okopmaz@uludag.edu.tr +90 224 294 19 62 Uludağ Üniversitesi, Mühendislik Mimarlık Fakültesi, Makine Mühendisliği Bölümü, Görükle, 16059 Bursa
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Website:
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Objective of the Course:
Teach advanced mathematical methods which are used in solving engineering problems.
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Contribution of the Course to Professional Development
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Learning Outcomes:
1
Students who attend this course learn advanced topics and methods of mathematics.;
2
They can model engineering problems, and solve them using mathematical methods.;
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Course Content:
Week
Theoretical
Practical
1
Review of ordinary differential equations. Series solutions of differential equations. Frobenius method.
2
Special differential equations. Bessel and modified Bessel differential equations. Classical and modified Bessel functions of first and second kind. 1st take-home.
3
Legendre differential equation and Legendre polynomials. General expansion theorem. Orthogonality and completeness. Orthogonal functions.
4
Fourier series. Fourier integrals and transform. Laplace transforms. 2nd take-home.
5
Partial differential equations. Deriving equations in engineering problems. One dimensional wave equation. D’Alembert solution.
6
Method of separation of variables. Initial and boundary value problems. Eigenvalue problems. Eigenvalues and eigenfunctions. Examples from vibrations theory and heat transfer. 3rd take-home.
7
Series solutions. Classification of second order partial differential equations. Elliptic, hyperbolic and parabolic equations. Characteristic curves.
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Repeating courses and midterm exam
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Calculus of variations. Variations. Variation problems in integral form. Euler-Lagrange equations.
Variational principles of mechanics. Lagrange equations of motion. Hamilton principle. 4th take-home.
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Functions of one complex variable. Limit, continuity and derivatives of a complex function. Analyticity. Cauchy-Riemann conditions. Cauchy and Cauchy-Morera theorems.
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Series expansions of complex functions. Taylor, Maclaurin and Laurent series. Theorem of residues. 5th take-home.
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Applications of residue theorem. Calculation of improper integrals. Obtaining inverse Laplace transforms.
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Textbooks, References and/or Other Materials:
C.R. Wylie - L. C. Barrett, Advanced Engineering Mathematics, McGraw Hill Publ. Comp. E. Kreyszig, Advanced Engineering Mathematics, J. Wiley Publ. Comp. B. Karaoğlu, Fizik ve Mühendislikte Matematik Yöntemler, Seçkin Yayıncılık.
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Assesment
TERM LEARNING ACTIVITIES
NUMBER
PERCENT
Midterm Exam
1
25
Quiz
0
0
Homeworks, Performances
5
25
Final Exam
1
50
Total
7
100
Contribution of Term (Year) Learning Activities to Success Grade
50
Contribution of Final Exam to Success Grade
50
Total
100
Measurement and Evaluation Techniques Used in the Course
Information
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ECTS / WORK LOAD TABLE
Activites
NUMBER
TIME [Hour]
Total WorkLoad [Hour]
Theoretical
14
3
42
Practicals/Labs
0
0
0
Self Study and Preparation
14
7
98
Homeworks, Performances
5
15
75
Projects
0
0
0
Field Studies
0
0
0
Midtermexams
1
2,5
2,5
Others
0
0
0
Final Exams
1
2,5
2,5
Total WorkLoad
220
Total workload/ 30 hr
7,33
ECTS Credit of the Course
7,5
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CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
