Abstract PD-024

18 . 024 – ESG Notes 3

In this set of notes, we will develop the basic theory of tensors and differential forms; we will learn what it means to integrate a differential form; and we will state the generalized Stokes’ Theorem in terms of differential forms. Caveat lector: there are several closely related meanings of the word tensor. We begin introducing some convenient terminology for which we will not give precise d...

18 . 024 – ESG Problem Set 12 Pramod

Pramod N. Achar Spring 2000 In this problem set you will prove an analogue of the Fundamental Theorem of Calculus, Stokes’ Theorem, etc. To set up the context of the problem, let us define an operator div◦ on vector fields on R by div◦(P (x, y)i + Q(x, y)j) = ∂Q ∂x − ∂P ∂y . Let C denote a curve in R with endpoints a and b. Let S denote a surface whose boundary is the closed curve BdS. Let V de...

Resume Ed 389 746 Tm 024 379

Some applications of Bayesian decision theory to intelligent tutoring systems are considered. How the problem of adapting the appropriate amount of instruction to the changing nature of a student's capabilities during the learning process can be situated in the general framework of Bayesian decision theory is discussed in the context of the Minnesota Adaptive Instructional System (MAIS) . Two b...

18 . 024 – ESG Notes 2 Pramod

Inverses and determinants of matrices are closely related and come up in many different contexts. In these notes we will develop some basics of the theory of these ideas. Our initial motivation is the solution of systems of linear equations, such as 2x − 5y + 4z = −3 x − 2y + z = 5 x − 4y + 6z = 10. To solve the system, we want to manipulate these equations to get new equations which only conta...

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