# GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
APPLIED MATHEMATICS FOR MECHANICAL ENGINEERS/MM 216 E
 Course Title: APPLIED MATHEMATICS FOR MECHANICAL ENGINEERS Credits 3 ECTS 5 Semester 4 Compulsory/Elective Compulsory
COURSE INFO
-- LANGUAGE OF INSTRUCTION
English
-- NAME OF LECTURER(S)
Assoc.Prof.Dr. Sinan Kılıçaslan, Assist.Prof.Dr. Cevdet Aygun, Assist.Prof.Dr.Nureddin Dinler, Assist.Prof.Dr. Muhittin Bilgili
-- WEB SITE(S) OF LECTURER(S)
http://www.websitem.gazi.edu.tr/site/skilicaslan, http://www.websitem.gazi.edu.tr/site/caygun, http://www.websitem.gazi.edu.tr/site/ndinler, http://www.websitem.gazi.edu.tr/site/bilgili
-- EMAIL(S) OF LECTURER(S)
caygun@gazi.edu.tr,ndinler@gazi.edu.tr,skilicaslan@gazi.edu.tr,bilgili@gazi.edu.tr
-- LEARNING OUTCOMES OF THE COURSE UNIT
The capability to solve the application problems with the aid of vector definitions in one and multidimensional space.
Knowledge of the methods for solving linear system of equations and apply these methods.
Knowledge about eigenvalues and eigenvectors of a matrix and find these values.
Knowledge of system of differential equations solutions methods and apply them.
Definitions of line, area and volume integrals, related integral theorems and learning how to apply them.

-- MODE OF DELIVERY
Face to face
-- PREREQUISITES AND CO-REQUISITES
None
-- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
None
 --COURSE CONTENT 1. Week Linear algebra: Matrices, vectors, determinants. Inverse of a matrix. Matrix algebra. Linear algebraic systems. Echelon form. 2. Week Gauss and Gauss-Jordan elimination method for the solution of linear systems. Rank of a matrix. Linear independence-dependence, 3. Week Vector spaces. Inner product spaces. Linear transformations. Singular-value decomposition and polar decomposition of a matrix. 4. Week Matrix eigenvalue problems: Eigenvalues and eigenvectros of a square matrix. Symmetric antisymmetric, and orthogonal matrices. Similarity of matrices 5. Week Basis of eigenvectors. Diagonalization. Transformation of quadratic forms from arbitrary to principal directions. 6. Week Application to differential systems.Vector differential calculus: Gradient, divergence, curl. 7. Week Midterm Exam I 8. Week Vector integral calculus: Line integral, double integral, triple integral, 9. Week Surface integrals, 10. Week Gauss divergence and Stokes’ integral theorems. 11. Week Complex numbers and complex elementary functions. Derivative. Analytic functions. 12. Week Midterm Exam II 13. Week Cauchy-Riemann equations. Line integral in the complex plane. 14. Week Cauchy’s integral theorem. 15. Week Cauchy’s integral formula. 16. Week Final Exams