Mathematics 2 the Seventh and Eighth Lectures Fifth

Mathematics 2 the Seventh and Eighth Lectures Fifth week ﻫـ 1438 /6 /10 - 6 ﺳﻤﺮ ﺍﻟﺴﻠﻤﻲ / ﺃ

Outline for today üOffice Hours ü fourth homework due üChapter One üFourier Transforms üChapter Two ü Dirac Delta Function

Office Hours üSunday, Tuesday and Thursday from 11 to 12 p. m. ü you can put any paper or homework in my mailbox in Faculty of Physics Department ü I will put any announcement or apology in my website (https: //uqu. edu. sa/smsolamy) , so please check it ü my email is smsolamy@uqu. edu. sa for any question. ü every Wednesday a homework will be submit at my mailbox (or email if you did not came to university ) üevery week a worksheet will be submit in class Time of Periodic Exams üThe first periodic exam in 20 - 21 -22 / 6 / 1438 h every in her group üThe second periodic exam in 11 -12 -13 / 8 / 1438 h every in her group

The Fourth Homework üI put the fourth homework in my website in the university at Friday ü homework Due Wednesday ﻫـ 1438 / 6 / 16 in my mailbox in Faculty of Physics Department üI will not accept any homework after that , but if you could not come to university you should sent it to me by email in the same day than put the paper next day in my mailbox

Chapter Three: Ch 15, pg. 647 üIntegral Transforms üFourier Transforms üSection 4, pg 647 – 654 (notice: in the 3 rd ed it will be ch 7 Section 12) üThe Dirac Delta Function Section 7, pg 669 (notice: in the 3 rd ed it will be ch 8 Section 11) Also, (will take Dirac Delta Function from another book (Introduction to Electrodynamics by David Griffiths & Reed College Ch 1 Section 5. 2, ) (this part will be as a PDF file in my website in Lectures https: //drive. uqu. edu. sa/_/smsolamy/files/Mathematics 2%201437% 20 -%201438%20 -%20 S 2/The%20 Dirac%20 Delta%20 Function. pdf)

q. Fourier Transforms Definition of fourier transforms The f(x) and g(α) a pair of fourier transforms g(α) is called the fourier transforms of f(x) is called the inverse fourier transforms of g(α) Common simply to ca either a fourier transforms of the other

q. Fourier Transforms fourier sine transforms fourier cosine transforms The fs(x) and gs(α) a pair of The fc(x) and gc(α) a pair of fourier sine transforms fourier cosine transforms Representing odd function Representing even function

q Fourier Transforms Let f(x) is a nonperiodic function , a) Find the exponential Fourier transform of f(x) and write f(x)as a Fourier integral ? b) or the Fourier cosine transform of f(x) and write it as a Fourier integral ?

q Fourier Transforms Let f(x) is a nonperiodic function , a) Find the exponential Fourier transform of f(x) and write f(x)as a Fourier integral ? b) or the Fourier sine transform of f(x) and write it as a Fourier integral ?

q Dirac Delta Function can be pictured as an infinitely high infinitesimally narrow “spike” with area 1 0 is generalized f(x) or distribution

q Dirac Delta Function Example: Evaluate the following integral

q Dirac Delta Function Proof of the At x=0 so

q Dirac Delta Function Proof of the At x=a so

q Dirac Delta Function Properties of delta function 1) if delta function of 2) k≠ 0 3) 4) a≠b

q Dirac Delta Function Proof of the y=kx limit integer So it is true that dy = k dx - to to x=y/k - for k is positive for k is negative

q Dirac Delta Function Proof of the u=x du = dx =0 - So it is true that

q Dirac Delta Function Fourier transform of a delta function Inverse transforms

q Dirac Delta Function Example: Evaluate the following integral (Worksheet )

Next class review ØGamma Function Ø Beta Function