FACULTY OF SCIENCE / MATHEMATICS / MAT3002 - THEORY OF COMPLEX FUNCTIONS II

Contents Of The Courses in a weekly Period

Week 
Subjects 
Sources 
1Harmonic Functions and their properties, The integral of a complex-valued function[1] p. 47-51, [2] p. 141-152, [3] p. 85-94, [4] p. 159-164,[1] p. 102-107, [3] p. 157-160, [4] p. 236-242
2Curves in Complex plane and The integral of a complex function along a curve[1] p. 107-115, [2] p. 195-218, [3] p. 160-175, [4] p. 242-256, [5] p. 111-125
3Cauchy-Goursat Theorem and its applications[1] p. 115-121, [2] p. 218-242, [3] p. 175-183, [5] p. 127-135
4A Simply connected domain and a multiply connected domain [1] p. 121-129, [2] p. 218-242, [3] p. 183-194, [4] p. 259-272, [5] p. 136-138
5Cauchy's Integral Theorem and Cauchy's Integral Formula and their applications[1] p. 129-133, [2] p. 243-249, [3] p. 195-200, [4] p. 272-278,
6Liouville?s Theorem, Mean Value Theorem and Morera?s Theorem[1] s. 133-140, [2] p. 255-284, [3] p. 201-207, [4] p. 278-284, [5] p. 145-149
7The Fundamental Theorem of Algebra, Maximum Modulus Principle its applications[1] p. 133-140, [2] p. 284-284, [3] p. 201-207, [4] p. 278-284
8Sequences and Series of Analytic Functions, uniform convergence[2] p. 164-173, [3] p. 208-213
9Taylor Series Representations and Laurent Series Representations [1] p. 145-155, [2] p. 285-282, [3] p. 214-232, [4] p. 313-335,
10Singularities, Zeros, and Poles [1] s. 170-194, [2] p. 293-308, [3] p. 232-243, [4] p. 335-342, [5] p. 167-174
11Calculation of Residues and The Residue Theorem[1] p. 170-194, [2] p. 308-331, [3] p. 244-252, [4] p. 342-361
12Compute integral of complex function along a curve by using residue[1] p. 170-194, [2] p. 308-331, [3] p. 252-260, [4] p. 342-361
13Trigonometric Integrals, Improper Integrals of Rational Functions [1] p. 170-194, [2] p. 308-331, [3] p. 260-274, [4] p. 342-363
14Generalized integrals involving trigonometric functions and summing series[2] p. 331-347, [3] p. 274-277, [4] p. 363-374, [5] p. 185-192