

The course continues the study of “linear operators” (introduced on the course “Introduction to Functional Analysis”) with special emphasis on unbounded operators and differential operators. In particular, the properties of linear operators are used to study the existence and properties of solutions of “elliptic partial differential equations”.Note that the lecture notes are intentionally very “incomplete”! Indeed, the coursework is centered around completing the proofs of the theorems and lemmas through discussions during the lecture sessions and as parts of homework.

**Lecture notes:**“Advanced Functional Analysis” by Lassi Paunonen, 2020. Updated 2022.

### Course "Mathematical Control Theory" (2016, 2019, 2021, 2023)

The course focuses on the study of how linear systems described by differential equations can be influenced with external “control”. In particular, the course covers the basic properties of linear systems with “control inputs” and “measured output”, and focuses on the analysis of Proportional-Integral Control (PI-Control) and other types of control design for linear and nonlinear dynamical systems.The contents of the course have evolved over the years. The current implementation focuses on control of systems described by linear and nonlinear ordinary differential equations. The first half of the course studies the linear case, and the second half is devoted to stability analysis and control of nonlinear systems.

The first three implementations focused on control of

*linear*ordinary differential equations, as well as

*partial differential equations*. The first part of this course utilised linear algebra, and the second part used functional analysis and theory of “strongly continuous semigroups” in control and analysis of controlled partial differential equations. The course was first taught in 2016 under the name “Linear Systems”. The first version of the lecture notes of in particular contain Chapter 5 on the “Output Tracking Problem”, and this material is not included in second and third versions of the lecture notes.

**Lecture notes:**"Mathematical Control Theory" by Lassi Paunonen, 2023.

**Matlab code:**Matlab codes for the LinSys routines and course examples (GitHub)

**Lecture notes:**"Mathematical Control Theory" by Lassi Paunonen, 2021 version (2019 version similar).

**Lecture notes:**"Linear Systems" by Lassi Paunonen, 2016.