Takaisin kotisivulle.
Oppimateriaaleja
TKK:n loputtua organisatorisesti jo vanhentuneita, mutta aihe on ikuinen.
-
TKK:n matematiikan peruskurssi S1:n differentiaaliyhtälöt:
pdf-tiedosto.
-
TKK:n matematiikan peruskurssi S1:n Laplace-muunnokset:
pdf-tiedosto.
-
Lyhyt kurssi säätöteoriasta mukaillen B. Francisin kirjaa
"A course in H-inf control theory":
pdf-tiedosto.
Koronakevään 2020 Lineaarialgebran MS-C1342/MS-C1342 Panopto-luennot englanniksi
- Solvability of linear systems of equations. Range and null space. Linear span and independence. Dimension of a subspace.
Luento 1a
- An example.
Luento 1b
- Dimension theorem.
Luento 2a
- Equivalent conditions for unique solvability. Inverse matrix.
Luento 2b
- Vector norms.
Luento 3a
- Inner product and inner product spaces. Orthogonality and orthonormality.
Luento 3b
- Triangle inequality and Cauchy-Schwarz inequality. Representation of inner products by positive definite matrices.
Luento 3c
- Matrix and operator norms. Inequalities associated to them.
Luento 4
- Cauchy sequences and completeness. Hilbert and Banach spaces.
Luento 5a
- Stability of the solution of a linear system of equation. Condition number.
Luento 5b
- Complex inner product spaces. Eivenvalue problem.
Luento 6a
- Computation of eigenvalues. Characteristic polynomial. Geometric multiplicity. Determinants.
Luento 6b
- Fundamental theorem of algebra. Existence of eigenvalues. Algebraic multiplicity. Linear independence of eigenvectors. Defective matrices.
Luento 6c
- Hermitian and unitary matrices. Spectral theory of hermitian matrices. Unitary diagonalisation. Computations with block matrices.
Luento 7
- Similarity transformations. Diagonalisation revisited. Matrix polynomials.
Luento 8a
- Schur decomposition. Unitary similarity with triangular matrices. Jordan blocks and matrices. Jordan canonical form.
Luento 8b
- Matrix exponential. Solution of first order systems of linear differential equations. Computations by canonical forms.
Luento 8c
- Qualitative analysis of systems of first-order differential equations. Stability of equilibria.
Luento 9a
- Least squares problems. Normal equations and least squares solutions. Parameter estimation in practical problems.
Luento 9a
- Singular value decomposition (SVD). Left and right singular vectors, singular values. Partial isometries.
Luento 12a
- Computation of SVD in "economic form" and matrix form.
Luento 12b
- Characterisation of various subspaces in terms of singular vectors. Normal equations and the SVD.
Luento 12c
Luennot 10 ja 11 olivat Nuutti Hyvösen pitämiä.
Koronasyksyn 2020 matematiikan peruskurssin "DiffInt1" (MS-A0103 ja MS-A0104) Panopto-luennot ("pitkän kaavan mukaisesti")
Koronakevään 2021 matematiikan peruskurssin "DiffInt2" (MS-A0203 ja MS-A0205) Panopto-luennot
Koronasyksyn 2021 matematiikan peruskurssin "DiffInt1" (MS-A0103 ja MS-A0104) Panopto-luennot (lyhyemmän kaavan mukaisesti)
Muuta yliopisto-outoutta
-
Absurdi, matematiikkaa sivuava kvasi-elämänkerrallinen novellini
"Aftermath", jolla osallistuin Nova'2003 Sci-fi
-kirjoituskilpailuun (sijoittunut jonnekin välille 11-20):
pdf-tiedosto.
-
TKK:n Matematiikan laitoksella testatut ohjeet perinteisen voipullan
leivontaan: pdf-tiedosto.
Not by myself but instructive nevertheless
- What is wrong with our regular mathematics teaching? Check this out:
TED.com.
- "The greatest shortcoming of the human race is our inability to understand the exponential function.":
Dr Albert Bartlett will now teach you.
-
Let me introduce you the great mathematician in showbiz, Tom Lehrer:
Selling out (is easy to do):
mp3.
- This reminds me of some research projects that I have been involved in:
jpg .
