Mathematical Methods In Physics I

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

yok

Course Contents

Definition of vector and scalar.Vector algebra.Differentiation of vectors.Scalar and vector fields.Definition of Gradient,Divergence and Curl.Line,surface and volume integrals.Green’s theorem in the plane,Stokes’ and divergence integral theorems. Orthogonal curvilinear coordinates:cylindrical,spherical and polar coordinates.Vector operators in orthogonal curvilinear coordinate.Green,Stokes and divergence integral theorems in orthogonal curvilinear coordinates.Complex numbers,complex functions,derivative of complex functions.Concept of analytic function,Cauchy-Riemann Conditions,some elementary complex functions.Complex integral,Cauchy’s theorem ,Cauchy’s integral formula.Series expansion of complex functions,critical points,Taylor and Laurent series.Residue theorem and its applications .Evaluation of definite integrals by use of Residue theorem.Conformal mapping and its applications.

Weekly Schedule

1) Definitions of vector and scalar,vector algebra
2) Differentiation of vectors.Scalar and vector fields.Definition of Gradient,Divergence and Curl
3) Line,surface and volume integrals
4) Green’s theorem in the plane,Stokes’ and divergence integral theorems
5) Orthogonal curvilinear coordinates:cylindrical,spherical and polar coordinates
6) Vector operators in orthogonal curvilinear coordinates
7) Green,Stokes and divergence integral theorems in orthogonal curvilinear coordinates
8) Midterm exam
9) Complex numbers,complex functions,derivative of complex functions
10) Concept of analytic function,Cauchy-Riemann Conditions,some elementary complex functions
11) Complex integral,Cauchy’s theorem ,Cauchy’s integral formula
12) Series expansion of complex functions,critical points,Taylor and Laurent series
13) Residue theorem and its applications
14) Evaluation of definite integrals by use of Residue theorem
15) Conformal mapping and its applications
16) Conformal mapping and its applications

Recommended or Required Reading

1- Fizik ve Muhendislikte Matematik Yontemler ,Bekir Karaoglu ,Seçkin Yayıncılık ,2012
2- Mühendislik ve Fizikte Matematik Metodlar,Coşkun Önem,Birsen Yayınevi,2011
3- Mathematical Methods for Physicists, George B. Arfken, Hans J. Weber,Academic Press,1985
4- Mathematical Methods in the Physical Sciences ,Mary L. Boas ,John Wiley,1983

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Self Study
6) Self Study
7) Self Study
8) Self Study
9) Problem Solving

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	35%
Contribution of Final Examination to Course Grade	65%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required