A philosophy for the use of computers during university lectures is presented. Tutorial-type comp... more A philosophy for the use of computers during university lectures is presented. Tutorial-type computer-aided instruction (CAI) methods often have disadvantages: the computer takes a central role "in the teaching process and the production of proper CAI lessons is tedious and often demands to many resources. The result might be "an electronic book" and the basic flavour of classroom lectures is missing. We propose a different use of computers in the classroom situation, based on cognitive views. If proper software and devices are available, the teacher could use the computer for preparing lectures, presenting them in the classroom and preparing support material. Some properties of the proposed principles are discussed. Practical experience is based on a few experimental lecture outlines for teaching data processing topics to computer science students at the University of Helsinki.
Basic concepts of asymptotic theory for discretization methods have been defined so that converge... more Basic concepts of asymptotic theory for discretization methods have been defined so that convergence is always equivalent to consistency and stability. The theory is then applied to a class of discretization methods for the initial value problems of ordinary differential equations, the so-called weakly nonlinear methods.
Generalized Hermite-Birkhoff interpolation gives a unifying method for constructing exponentially... more Generalized Hermite-Birkhoff interpolation gives a unifying method for constructing exponentially fitted linear multistep methods explicitly. Fitting may be done at any set of given (real) parameters. The construction principle permits study of the convergence and stability properties of these methods. Moreover, it shows how the properties depend on the corresponding properties of classical linear multistep methods with constant coefficients. The theoretical results are illustrated by some examples. x), X(to) = x o, which we assume to have a unique solution x ~ C1(I, R). We want to approximate values x(tl) of this solution by values Yl in an equally spaced set of points I m = {t t = t o + ih [ i = 0, 1 .... , m; mh = T}. The device that produces values Yi is called numerical method. Several authors, e.g. Liniger and Willoughby [6], Bjurel [1], van der ttouwen [4], have proposed exponentially fitted methods to obtain stability properties suitable for stiff (cf. e.g. Lambert [5], chapter 8, and Bjurel et al. [2] ) differential equations. A numerical method is said to be exponentially fitted of order p at a value A if it integrates exactly problems (1.1) that have solutions of the form P(t)e ~ where P(t) is any polynomial of degree not exceeding p. I.e. the method yields values of the exact theoretical solution P(t)e ~t provided that the exact initial conditions are used and the computations are exact. This definition implies that a method which integrates exactly problems with solutions in the linear space Ars spanned by
A procedure to habituate Highland Cattle calves to humans evolved with four years' experiment... more A procedure to habituate Highland Cattle calves to humans evolved with four years' experimentation on one farm by one male human handler. Data includes results of 18 bull and 20 heifer calves, from 14 dams and 4 sires. In 24 cases, they were fearless and easy to handle all the time. Fearful 8 heifer and 6 bull calves got little or unpleasant handling during first weeks.
A philosophy for the use of computers during university lectures is presented. Tutorial-type comp... more A philosophy for the use of computers during university lectures is presented. Tutorial-type computer-aided instruction (CAI) methods often have disadvantages: the computer takes a central role "in the teaching process and the production of proper CAI lessons is tedious and often demands to many resources. The result might be "an electronic book" and the basic flavour of classroom lectures is missing. We propose a different use of computers in the classroom situation, based on cognitive views. If proper software and devices are available, the teacher could use the computer for preparing lectures, presenting them in the classroom and preparing support material. Some properties of the proposed principles are discussed. Practical experience is based on a few experimental lecture outlines for teaching data processing topics to computer science students at the University of Helsinki.
Basic concepts of asymptotic theory for discretization methods have been defined so that converge... more Basic concepts of asymptotic theory for discretization methods have been defined so that convergence is always equivalent to consistency and stability. The theory is then applied to a class of discretization methods for the initial value problems of ordinary differential equations, the so-called weakly nonlinear methods.
Generalized Hermite-Birkhoff interpolation gives a unifying method for constructing exponentially... more Generalized Hermite-Birkhoff interpolation gives a unifying method for constructing exponentially fitted linear multistep methods explicitly. Fitting may be done at any set of given (real) parameters. The construction principle permits study of the convergence and stability properties of these methods. Moreover, it shows how the properties depend on the corresponding properties of classical linear multistep methods with constant coefficients. The theoretical results are illustrated by some examples. x), X(to) = x o, which we assume to have a unique solution x ~ C1(I, R). We want to approximate values x(tl) of this solution by values Yl in an equally spaced set of points I m = {t t = t o + ih [ i = 0, 1 .... , m; mh = T}. The device that produces values Yi is called numerical method. Several authors, e.g. Liniger and Willoughby [6], Bjurel [1], van der ttouwen [4], have proposed exponentially fitted methods to obtain stability properties suitable for stiff (cf. e.g. Lambert [5], chapter 8, and Bjurel et al. [2] ) differential equations. A numerical method is said to be exponentially fitted of order p at a value A if it integrates exactly problems (1.1) that have solutions of the form P(t)e ~ where P(t) is any polynomial of degree not exceeding p. I.e. the method yields values of the exact theoretical solution P(t)e ~t provided that the exact initial conditions are used and the computations are exact. This definition implies that a method which integrates exactly problems with solutions in the linear space Ars spanned by
A procedure to habituate Highland Cattle calves to humans evolved with four years' experiment... more A procedure to habituate Highland Cattle calves to humans evolved with four years' experimentation on one farm by one male human handler. Data includes results of 18 bull and 20 heifer calves, from 14 dams and 4 sires. In 24 cases, they were fearless and easy to handle all the time. Fearful 8 heifer and 6 bull calves got little or unpleasant handling during first weeks.
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