       ## Syllabus ( ME 584 )

 Basic information Course title: Advanced Engineering Mathematics Course code: ME 584 Lecturer: Prof. Dr. İlyas KANDEMİR ECTS credits: 7.5 GTU credits: 3 (3+0+0) Year, Semester: 1/2, Fall and Spring Level of course: Second Cycle (Master's) Type of course: Compulsory Language of instruction: Turkish Mode of delivery: Face to face Pre- and co-requisites: None Professional practice: No Purpose of the course: The purpose of this course is to provide participants with the skills, knowledge and attitudes required to perform mathematical procedures and processes for solution of engineering problems, particularly the use of systems of ordinary differential equations, power series methods, various transformations, and partial differential equations.
 Learning outcomes Upon successful completion of this course, students will be able to:

1. focus on the solution of the ordinary differential equations and the related application areas.

### Contribution to Program Outcomes

1. Define and manipulate advanced concepts of Mechanical Engineering
2. Formulate and solve advanced engineering problems,
3. Do modeling, simulation, and design of dynamical systems.
4. Acquire scientific knowledge
5. Apply knowledge in a specialized area of mechanical engineering discipline and use variety of CAD/CAM/CAE tools.

### Method of assessment

1. Written exam
2. focus on the solutions of the partial differential equations and the related application areas.

### Contribution to Program Outcomes

1. Define and manipulate advanced concepts of Mechanical Engineering
2. Formulate and solve advanced engineering problems,
3. Do modeling, simulation, and design of dynamical systems.
4. Acquire scientific knowledge
5. Develop an awareness of continuous learning in relation with modern technology
6. Apply knowledge in a specialized area of mechanical engineering discipline and use variety of CAD/CAM/CAE tools.

### Method of assessment

1. Written exam
3. solve the problems related to complex analysis and Fourier analysis.

### Contribution to Program Outcomes

1. Define and manipulate advanced concepts of Mechanical Engineering
2. Formulate and solve advanced engineering problems,
3. Do modeling, simulation, and design of dynamical systems.
4. Acquire scientific knowledge
5. Find out new methods to improve his/her knowledge.
6. Apply knowledge in a specialized area of mechanical engineering discipline and use variety of CAD/CAM/CAE tools.

### Method of assessment

1. Homework assignment
 Contents Week 1: Matrix Algebra, Gauss Elimination and Cofactor Methods-Recall, Systems of Equations, Linearity, Homogenous Systems, Existance of Solution. Homework 1 Week 2: Eigenvalue Problem, Eigenvectors, Homogenous and Nonhomogenous Ordinary Differential Equations, Modelling of Dynamics Systems. Homework 2 Week 3: Higher Order Ordinary Differential Equations, Systems of Homogenous and Nonhomogenous Ordinary Differential Equations, General and Particular Solutions. Homework 3 Week 4: Laplace Transformations: Derivative, Integral, Convolution, Periodic Functions. Homework 4 Week 5: Solution of Nonhomogenous Ordinary Differential Equations using Fourier Series, Fourier Sine, Fourier Cosine. Homework 5 Week 6: Solution of Ordinary Differential Equations using Power Series, Frobenius Method. Homework 6 Week 7: Midterm exam, Introduction to Partial Differential Equations Week 8: Partial Differential Equations, Simplifications by Variable Transformations, Basic Operators: Gradient, Laplacien, etc. Week 9: Solution of Partial Differential Equations by Laplace Transformation. Week 10: Solution of Partial Differential Equations by Seperation of Variables. Homework 7 Week 11: Solution of Partial Differential Equations by Combination of Variables, Similarity Solutions. Week 12: Partial Differential Equations, Simplifications by Variable Transformations in Wave Equation, Initial and Boundary Conditions. Week 13: Problems in Polar and Cylindrical Coordinates, Circular Membrane Problem, Bessel and Legendre Functions. Week 14: Applications to Thermal Problems, Heat Generation and Conduction, Applications in Various Coordinate Systems. Week 15*: - Week 16*: Final exam. Textbooks and materials: Advanced Engineering mathematics, Kreyszig,Erwin, John Wiley. Recommended readings: Schaums Outline of Advanced Mathematics for Engineers and Scientists, Spiegel, Murray Advanced Engineering mathematics,Peter V. ONeil, Brooks Cole. * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
 Assessment Method of assessment Week number Weight (%) Mid-terms: 7 30 Other in-term studies: 0 Project: 0 Homework: 1,2,3,4,5,6,10 10 Quiz: 0 Final exam: 16 60 Total weight: (%)
 Workload Activity Duration (Hours per week) Total number of weeks Total hours in term Courses (Face-to-face teaching): 3 14 Own studies outside class: 4 14 Practice, Recitation: 0 0 Homework: 8 7 Term project: 0 0 Term project presentation: 0 0 Quiz: 0 0 Own study for mid-term exam: 10 1 Mid-term: 1 1 Personal studies for final exam: 15 1 Final exam: 2 1 Total workload: Total ECTS credits: * * ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)
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