MECH4101 Continuum mechanics and thermodynamics Emneplan

This course covers the fundamentals of continuum mechanics and thermodynamics. Focus is on solid mechanics of deformable bodies treated as continuous distribution of matter disregarding their molecular structure and is intended to be a comprehensive treatment of the subject at an intermediate level. While mathematicians deal with geometric continuum mechanics using differential geometry and Lie derivatives and engineers study it using traditional strength of material approach, the course here is an in-between approach, covering enough of the general theory to be able to solve problems of interest in solid mechanics.

Knowledge

The candidate:

• can explain the linear elastic theory of continuum mechanics
• can explain the fundamental thermodynamic potentials and Legendre transforms
• can recognize the difference between continuous and discrete systems, can identify each of them through examples and can identify the equations for the former
• can explain the formalism associated with change of configuration (kinematics), the concepts of stress and constitutive relations
• can explain the difference between modelling dimensions and restrictions imposed on deformation fields for reductions as plane strain, axisymmetry and shell
• can identify the limitations and explain the meaning of such restrictions imposed on constitutive models through the principles of thermodynamics.

Skills

The candidate:

• can calculate the values for fundamental parameters i.e., stress, strain, and displacement in static problems of linear elasticity in 1-, 2-, and 3-D domains
• can solve the governing differential equations for the field variables at various locations analytically for simple geometries
• can conduct an independent, limited research project under supervision and in accordance with applicable norms for research ethics
• can apply relevant mathematical methods, such as partial differentiation, multiple integration, or Fourier analysis, in derivation and solution of governing PDEs

General competence

The candidate:

• can reflect upon, explain, and critically assess the solution and its procedure applied to solid mechanics problems in 1-, 2-, and 3-D using the appropriate methods
• can communicate independent research work using the correct terminology with peers and academics and to some extent with non-experts
• can explain what continuum mechanics and thermodynamics are used for and how the formulation of continua differs from that of discrete systems conceptually and mathematically.

Lectures and tutorials.

The course covers the foundations and recent advances in Machine Learning from the point of view of Statistical Learning Theory. The goal of this course is to provide students with the practical skills to support the theoretical knowledge to (1) develop machine learning solutions to challenging problems and (2) to be able to develop the acquired expertise further.

The theoretical aspects of statistical learning will be illustrated with concrete problems and tasks in Python.

No formal requirements over and above the admission requirements.

The student should have the following outcomes upon completing the course:

Knowledge

Upon successful completion of the course, the student:

• will have a good understanding the different concepts and methods of supervised and unsupervised statistical learning and how to apply them on large data.
• has advanced knowledge of probabilistic formulation of the various learning problems.
• has focused knowledge of theoretical aspects of the different methods in machine learning and statistical learning, as well as a deep knowledge of concepts and assumptions behind each method.

Skills

Upon successful completion of the course, the student:

• can apply different high-dimensional regression techniques on data
• can apply different classification techniques on data
• can apply clustering techniques on data
• can apply dimension reduction techniques on data
• can make informed decisions on which method suits best for a particular problem and/or data set
• can derive learning algorithms for new models and analyze new data with them.

General competence

Upon successful completion of the course, the student:

• can apply different predictive models on data and assess their performance
• can use supervised and unsupervised learning in different real life problem

This course has three main parts.

The first three weeks cover revisions on statistics and scientific method, briefly presenting also the basics in (Python) programming, selection of a problem, etc. (i.e. revisions of several of the focus points in DATA3800).

After that there will be 7 weeks with presenting and solving exercises, covering the book "Introduction to Statistical Learning".

Finally the course has 3 to 4 weeks bridging the content presented during the weeks before with other scientific fields and topics, namely in Applied AI and in Mathematical Modelling. In particular, connections to the courses " Applied and Computational Mathematics (ACIT4310)" and "Evolutionary Artificial Intelligence and Robotics (ACIT4610)" will be addressed.

The weekly classes will be divided in three parts: (1) a theoretical exposition of the new content introduced each week, (2) one set of exercises/problems implementing the content presented during the theoretical exposition, and (3) supervision of each student in his/her specific project (see "Assignment").

The following required coursework must be approved before the student can take the exam:

A project plan document containing a description of the chosen data set, a preliminary research question and suggested tools and method to apply.