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Complex Variables, Special Functions and Numerical Analysis

What Will Learn?

  • Course Aims
    The aim of this course is to provide students with core material in the area of special functions, series solutions of differential equations and using it to solve Bessel and Legendre’s differential equations. The course also provides a solid foundation in functions of complex variables.
  • Course Goals
  • Quality Education

Requirements

PHM112

Description

  • English Description

    Functions of complex variables and their derivatives, Complex integrals, Cauchy integral theorems, Complex series, Taylor and Laurent series, Singularities and the residue theorem, Conformal mapping. Special functions, Gamma and Beta function, Series solution of linear differential equations, Bessel functions and Legendre polynomials, Bessel and Legendre series, Numerical solutions for ordinary differential equations, Numerical solutions for partial differential equations.
  • Arabic Description

    Functions of complex variables and their derivatives, Complex integrals, Cauchy integral theorems, Complex series, Taylor and Laurent series, Singularities and the residue theorem, Conformal mapping. Special functions, Gamma and Beta function, Series solution of linear differential equations, Bessel functions and Legendre polynomials, Bessel and Legendre series, Numerical solutions for ordinary differential equations, Numerical solutions for partial differential equations.
  • Department
    Engineering Physics and Mathematics
  • Credit Hours
    3
  • Grades
    Total ( 100 ) = Midterm (25) + tr.Major Assessment (30 = tr.Industry 0% , tr.Project 0% , tr.Self_learning 0% , tr.Seminar 35% ) + tr.Minor Assessment (5) + Exam Grade (40)
  • Hours
    Lecture Hours: 3, Tutorial Hours: 1, Lab Hours: 0
  • Required SWL
    100
  • Equivalent ECTS
    4
  • 1) “Advanced Engineering Mathematics", Erwin Kreyszig 10th edition. (2011), Wiley Int. Edition. (ISBN 978-0-470-45836-5).
  • 2) Student solution manual, Advanced Engineering Mathematics, Volume 1 (ISBN 978-1-11-800740-2/pbk). 260 p. (2011).
  • 3) Student solution manual, Advanced Engineering Mathematics, Volume 2 (ISBN 978-1-118-26670-0/pbk). 200 p. (2014). - Advanced Engineering Mathematics, Erwin Kreyszig 10th edition. (2011), Wiley Int. Edition. (ISBN 978-0-470-45836-5).