Ders Notu 2
Dear Students,
The Week 2 lecture notes for ME216 – Applied Mathematics for Mechanical Engineers have now been uploaded to the course portal.
Dear Students,
The Week 1 lecture notes for ME216 – Applied Mathematics for Mechanical Engineers have now been uploaded to the course portal.
Duyuru 1
GAZI UNIVERSITY FACULTY OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING
ME216 APPLIED MATHEMATICS FOR MECHANICAL ENGINEERS
Rules and Regulations for 2nd Semester of 2025/2026 Academic Year
Teaching Staff:
Dr. Alkım Aydın
Credit Structure:
(3-0) 3
Course Objectives and Related Learning Outcomes:
The course is designed for fourth semester mechanical engineering students. At the end of this course, the students will,
• Learn the basic concepts used in advanced vector analysis,
• Learn the evaluation of line, surface and volume integrals,
• Learn the basic concepts of linear algebra and their applications for analysis and solution of engineering problems,
• Learn complex function analysis and their application towards analysis and solution of engineering problems.
Textbook:
O’Neil, P. V., Advanced Engineering Mathematics, 8th Ed., Cengage Learning, 2018.
Recommended Reading:
• Kreyszig, E., Advanced Engineering Mathematics, 10th Ed., John Wiley&Sons, 2011.
• Jeffrey, A., Advanced Engineering Mathematics, 1st Ed., Academic Press, 2002.
Course Outline:
1. Linear algebra: Matrices, vectors, determinants. Inverse of a matrix. Matrix algebra. Linear algebraic systems. Echelon form.
2. Gauss and Gauss-Jordan elimination method for the solution of linear systems. Rank of a matrix. Linear independence-dependence.
3. Vector spaces. Inner product spaces. Linear transformations. Singular-value de-composition and polar decomposition of a matrix.
4. Matrix eigenvalue problems: Eigenvalues and eigenvectors of a square matrix. Symmetric, antisymmetric, and orthogonal matrices. Similarity of matrices.
5. Basis of eigenvectors. Diagonalization. Transformation of quadratic forms from arbitrary to principal directions.
6. Application to differential systems. Vector differential calculus: Gradient, divergence, curl.
7. Vector integral calculus: Line integral, double integral, triple integral.
8. Surface integrals.
9. Gauss divergence and Stokes’ integral theorems.
10. Complex numbers and complex elementary functions. Derivative. Analytic functions.
11. Cauchy-Riemann equations. Line integral in the complex plane.
12. Cauchy’s integral theorem.
13. Cauchy’s integral formula.
Prerequisites:
None
Assessment Method:
Midterm examination (2 Midterm) %60
Final examination %40
Absences:
A minimum of 70% attendance is compulsory.
GOOD LUCK