487 ريض (التحليل المركب 1)

Complex numbers: Algebr aic (arithmetic) properties. Complex (and extended) plane (Cartesian and Polar forms of complex

numbers). Powers and roots of complex numbers. Pla ner sets (aspects of connectedness).
Functions of a complex variable: Limits and continuity. Differentiability and holomorphy. Cauchy-Riemann theory. Harmonic functions.
Elementary functions: Exponential, Trigonometric and hyperbolic functions. Logarithmic functions and Branch concepts. The inverses of such functions.
Complex integration: Contour (line) integrals. Cauchy’s theorem. Cauchy’s integral formula and its applications (such as: Maximum modulus principle, Mean value property (analytic and harmonic), Cauchy’s estimate, Liouville’s theorem, Fundamental theorem of algebra…).
Series representation for analytic functions: Sequences and infinite series. Taylor series. Power series and analyticity. Laurent series.
Residue theory: Zeros and singularities of complex variable functions. The residue theorem. Applications to trigonometric integrals. Application to improper integrals. Application to series summations.

ملف مرفق: 
المرفقالحجم
PDF icon chapter1.pdf259.4 كيلوبايت
PDF icon chapter2.pdf144.57 كيلوبايت
PDF icon chapter3.pdf185.03 كيلوبايت
PDF icon chapter4.pdf157.3 كيلوبايت
PDF icon chapter5.pdf243.85 كيلوبايت
PDF icon homework-1-summer-semester1437-1438h.pdf1.01 ميغابايت
PDF icon homework-exam.pdf258.35 كيلوبايت
PDF icon Answer Sheet Final exam Summer semester 1435-1436H322.54 كيلوبايت
PDF icon Answer Sheet Second midterm exam summer semester 1437-1438H275.54 كيلوبايت
PDF icon Answer sheet Final exam4.8 ميغابايت
PDF icon Answer sheet Final exam3.23 ميغابايت
PDF icon hw2.pdf401.72 كيلوبايت
PDF icon hw3.pdf417.34 كيلوبايت
PDF icon hw4.pdf486.8 كيلوبايت
PDF icon hw5.pdf406.9 كيلوبايت
PDF icon answersheet-finalexam-math487-firstsemester-1436-1437h.pdf1.69 ميغابايت
PDF icon answersheet-first-second-midtermexammath487-first_semester-1436-1437h.pdf1.77 ميغابايت
ملحقات المادة الدراسية