MA601 :

Department

Department of Statistics

Academic Program

Master in Statistics

Type

Compulsory

Credits

03

Prerequisite

Overview

The overall aim of the course is to give a good understanding of

· Complex Numbers, variables and functions (revision).

· Cauchy-Riemann equations, complex integrals, power series and its convergence.

· Cauchy’s theorem and integrals formula, Taylor’s theorem and Laurent expansion, Residues and Jordan’s theorems, evaluating (improper) real integrals.

· Integrals transforms of Laplace, Fourier, Mellin, Complex Fourier and their inversion integrals.

· Generating and characteristic Functions, complex approach to obtain the distribution of sum, differenceand product of continuous independent random variables.

Intended learning outcomes

أ‌. (Knowledge & understand)

أ.1

The student will be able to understand the concepts of complex numbers, variables and functions.

أ.2

The student will be able to deal with Cauchy-Riemann equations, complex integrals, power series and its convergence.

أ.3

The student will be able to study Cauchy’s theorem and integrals formula, Taylor’s theorem and Laurent expansion, Residues and Jordan’s theorems, evaluating (improper) real integrals.

أ.4

The student will be able to studyintegral transforms of Laplace, Fourier, Mellin, Complex Fourier and their inversion integrals.

أ.5

The student will be able to deal with generating and characteristic Functions, complex approach to find the distribution of sum, differenceand product of continuous independent random variables.

ب‌. (Mental skills)

ب.1

The student can understand the concepts of complex numbers, variables and functions.

ب.2

The student can deal with Cauchy-Riemann equations, complex integrals, power series and its convergence.

ب.3

The student can study Cauchy’s theorem and integrals formula, Taylor’s theorem and Laurent expansion, Residues and Jordan’s theorems, evaluating (improper) real integrals.

ب.4

The student can studyintegral transforms of Laplace, Fourier, Mellin, Complex Fourier and their inversion integrals.

ب.5

The student can deal with generating and characteristic Functions, complex approach to find the distribution of sum, differenceand product of continuous independent random variables.

ت‌. (Practical & professional skills)

ج.1

The ability to understand the concepts of complex numbers, variables and functions.

ج.2

The ability to deal with Cauchy-Riemann equations, complex integrals, power series and its convergence.

ج.3

The ability to study Cauchy’s theorem and integrals formula, Taylor’s theorem and Laurent expansion, Residues and Jordan’s theorems, evaluating (improper) real integrals.

ج.4

The ability to studyintegral transforms of Laplace, Fourier, Mellin, Complex Fourier and their inversion integrals.

ج.5

The ability to deal with generating and characteristic Functions, complex approach to find the distribution of sum, differenceand product of continuous independent random variables.

ث‌. (Generic and transferable skills)

د.1

The student can communicate in writing and orally and give a good opinion.

د.2

The student has weight in dealing with the work team and consulting in solving issues.

د.3

The student will be able communicates with the interested teams on the written and oral sides.

Teaching and learning methods

•Lectures.• Solve exercises.