5568303175

	1.2	Linearny property ol'Laplacc Transform, First Shitling property, Second Shifting property, Change of Scalę property of L.T., l Ąf J/i ^Jjjr"| (^ul,lK>ul pfooO Meaviside Unitstep function, Dircct Delta function, Pcriodic functions and their Laplacc Transform
II.	2. lmerse Laplacc 1 ransform		5
	2.1	lnvcrsc Laplacc Iransform: L.incarity property', usc of theorems to iind invcrsc lepiące Transform, Partial fractions method and convolution theorem (without proof).
	2.2	Applications to so!ve initial and boundary valuc problcms invoJvmg ord mary diffcrcntial cquations with one dependent vanaWc.
III.	Complcs sariables		10
	3.1	Functions of complcx vanablc, Analytic function, ncccssary and sufficient conditions lor f Ą to be analytic (without proof), Cauchy-Ricmann cquations inpolar coordinates.
	3.2	Milnc- Thomson method to determinc analytic function / ^ when it's rcal or imagmary or its combination is given. Harmonie function, orthogonal traiectoncs-
	3J	Mapping; Conformal mapping, lincar, bilincar mapping. cross ratio, fixcd points and standard transformations such as Rotation and magnification, imersion and rctlection, translation.
IV.	4. Complri Integration		10
	4.1	Linc intcgral of a function of a complcx variable, Cauchy’s theorem for analytic function, Cuuchv’s Goursat theorem (without proof), propcrtics of linc intcgral, Cauchy’s intcgral formula and deductioas.
	4.2	Singuianttcs and poles:
	4J	Taylor’s and Laurenfs senes dcvclopmcnł (without proof)
	4.4	Residue at isolatcd singularity and its evaluation.
	4.5	Residuc theorem, applicution to evaluatc rcal intcgral of typc j/<os&sin0j/0, & j/<>- o -te
V.	5. Fourier Stries		10
	5.1	Orthogonal and orthonormal functions, Lxprcssions of a function in a senes of orthogonal functions. Dtnchlet*s conditions, Fourier senes of pcriodic