Mathematical methods lecture 25 of 34

mathematical methods lecture 25 of 34

The list below gives the names of topics in the lecture notes. Philippe Dennery,Andre Krzywicki, Chapter 1, 2, 3 and 4 for the second part of the course lectures However prof. Narain did not teach all the chapters either did not give several proves rather described how we can use several theorems to come over problems in physicsso the main topics are discussed as the following:. Mathematical Methods. Explore Media Library Categories. Like Pop Out Shrink Share. Mathematical Methods Lecture 1 of 34 September 5, by K.

NarainICTP Overview of the course Guide to accessing online material for this course: Video recordings of the lectures are linked under the respective lecture headings. The course had 35 lectures and in addition it included 14 tutorials. Narain did not teach all the chapters either did not give several proves rather described how we can use several theorems to come over problems in physicsso the main topics are discussed as the following: Topics presented: 1-Linear algebra 1 st chapter which includes 7or 8 lectures 2-Complex analysis 2 nd chapter includes 8 lectures 3-Function spaces and Fourier transform 8 lectures 4-Differential equations 8 lectures Notes for individual chapters will not be linked so we link every video in its own lecture.

The rules of vectors in 2 and 3 dims have been included. Rules of addition and multiplication by numbers and all properties of Null vector have been said. Bra-ket notation and negative operator and negative vector discussed.

All properties beyond 2 dims mentioned as commutative rule, associative rule, multiplication rule ,associative law for multiplication. Distributive law for addition of numbers and distributive law for addition of vectors are involved. The list below gives the names of Categories Mathematical Methods.

See All Tags Tags This does not have any associated tags.This lesson starts by the introduction of Generalized function and its applications in physics, an example is the Dirac delta functionthat have a direct application in physics, for example in the point particle limit the Charge density is a Dirac delta function.

Some properties of the delta function are used. Nevertheless this delta function is not continuous and is better to work with continuous functions for this reason the Generalized functions were introduced to better define the delta functions.

mathematical methods lecture 25 of 34

The definition for a fairly good functions was also given: A fairly good function is a function that is differentiable any number of time and converge to zero when Abs[x] goes to infinity as Abs[x] n for some finite value of n.

If was noticed that if a function is a good function then its Fourier transform is also a good function. It was shown that any good function can be always written as a Generalized function. In the second part of this lesson attention was given to the properties of the Generalized functions. It was obtained that the linear combination of generalize functions is also a generalize function.

The multiplication between a fairly good functions and a generalize function was defined and it was shown to give as a result also a generalize function. Note that the product of two generalize functions it is not defined. Mathematical Methods. Explore Media Library Categories. Like Pop Out Shrink Share. Mathematical Methods Lecture 22 of 34 November 17, by K. NarainICTP This lesson starts by the introduction of Generalized function and its applications in physics, an example is the Dirac delta functionthat have a direct application in physics, for example in the point particle limit the Charge density is a Dirac delta function.

NarainICTPThis lesson starts by the introduction of Generalized function and its applications in physics, an example is the Dirac delta functionthat have a direct Categories Mathematical Methods.

mathematical methods lecture 25 of 34

See All Tags Tags This does not have any associated tags.To calculate the Green's function for a second order differential operator it was used the fact that the first derivative of the Step function H x-y is the Dirac delta function?

On the other hand for x?

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Finally by using a linear combination of the two possible solutions U 1 x and U 2 x to the homogeneous differential equation with coefficients that are function of y and using the previous conditions the green function G x,y is obtained and it was demonstrated that the solution is unique. Finally G x,y was obtained for some simples examples.

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Mathematical Methods. Explore Media Library Categories.

Like Pop Out Shrink Share. Mathematical Methods Lecture 26 of 34 November 28, by K. NarainICTPThis lesson continues with the study of the Green's function and at the first step it was demonstrated that the necessary and sufficient condition for G x,y to exist is that there is not a trivial solution to the equation Categories Mathematical Methods. See All Tags Tags This does not have any associated tags.Special attention was given in the beginning of the lesson to the boundary conditions and the definition of homogeneous boundary conditionthis definition implies that the set of functions that satisfy this type of boundary conditions form a vector space.

In the examples different boundary conditions were used the Dirichlet boundary condition, Neumann boundary condition and periodic boundary conditions. The idea of introducing the Green's function is to have a function G x,y with the propertie that L x acting in G x,y give the identity function in function space, that is the Dirac delta function? It is stated that G x,y as a function of x must satisfy the boundary conditions.

Finally and as an example the derivation of the Green's function for a second order differential operator was started. Mathematical Methods. Explore Media Library Categories. Like Pop Out Shrink Share.

Fluid Mechanics: Similitude (24 of 34)

Mathematical Methods Lecture 25 of 34 November 25, by K. NarainICTPThis lesson continues with the study of the second order differential operator L and its adjoint operator Categories Mathematical Methods.

See All Tags Tags This does not have any associated tags.Mathematical Methods. Explore Media Library Categories. Like Pop Out Shrink Share. Mathematical Methods Lecture 7 of 34 September 26, by K.

TEST K. NarainICTP lecture 7 Characteristic Polynomials, Note that in order to be more specific for this semester several things in chapter one have not been mentioned just like tensor calculation and so on.

Some examples are also given. Defining some subspaces with some special examples have been said. Decomposing several vectors as a linear combination of the matrices realized. Making some subspaces which consist of generalized eigen vectors with rank less than r used. Taking basis for any vector by taking into account generalized eigen vectors has been used. We proved that generalized igen vectors from different subspaces are linearly independent was given in the class. We talked a little bit about hamiltonian theorem.

NarainICTPlecture 7 Characteristic Polynomials, Note that in order to be more specific for this semester several things in chapter one have not been mentioned just like tensor calculation and so on.

The definition of characteristic Categories Mathematical Methods. See All Tags Tags This does not have any associated tags.The important part is how you set the file settings and image sizing:Everything else is up to you, or self-explanatory. There you have it. If you try this, please post an image of your setup and a final image so everyone can see what you did.

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mathematical methods lecture 25 of 34

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