Head of department: Prof Peter Lund, tel. 451 3197
Administrative officer: Katriina Sippola, tel. 451 3000, fax 451 5777
Planning officer (Study Affairs): Anna-Kaarina Hakala, tel. 451 3183
Department secretary: Taru Bister-Hämäläinen, tel. 451 3005
International study adviser: Kaisa Kautto, tel. 451 3004, e-mail: fkvopinto@hut.fi
Department office: Otakaari 3 A, tel. 451 3005, fax 451 3014
Office open 9 a.m.-11 a.m.

Chairs:
Mat-1 Mathematics
Mat-2 Applied Mathematics
Mat-5 Theoretical and Applied Mechanics
Tfy-3 Physics
Tfy-44 Engineering Physics, Materials Physics
Tfy-56 Engineering Physics, Advanced Energy Systems
Tfy-99 Engineering Physics, Biomedical Engineering
Tfy-105 Physics, Computational Physics

Mat-1 MATHEMATICS

Prof: Olavi Nevanlinna, tel. 451 3034, room U 302A
Prof: Timo Eirola, tel. 451 3033, room U 302B
Prof: Gustaf Gripenberg, tel 451 3025, room U339
Prof: Stig-Olof Londen, tel. 451 3035, room U 301
Prof: Juhani Pitkäranta, tel. 451 3024, room U 338
Prof: Jerry Segercrantz, tel. 451 3028, room U 307
Prof: Erkki Somersalo, tel. 451 2825, room Y 309C
Prof: Gennadi Vainikko, tel. 451 3050, room U 340

The mathematics curriculum of an engineering student consists of three one-term courses (6 credits each) given in the first three consecutive terms. There are curricula given in Finnish, Swedish and English. The Finnish courses are given in four variations according to the programme. The variations are denoted by the letters C (Mat-1.411 / 412 / 413), V (Mat-1.414 /.415), K (Mat-1.431 / 432 / 433), P (Mat-1.441 / 442 / 443), and S (Mat-1.421 / 422 / 423). The codes for the Swedish courses are Mat-1.451 / 452 / 453.
Furthermore, there is an extended curriculum in mathematics (denoted by L, Mat-1.401 / 402 / 403 / 404, 6 credits each) and physics (denoted by G, Tfy-3.102 / 103, 5 credits each) available to selected students. The extended curriculum in mathematics is also followed by all students of the degree programme of Engineering Physics.
The postgraduate and advanced courses in mathematics are lectured in a language appropriate to the needs of the audience. The postgraduate level courses are not lectured every year. An English exam is given, on request, in all the courses in mathematics.

Mat-1.401 Basic course in Mathematics L 1 (6 cr)

Autumn
Lecturer: Prof Juhani Pitkäranta
Contents: Numbers and number sequences. Vectors and analytical geometry. Complex numbers. Functions of one, two and three variables. Continuity concepts and continuous functions. Derivative with applications. Integral.  One exercise group is in Swedish. Basic courses in Mathematics L 1-L4 are intended for the degree programme TFY and the students selected into the extended curriculum in basic studies.
Literature: Supplementary material.
Language: Finnish.

Mat-1.402 Basic course in Mathematics L 2 (6 cr)

Spring
Lecturer: Prof Juhani Pitkäranta
Contents: Linear system of equations and matrices. Functions of many variables and partial derivatives. Differential equations. Integrals of many variables with applications. Fourier series. One exercise group is in Swedish.
Literature: Supplementary material.
Prerequisites: Mat-1.401.
Language: Finnish.

Mat-1.403 Basic course in Mathematics L 3 (6 cr)

Autumn
Lecturer: Prof Olavi Nevanlinna and Prof Timo Eirola
Contents: Functions of one complex variable, linear algebra, systems of differential equations and solving them numerically.
Literature: To be announced later + supplementary material.
Prerequisites: Mat-1.401 and Mat-1.402
Language: Finnish.

Mat-1.404 Basic course in Mathematics L 4 (6 cr)

Spring
Lecturer: Prof Timo Eirola
Contents: Basic types of linear partial differential equations; their qualitative properties and numerical solution. Introduction to integral equations and their numerics. Examples of nonlinear partial differential equations.
Literature: Supplementary material.
Prerequisites: Basic courses in Mathematics 1 - 3
Language: Finnish.

Mat-1.411 Basic course in Mathematics C 1 (TIK, AUT, TUO,MAA, INF) (6 cr)

Autumn
Lecturer: Harri Hakula, researcher
Contents: Linear algebra, linear systems of equations, calculus of one variable, introduction to number theory, elementary graph theory. Basic courses in Mathematics C1-3 are intended for the degree programmes TIK, AUT, TUO and MAA and C1 also for the degree programme INF.
Literature: S. K. Kivelä, 1989. Algebra ja geometria, Otatieto. S. K. Kivelä, 1992. Reaalimuuttujan analyysi, Otatieto. S. Ilkka, 1989. Diskreettiä matematiikkaa. Otatieto. Supplementary material.
Language: Finnish.
Additional information:http://www.math.hut.fi/teaching/c1/

Mat-1.412 Basic course in Mathematics C 2 (TIK, AUT, TUO, MAA) (6 cr)

Spring
Lecturer: Harri Hakula, researcher
Contents: Ordinary differential equations, sequences and series, power series, vector calculus, introduction to algebra.
Literature: E. Kreyszig, 1999. Advanced Engineering Mathematics. John Wiley & Sons.S. Ilkka, 1989. Diskreettiä matematiikkaa. Otatieto. Supplementary material.
Prerequisites: Mat-1.411.
Language: Finnish.
Additional information: http://www.math.hut.fi/teaching/c2/
 

Mat-1.413 Basic course in Mathematics C 3 (TIK, AUT, TUO, MAA) (6 cr)

Autumn
Lecturer: Juha Kinnunen, senior assistant
Contents: Complex analysis, linear analysis, Fourier-analysis and partial differential aquations.
Literature: E. Kreyszig, 1988/ 1993. Advanced Engineering Mathematics. John Wiley & Sons (Sixth/Seventh Edition). Supplementary material.
Prerequisites: Basic courses in Mathematics L/C 1-2.
Language: Finnish.

Mat-1.414 Basic course in Mathematics V 2 (INF) (6 cr)

Spring
Lecturer: Heikki Apiola, lecturer
Contents: Complex numbers and functions, calculus of several variables, numerical methods, series, optimization, difference and differential equations, various applications, use of Mathematical software, especially Matlab and Maple.
Prerequisites: Mat-1.411.
Additional information: http://www.math.hut.fi/teaching/v/2/
Language: Finnish.

Mat-1.415 Basic course in Mathematics V 3 (INF) (6 cr)

Autumn
Lecturer: Heikki Apiola, lecturer
Contents: Complex variables, linear algebra, systems of difference and differential equations, Fourier series, Laplace- Fourier- and Z-transforms, probability and statistics, elements of PDE, numerical methods, use of Mathematical software, especially Matlab and Maple.
Prerequisites: Mat-1.411 and Mat-1.414.
Additional information: http://www.math.hut.fi/teaching/v/3/
Language: Finnish.

Mat-1.421 Basic course in Mathematics S 1 (ES, TLT) (6 cr)

Autumn
Lecturer: Prof Gustaf Gripenberg
Contents: Vector and matrix algebra, linear systems of equations, eigenvalues, real and complex numbers, analytical geometry, differential and integral calculus for functions of one variable, interpolation, numerical quadrature, curves.
Literature: R. A. Adams, 1999. Calculus, A Compelete Course. Addison-Wesley Ltd. E. Kreyszig, 1999. Advanced Engineering Mathematics. John Wiley & Sons.
Language: Finnish.

Mat-1.422 Basic course in Mathematics S 2 (ES, TLT) (6 cr)

Spring
Lecturer: Prof Erkki Somersalo and Seppo Weikkolainen, specialist teacher
Contents: Series, power series, ordinary differential equations, numerical methods, vector calculus, vector fields, Gauss's and Stokes's theorems, curvilinear coordinates.
Literature: R. A. Adams, 1999. Calculus, A Compelete Course. Addison-Wesley Ltd.
Prerequisites: Mat-1.421.
Language: Finnish.

Mat-1.423 Basic course in Mathematics S 3 (ES, TLT) (6 cr)

Autumn
Lecturer: Prof Erkki Somersalo
Contents: Functions of complex variable, residue calculus, potential theory, Laplace-, Fourier, and Z-transforms. Matrix calculus: LU and QR decompositions, numerical methods, matrix series. Systems of differential equations: properties of solutions, stability, numerical methods.
Basics of partial differential equations; Laplace-, heat-, and wave equations.
Literature:E. Kreyszig, 1999. Advanced Engineering Mathematics, John Wiley & Sons. Supplementary material.
Prerequisites: Mat-1.421 and Mat-1.422
Language: Finnish.

Mat-1.431 Basic course in Mathematics K 1 (KON, RYK, ARK, MAA) (6 cr)

Autumn
Lecturer: N.N.
Contents: Vector and matrix algebra, lines and planes, matrices, 2nd degree curves and surfaces. Functions of one variable: Continuity, derivative, Newton's method, integrals (analytically and numerically), Taylor's polynomial and theorem.
Literature: R. A. Adams, 1999. Calculus, A Compelete Course. Addison-Wesley Ltd. Supplementary material.
Language: Finnish.
Additional information: http://www.math.hut.fi/opetus/k1/index.html.fi

Mat-1.432 Basic course in Mathematics K 2 (KON, RYK, ARK, MAA) (6 cr)

Spring
Lecturer: N.N. and Prof Jerry Segercrantz
Contents: Theory of curves, calculus of several variables: differential calculus, extreme values, regression lines, double and triple integrals. Vector fields: Green's, Gauss's and Stokes's theorems. Complex numbers. Differential equations. Series.
Literature: R. A. Adams, 1999. Calculus, A Compelete Course. Addison-Wesley Ltd.  Supplementary material.
Prerequisites: Mat-1.431
Language: Finnish.
Additional information: http://www.math.hut.fi/opetus/k2/index.html.fi

Mat-1.433 Basic course in Mathematics K 3 (KON, RYK, ARK, MAA) (6 cr)

Autumn
Lecturer: Pekka Alestalo, researcher
Contents: Matrices and eigenvalues, systems of differential equations, Laplace-transform, complex analysis, Fourier series, elements of partial differential equations, numerical methods.
Literature: E. Kreyszig, 1999. Advanced Engineering Mathematics, John Wiley & Sons.
Prerequisites: Mat-1.431 and Mat-1.432.
Language: Finnish.
Additional information: http://www.math.hut.fi/opetus/k3/index.html.fi

Mat-1.441 Basic course in Mathematics P 1 (KEM, MAK, PUU) (6 cr)

Autumn
Lecturer: Prof Gennadi Vainikko
Contents: Vector algebra, lines and planes, matrices, conic sections, quadric surfaces. Functions of one variable: continuity, derivative, solving equations, integral (analytically and numerically), theory of curves, Taylor polynomials, interpolation. Basic courses in Mathematics P 1-3 are intended for the degree programmes KEM, MAK and PUU.
Literature: S. I. Grossman, 1998. Calculus. Saunders College Publishing. S. I. Grossman, 1995. Multivariable Calculus, Linear Algebra and Differential Equations. Saunders College Publishing.
Language: Finnish.

Mat-1.442 Basic course in Mathematics P 2 (KEM, MAK, PUU) (6 cr)

Spring
Lecturer: Pekka Alestalo, researcher
Contents: Calculus of several variables, method of least squares; plane, space and line integrals; Green, Gauss and Stokes formulas, differential equations, series.
Literature: S. I. Grossman, 1992. Calculus. Saunders College Publishing. Or S. I. Grossman, 1995. Multivariable Calculus, Linear Algebra and Differential Equations. Saunders College Publishing.
Additional information: http://www.math.hut.fi/teaching/p2/ index.html.fi
Prerequisites: Mat-1.441.
Language: Finnish.

Mat-1.443 Basic course in Mathematics P 3 (KEM, MAK, PUU) (6 cr)

Autumn
Lecturer: Pekka Alestalo, researcher
Contents: Matrices and eigenvalues, numerical linear algebra, systems of differential equations, integral transforms, Fourier series, partial differential equations, complex analysis.
Literature: E. Kreyszig, 1999. Advanced Engineering Mathematics. John Wiley & Sons. Supplementary material.
Additional information: http://www.math.hut.fi/teaching/p3/ index.html.fi
Prerequisites: Mat-1.441 and Mat-1.442.
Language: Finnish.

Mat-1.451 Basic course in Mathematics 1 (6 cr)

Autumn
Lecturer: Georg Metsalo, lecturer
Contents: Complex numbers, vector algebra, systems of linear equations, matrices, eigenvalues and -vectors. Functions of a real variable, continuity, the derivative and its applications, Taylor's theorem. Integration of elementary functions, numerical integration, applications of definite integrals. Taylor's series.
Literature: R. A. Adams, 1999. Calculus, A Complete Course. Addison-Wesley Ltd. (4th ed.). E. Kreyszig, 1999. Advanced Engineering Mathematics. John Wiley & Sons, (8th ed.).
Language: Swedish.

Mat-1.452 Basic course in Mathematics 2 (6 cr)

Spring
Lecturer: Georg Metsalo, lecturer
Contents: Vector valued functions. Functions of a vector variable, continuity, differentiation, extremal values. Quadratic curves and surfaces.  Integrals over curves, planes, surfaces and solids, nabla, Green's, Gauss' and Stokes' theorems. Ordinary differential equations (analytical and numerical methods). Sequenses and series.
Literature: R. A. Adams, 1999. Calculus, A Complete Course. Addison-Wesley Ltd. (4th ed.). E. Kreyszig, 1999. Advanced Engineering Mathematics. John Wiley & Sons (8th ed.).
Prerequisites: Mat-1.451.
Language: Swedish.

Mat-1.453 Basic course in Mathematics 3 (6 cr)

Autumn
Lecturer: Prof Jerry Segercrantz
Contents: Complex analysis, Laplace and Fourier transforms, Fourier series, series and discretization solutions of partial differential equations (Laplace's equation, heat equation, wave equation), matrix methods for systems of differential equations.
Literature: Litteratur: E. Kreyszig, 1999. Advanced Engineering Mathematics. John Wiley & Sons (8. ed.). Supplementary material.
Prerequisites: Mat-1.451 and Mat-1.452.
Language: Swedish.

Mat-1.461 Mathematics 1 (6 cr)

Autumn
Lecturer: N.N.
Contents: Vector and matrix algebra, lines and planes, matrices, 2nd order curves and surfaces. Functions of one variable: Conti-nuity, derivative, Newton's method, integrals (analytically and numerically), theory of curves, curvature, Taylor's polynomial and theorem. Interpolation.
Literature: H. Anton, 1995. Calculus with Analytic Geometry. John Wiley & Sons (5th ed.). Or R. A. Adams, 1999. Calculus, A Compelete Course. Addison-Wesley Ltd. Supplementary material.
Language: English.

Mat-1.462 Mathematics 2 (6 cr)

Spring
Lecturer: N.N.
Contents: Calculus of several variables: Differential calculus, extreme values, regression lines, double and triple integrals. Vec-tor fields: Green's, Gauss's and Stokes's theorems. Complex numbers. Differential equations. Series.
Literature: H. Anton, 1995. Calculus with Analytic Geometry. John Wiley & Sons (5th ed). Or R. A. Adams, 1999. Calculus, A Compelete Course, Addison-Wesley Ltd. Supplementary material.
Prerequisites: Mat-1.461.
Language: English.

Mat-1.463 Mathematics 3 (6 cr)

Autumn (Exercises, no lectures)
Lecturer: N.N.
Contents: Vector and matrix algebra. Eigenvalue theory. Met-hod of least squares. Theory and numerical methods of differen-tial equations and systems of differential equations. The Laplace transform. Power and Fourier series. Elements of complex func-tions and partial differential equations.
Literature: E. Kreyszig, 1999. Advanced Engineering Mathematics. J. Wiley & Sons. Supplementary material.
Prerequisites: Mat-1.461 and Mat-1.462.
Language: English.

Mat-1.015 Foundations of Modern Analysis (2.5 cr)

Spring
Lecturer: Prof Olavi Nevanlinna
Contents: This course provides material on fundamental concepts and methods in analysis for later studies in mathematics. Principles of topology in metric spaces, continuity and derivation, basics in distribution theory.
Literature: R. F. Gariepy, W. P. Ziemer;  Modern real analysis, Boston [Mass.]: PWS-Publishing, cop. 1995
Prerequisites: Basic course in Mathematics 1 (L/C/S).
Language: Finnish.

Mat-1.020 Basic Ideas in Mathematics (2-4 cr)

Lectures / requirements of the course must be discussed with the teacher.
Lecturer: Kari Eloranta, researcher
Contents: In the course a few fundamental mathematical constructions are presented together with concrete examples illustrating their significance. Special emphasis is on geometric intuition and the interplay between geometry and analysis. Topics: Geometric and abstract symmetries, groups, matrices, tilings, duality. The course aims to deepen the understanding of mathematics of architects and engineering students.
Language: Finnish.

Mat-1.041 History of Science (2-4 cr) P

Not lectured 2001-2002.

Mat-1.042 Philosophy of Science (2-4 cr) P

Not lectured 2001-2002.

Mat-1.080 Principles of Mathematical Logic (1 cr) P

Spring
Lecturer: Seppo Ilkka, lecturer
Contents: About the logical basis of some theories in mathematics and its applications. Formal logic, propositional calculus and predicate calculus. Foundations of set theory and number theory. Decidability problem, and Turing machines and Gödel's theorem. Classical paradoxes. Classical and non-classical systems of logic.
Literature: Supplementary material.
Language: Finnish.

Mat-1.100 Mathematical software as a tool (1 cr)

Autumn (two weeks in August-September)
Lecturer: Simo Kivelä, lecturer
Contents: The use of symbolic mathematical software (e.g. Mathematica, Maple) in mathematical problem solving.
Requirements: Compulsory exercises and a larger individual work.
Literature: Digital study material.
Language: Finnish, possibility to get study material in English.

Mat-1.125 Individual Research Project in Mathematics (3-6 cr)

Lecturer: Prof Olavi Nevanlinna
Contents: Individual research work related to mathematical problems in practice.
Language: Finnish / English / Swedish.

Mat-1.128 Discrete Mathematics (3 cr)

Spring
Lecturer: Seppo Ilkka, lecturer
Contents: Combinatorics, counting problems, generating functions, groups of permutations, and the theorems of Burnside and Polya. Number theory, congruence arithmetics, pseudoprimes, and principles of cryptology. Algebra, finite fields, and elementary coding theory.
Literature: Supplementary material. Highly recommended are also R.P.Grimaldi, 1999. Discrete and Combinatorial Mathematics. Addison-Wesley. And K.H. Rosen, 1993. Elementary Number Theory and its Applications. Addison-Wesley.
Prerequisites: Basic courses in Mathematics 1-2.
Language: Finnish.

Mat-1.129 Applied Geometry (2 cr)

Not lectured 2001-2002.
Lecturer: Seppo Ilkka, lecturer
Contents: Some geometrical constructions. Projective geometry, spherical geometry, linear and curved coordinate systems, and their transformations, volumes of solids, areas of surfaces, and lengths of curves with their numerical calculation.
Literature: Supplementary material.
Language: Finnish.

Mat-1.131 Mathematical Methods of Chemical Engineering (3 cr)

Lecturer: Pekka Alestalo, researcher
Requirements: The fulfilling of the requirements must be discussed with the teacher. Registration for the course is in connection with the course Mat-1.443 Basic course in Mathematics P 3.
Prerequisites: Basic courses in Mathematics 1-2.
Language: Finnish.

Mat-1.132 Mathematical Methods of Physics (2.5 cr)

Autumn
Lecturer: Seppo Weikkolainen, specialist teacher
Contents: Special functions, introduction to calculus variations, orthogonal functions and Sturm-Liouville problem.
Literature: Arfken. Mathematical Methods for Physicists.  E. Kreyszig. Advanced Engineering Mathematics. John Wiley & Sons. Supplementary material.
Prerequisites: Basic course in Mathematics L1-L3.
Language: Finnish.

Mat-1.140 Principles of Functional Analysis (4 cr) P

Autumn
Lecturer: Prof Gennadi Vainikko
Contents: Banach- and Hilbert spaces. Theory of linear operators. Applications to differential and integral equations and to numerical analysis.
Literature:E. Kreyszig, 1989. Introductory Functional Analysis with Applications, John Wiley & Sons.
Prerequisites: Basic courses in Mathematics 1-2 and Mat-1.015.
Language: Finnish / English.

Mat-1.141 Applied Functional Analysis (2-4 cr) P V

Not lectured 2001-2002.
Lecturer: Prof Gennadi Vainikko
Contents: Ill-posed problems (e.g. inverse problems) and the regularization of these. Iteration methods.
Prerequisites: Mat-1.140.
Language: Finnish / English.

Mat-1.142 Seminar on Mathematics (1.5-3 cr) P V

Autumn+spring
Lecturer: Prof. Stig-Olof Londen and Juha Kinnunen, senior assistant
Contents: To be announced later.
Language: English on demand.

Mat-1.143 Mathematical Principles of Physics (2-4 cr) P V

Lectures / requirements of the course must be discussed with the teacher.
Lecturer: Kari Eloranta, researcher
Contents: Fundamentals of statistical physics and dynamical systems, in particular deterministic and stochastic lattice models (Ising etc.), cellular automata and more general symbolic dynamics.
Language: Finnish / English.

Mat-1.144 Non-Linear Functional Analysis (2-4 cr) P

Not lectured 2001-2002.
Lecturer: Prof Gennadi Vainikko
Contents: Banach fixed point theorem, derivatives of non-linear operators, applications to optimization theory, Newton method for solving non-linear equations, Schauder fixed point theorem, monotone operators, introduction to degree theory, bifurcations.
Literature: V. Hutson & J.S. Pym, 1980. Applications of Functional Analysis and Operator Theory. Academic Press.
Prerequisites: Mat-1.140.
Language: Finnish / English.

Mat-1.145 Periodic Pseudodifferential Equations (2-4 cr) P

In spring 2002 the scope of the course is 4 cr.
Lecturer: Prof Gennadi Vainikko
Contents: Integral equations on a closed curve, theory of periodic integral and pseudodifferential operators, fast solution of equations.
Literature: J. Saranen & G. Vainikko. Periodic Integral and Pseudodifferential Equations with Numerical Approximation. Springer (manuscript).
Prerequisites: Mat-1.140.
Language: Finnish / English.

Mat-1.146 Basic Algebra (4 cr) P

Autumn
Lecturer: Seppo Ilkka, lecturer
Contents: Groups, rings, integral domains, fields, and vector spaces. Homorphisms and isomorphisms. Polynomial rings, and field extensions.
Literature: W. K. Nicholson, 1999. Abstract Algebra. Wiley. Or supplementary material.
Prerequisites: Basic courses in Mathematics 1-3.
Language: Finnish.

Mat-1.150 Real Analysis (2-4 cr) P V

Lectured autumn 2002.
Lecturer: Prof Stig-Olof Londen
Contents: Lebesguen measure and integration theory, Borel measures, complex measures, Lp-spaces, Riesz representation theorem, product integrals, absolute continuity, differentiation. Literature: Rudin: Real and Complex Analysis, ch. 1-9.
Prerequisites: Basic courses in Mathematics 1-2 and Mat-1.015.
Language: English on demand.

Mat-1.151 Complex Analysis (4 cr) P V

Not lectured 2001-2002.
Lecturer: Prof Stig-Olof Londen
Contents: Properties of analytic functions, harmonic functions, maximum principle, conformal mappings, Hp-spaces.
Literature: To be announced later.
Language: English on demand.

Mat-1.152 Special Course in Functional Analysis (4 cr) P V

Not lectured 2001-2002.
Lecturer: Prof Olavi Nevanlinna
Language: Finnish / English.

Mat-1.155 Theory of Partial Differential Equations (4 cr) P V

Spring
Lecturer: Juha Kinnunen, senior assistant
Contents: Basic properties of Sobolev spaces and applications to partial differential equations.
Prerequisites: Basic courses in mathematics.
Literature: To be announced later.
Language: Finnish/ English.

Mat-1.156 Integral Equations (3 cr) P V

Not lectured 2001-2002.
Lecturer: Prof Gennadi Vainikko
Contents: Theory and numerical methods for Fredholm and singular integral equations. Prerequisites: Mat-1.140
Language: Finnish/ English.

Mat-1.158 Basics of Fourier Analysis (3 cr) P

Not lectured 2001-2002.
Requirements of the course must be discussed with the teacher.
Lecturer: Prof Gustaf Gripenberg
Contents: Fourier series, Fourier transform of L1 - and L2 -functions and distributions, discrete Fourier transform, applications.
Prerequisites: Basic courses in Mathematics 1 (and 3).
Language: Finnish/ English.

Mat-1.159 Harmonic Analysis and Partial Differential Equations (2-4 cr) P V

Spring
Lecturer: Prof Stig-Olof Londen
Contents: To be announced later.
The scope of the course is 4 cr this year.
Language: English on demand.

Mat-1.162 Distributed Parameter Systems (2-4 cr) P V

Autumn
Lecturer: Olof Staffans, Docent
Contents: Formulation as distributed parameter systems as abstract differential equations or semigroups, the basic theory of semigroups, initial value problems, feedback, time dependent systems, controllability and observability, stabilizability and detectability, optimal control.
Literature: R. Curtain & H. Zwart, 1995. An Introduction to Infinite-Dimensional Systems Theory. Springer-Verlag.
Prerequisites: Mat-1.015 or Mat-1.140 and AS-74.170 are recommended.
The scope of the course is 2 cr this year.
Language: English/ Finnish/ Swedish.

Mat-1.163 Transfer Function Theory (2-4 cr) P V

Spring
Lecturer: Jarmo Malinen, researcher
Contents: Some additions to complex function theory, such as the theory of the function spaces H2 and H-infinity, and factorization of
analytic functions. The mapping of discrete time transfer functions onto continuous time transfer functions and reversely. Parameterization
of all stabilizing compensators, H2- and H-infinity control. Optimal compensators and robust systems.
Prerequisites: Mat-1.423 (or equivalent) and basic courses in control theory.  Mat.162 is also highly recommended.
The scope of the course is 2 cr this year.
Language: English/ Finnish/ Swedish.

Mat-1.165 Dynamical Systems (2-4 cr) P V

Not lectured 2001-2002.
Lecturer: Prof Stig-Olof Londen
Contents: Theory of ordinary differential equations and dynamical systems.
Language: English on demand.

Mat-1.166 Differential Geometry (2-4 cr) P V
Spring
Lecturer: Kirsi Peltonen, researcher
Contents: Topics related to differential geometry varying from classical Riemannian geometry to modern geometries. More specified topics will be announced later.
Prerequisites: Basic courses in Mathematics 1-3 and Mat-1.015.
The scope of the course is 4 cr this year.
Language: Finnish.

Mat-1.169 Finite Difference Methods (2.5 cr) P
Autumn
Lecturer: Prof Olavi Nevanlinna
Contents: Difference methods for the numerical solutions of ordinary and partial differential equations; in particular stability and convergence for systems of ordinary differential equations and for basic elliptic, parabolic and hyperbolic equations.
Prerequisites: Basic courses in Mathematics 1-3.
Language: Finnish, English on demand.

Mat-1.170 Theory of Approximation (3 cr) P
Not lectured 2001-2002.
Lecturer: Prof Timo Eirola
Contents: Approximation of functions with polynomials, splines, trigonometric functions and wavelets in different norms.
Literature: Lecture notes.
Prerequisites: Mat-1.015 (or equal).
Language: Finnish / English.

Mat-1.171 Principles of Finite Element Method (2,5 cr) P
Spring
Lecturer: Ville Havu, researcher
Contents: Sobolev spaces, elliptic variational problems, mathematical background of finite element method, most common element types, approximation properties of polynomials, practical aspects.
Literature: D. Braess, 1997. Finite elements. Cambrigde, University Press.
Prerequisites: Basic courses in Mathematics 1-3/4.
Language: Finnish.

Mat-1.174 Computational Methods of Partial Differential Equations (2-4 cr) P V

Not lectured 2000-2001.
Lecturer: Heikki Apiola, lecturer
Contents: Handling, implementation and analysis of algorithms based on FD- and FEM-methods. Matlab and Maple are in heavy use, especially the PDE-toolbox (or Femlab).
Prerequisites: Mat-1.169 and Mat-1.171 (or equal).
Additional information: http://www.math.hut.fi/teaching/osdylask/index.html.en
Language: English on demand.

Mat-1.178 Summer School in Numerical Analysis (0.5-10 cr) P V

Lecturer: Prof Olavi Nevanlinna
Contents: Graduate course, time and topics vary. Subject and scope of the course will be announced separately.
Language: Finnish / English.

Mat-1.179 Special Course in Numerical Analysis (2-4 cr) L V

36+18 (9 x (4+2)) sl
Lecturer: Prof Timo Eirola
Contents: Discretization methods for ordinary differential equations and their analysis. Qualitative numerical integration.
Literature: Parts of books  E. Hairer, S. P. Nørsett & G. Wanner, 1993.  Solving Ordinary Differential Equations I. Springer-Verlag.  E. Hairer & G. Wanner, 1996. Solving Ordinary Differential Equations II. Springer-Verlag.
 

Mat-1.180 Complex Analysis (2-5 cr) P V

Not lectured 2001-2002.
Lecturer: Prof Olavi Nevanlinna
Language: Finnish / English.

Mat-1.187 Special Course in Dynamical Systems (2-4 cr) P V

Not lectured 2001-2002.
Lecturer: Prof Timo Eirola
Contents: Varying yearly.
Language: Finnish / English.

Mat-1.188 Fuzzy Sets (2 cr) P

The fulfilling of the requirements must be discussed with the teacher.
Lecturer: Seppo Ilkka, lecturer
Contents: Crisp and fuzzy definitions in set theory, fuzzy operations for basic arithmetic and analysis. Fuzzy graphs and relations. About possibility and probability. Fuzzy logic and approximate reasoning.  Applications.
Literature: H.-J. Zimmermann. Fuzzy Set Theory and Its Applications.  Kluwer-Nijhoff Publishing. Or supplementary material.
Prerequisites: Basic courses in Mathematics 1-3.
Language: Finnish.

Mat-1.189 Discrete Mathematical Methods (2-4 cr) P V

Autumn
Lecturer: Seppo Ilkka, lecturer
Contents: Combinatorics, finite incidence structures, finite geometries and B.I.B.D.-designs, applications to design of experiments and coding theory.
Literature: Supplementary material.
Prerequisites: Basic courses in Mathematics 1-3.
Language: Finnish.
In autumn 2000 the scope of the course is 3 cr.

Mat-1.190 Computational Complexity (2 cr) P

The fulfilling of the requirements must be discussed with the teacher.
Lecturer: Seppo Ilkka, lecturer
Contents: The computational complexity of algorithms. Estimates of magnitude and growth rate of functions, recursive algorithms. About the computational strategies. Graph problems. Complexity analysis.
Literature: H. S. Wilf, 1986.  Algorithms and Complexity. Prentice-Hall. Or supplementary material.
Prerequisites: Basic courses in Mathematics 1-3.
Language: Finnish.

Mat-1.191 Number Theory (2 cr) P

The fulfilling of the requirements must be discussed with the teacher.
Lecturer: Seppo Ilkka, lecturer
Contents: Divisibility of integers, prime numbers, and pseudoprimes. Diophantine equations, and congruence arithmetic. Squares and non-squares in congruence arithmetic. Primitive roots. Continued fractions. Some methods of cryptology.
Literature: K.H. Rosen, 1993. Elementary Number Theory and its Applications. Or supplementary material.
Prerequisites: Basic courses in Mathematics 1-3.
Language: Finnish.

Mat-1.192 Numeric and Symbolic Computation (2-4 cr) P

Not lectured 2000-2001.
Lecturer: Heikki Apiola, lecturer
Contents: Flexible use of Numeric and symbolic software (Maple and Matlab). Numerical methods, mathematical modelling, project work.
Prerequisites: Basic courses in Mathematics 1-3
Additional information: http://www.math.hut.fi/teaching/numsym/ index.html.en
Language: English on demand.

Mat-1.194 Engineering Mathematics (2-4 cr) P V

Not lectured 2001-2002.
Lecturer: Prof Juhani Pitkäranta
Contents: The course reviews the mathematical and computational methods, both traditional and modern, in different fields of engineering science from a problem oriented point of view. The theme is variable.
Literature: Supplementary material.
Prerequisites: Basic courses in Mathematics 1-3.
Language: Finnish, English on demand.
 

Mat-1.196 The Mathematics of neural computing (2 cr) L

Spring
Lecturer: prof. Gustaf Gripenberg
Contents: To be announced later.
Literature: Supplementary material.

Mat-1.197 Inverse Theory (2-4 cr) P V

Spring
Lecturer: Prof Erkki Somersalo
Contents: The lectures in spring 2002 will concentrate on numerical and computational aspects of inverse problems. The main emphasis is
on statistical methods applied to inverse problems, based on the Bayesian point of view. Topics discussed during the course: Regularization methods and their statistical interpretation, interpretation of the prior information, dynamic inverse problems, Monte Carlo methods for exploring the posterior distributions. The scope of the course is 4 cr.
Literature: Course material will be distributed during the course.
Language: English on demand.

Mat-1.198 Scattering Theory (2-4 cr) P

Not lectured 2001-2002.
Lecturer: Prof Erkki Somersalo
Contents: Scattering of acoustic and electromagnetic waves, scattering operator, radiation conditions, surface integral methods, quantum mechanical scattering, inverse problems. The contents may vary yearly.
Prerequisites: Mat-1.015 (or equal).
Language: English on demand.

Mat-1.199 Research Forum in Computational Engineering (3 cr) P V

Not lectured 2000-2001.
Lecturer: Prof Juhani Pitkäranta
Contents: The course is arranged in seminar form. The seminar is intended mainly for postgraduate students who have mathematics as a secondary, or possibly primary, subject and have specialized (or plan to specialize) in computational methods in some field of engineering science or physics.
Language: English on demand.

Mat-1.217 Differential Equations of Mathematical Physics (2-4 cr) P

Not lectured 2001-2002.
Lecturer: Prof Erkki Somersalo
Contents: The course concentrates on certan partial differential equations encountered in central areas of physics, including the Schrodinger
equation, the wave equations and Maxwell's equations. The contents of the course varies from year to year.
Literature: R. Leis. Initial Boundary-value Problems in Mathematical Physics. Teubner.  Reed & Simon. Methods of Mathematical Physics I-IV. Academic Press.
Language: English on demand.

Mat-1.218 Seminar on Inverse Problems (1.5-4 cr) P V

Not lectured 2001-2002.
Lecturer: Prof Erkki Somersalo
Contents: The seminar will assembly irregularly in times that are announced separately. For seminar information, the students are asked to announce their contact information to the lecturer. The topics of the seminar include actual research topics as well as topics of the diploma, licentiate and doctoral thesises.
Language: English on demand.

Mat-1.501 Martingale Theory II (2 cr) P

Not lectured 2001-2002.
Lecturer: Prof Stig-Olof Londen
Contents: To be announced later.
Language: English on demand.