## Content of Courses for Mechanical Engineering MSc Program

**MAK701 Advanced Thermodynamics (3 0 3) 6 ECTS**

Definition of thermodynamics and fundamental thermodynamic principles. 1st law of thermodynamics for closed systems. Work transfer. Applications of 1st law of thermodynamics for open systems. Application of 2nd law of thermodynamics for closed and open systems. Entropy generation and irreversibilities. Single phase and multi phase systems.

**MAK703 Advanced Fluid Mechanics (3 0 3) 6 ECTS**

Fundamental equations of fluid dynamics. Analysis of motion. Analysis of force and stress. Potential flow theory of incompressible fluids. Turbulent flow of viscous fluids. Boundary layer theory. Diffusion. Dispersion.

**MAK704****Boundary Layer Theory****(3 0 3) 6 ECTS**

Boundary layer theory; boundary layer equations and solutions for inner and outer flows in laminar, transient and turbulent flow cases. Drag and friction coefficients.

**MAK705 Similitude and Modelling Techniques (3 0 3) 6 ECTS**

Dimensions of physical quantities and unit systems. Dimensional analysis. Similarity theory. Graphical representations of experimental results. Empirical equations.

**MAK707 Advanced Heat Transfer I (3 0 3) 6 ECTS**

General equation of heat conduction. Steady state and transient heat conduction in 2D and 3D. Fins. Varying cross section fins. Heat transfer from fin surfaces. Numerical methods for heat transfer.

**MAK708 Theory and Design of Turbomachines (3 0 3) 6 ECTS**

Similitude and dimensional analysis in turbomachines, characteristics of performans, Reynolds effects and scale effects. Cordier diagram, classification with dimensionless speed. Energy changes and fundamentals of thermodynamics, definitions of efficiency. Cascade blade system, determination with cascade and insulated blade. Design of radial, half-axial and axial turbomachines. Three-dimensional flow. Cavitation.

**MAK709 Advanced Mechanism Analysis (3 0 3) 6 ECTS**

Basics of modern kinetic analysis. Euler-Savary equation. Curve theory. High degree accelerations. Kinetics of space mechanisms. Skew algebra and space mechanisms applications. Introduction to robot kinematics.** **

**MAK713 Advanced Vibration Analysis****(3 0 3) 6 ECTS**

Generalized coordinates. Lagrange’s equations for conservative discrete systems. Matrix representations of potential and kinetic energy. Dynamic system modelling. Impact factor method. Matrix method analysis. Frequency response function. Mode solution. Critical speed calculations for multi degree-of-freedom systems.

**MAK715 Engineering Mathematics I (3 0 3) 6 ECTS**

Ordinary differential equations (ODE). Elementary solutions for ODEs. Serial solutions for ODEs. Bessel functions. Legendre equivalences. Laplace transforms. Fourier series.

**MAK716 Engineering Mathematics II (3 0 3) 6 ECTS**

Classification of partial differential equations (PDE). Formulation and modelling of elementary engineering problems with using partial differential systems. Sturm-Liouville theory. Complex numbers and Cauchy-Riemann equations. Fourier transforms, Laplace transforms, Hankel transforms, Mellin transforms.

**MAK717 Numerical Methods in Engineering (3 0 3) 6 ECTS**

Modelling, computers and error analyisis. Roots of equations. Lineer algebric equations, Optimization. Curve fitting. Numerical differentials and integrals. Numerical solution of ordinary differantial equations. Numerical solution of partial differential equations.

**MAK719****Analytical Methods in Space Mechanism****(3 0 3) 6 ECTS**

Deriving valid rotation and translation matrix components for plane and space. Transformations of 3D rigid body. Position, velocity and acceleration analysis of space mechanisms. Synthesis problems for space mechanisms. Skew algebra. Robotic kinetics applications.

**MAK723 Design of Air Conditioning and Cooling Systems (3 0 3) 6 ECTS**

Determination of heat gains and load calculations. Air duct design. Project designing of devices (evaporators, condensers, serpentines, etc.) that using in systems. Determining pressure losses.

**MAK724****Dynamics of Mechanical Systems (3 0 3) 6 ECTS**

Fundamental numerical techniques, matrix methods and solutions. Time response notion, modelling and numerical solutions. Analyzing some elementary mechanisms with time response method. Review of virtual work and its applications. Deriving Lagrange’s equations of motion and its various examples of mechanic system applications. Analyzing with Lagrange equation. Revising static and dynamic equilibrium methods. Moment equilibrium for elementary mechanisms that have force equilibrium. Equilibrium effects of initial moment. Numerical works for equilibrium. Notion of elastic bar. Elastic bar’s planar motion and modelling. Stiffness matrix. Elastic member model. Modelling of elastic systems and solution methods.

**MAK727 Welding Methods and Equipments (3 0 3) 6 ECTS**

Definition and classification of welding. Weldability. Welding machines. Fusion welding. Arc welding methods. Thermal cutting techniques. Distortion and residual stresses in welded assemblies. Welding defects. Electric resistance welding. Friction welding. Feed welding. Other welding methods. Welding methods used for to join plastic materials. Fundamentals of welded manufacturing. Work safety for welding.

**MAK728****Heat Convection (3 0 3) 6 ECTS**

Fundamental equations of heat transfer. Continuity, momentum and energy balances. Boundary equations. Energy equations. Forced convection in turbulent flow. Steady-state turbulent flow equations. Friction factor in turbulent flow. Time dependent convection in a channel. Heat transfer in natural convection. Heat transfer of high velocity flow.

**MAK729 Industrial Materials (3 0 3) 6 ECTS**

Material economy and material selection. Iron-based materials. Light metals and alloys. Heavy metals and alloys. Plastic materials. Tool materials. Material selection criterions for low temperatures. High temperature materials, refractory and ceramic materials. High-polymer materials, metallic coating materials.

**MAK730 Advances in Casting Technology (3 0 3) 6 ECTS**

Advances in template materials. Template slabs. Mold and core materials. Fasteners. Advances in production technology for molds.

**MAK732 Optical Metal Microscopy (3 0 3) 6 ECTS**

Definitions of characteristic properties of metals. Metal knowledge. Atomic and crystal structures. Single-phase and two-phase structures. Grain types and relation between grain and properties. Sample selection. Etching and etching materials, macro and micro etching. Phase discrimination, determination of grain sizes and shapes.** **

**MAK733 Finite Element Method (3 0 3) 6 ECTS**

Elementary definitions. Matrix algebra. 1D problems. Cages. 2D problems. Axial symmetric problems. 2D isoparametric elements and numerical integration. Beams and frames. 3D problems in stress analysis. Scalar field problems. Dynamic problems.

**MAK735 Mechanics of Composite Materials (3 0 3) 6 ECTS**

Consept of Solid Mechanics. 3-D Constitutive Equations. Plane Streess Constitutive Equations. Lamination Theory. Interlaminar Stresses. Failure and Damage. Micromechanics. Laminated Tubes. Wowen Type Composites.

**MAK736 Destructive and Non-Destructive Test Methods (3 0 3) 6 ECTS**

Hardness measurement. Tensile test. Compression test. Torsion test. Forward and backward bending tests. Collapse tests for sheet metals and metal bands. Creep and stress relaxation tests. Fracture and fracture toughness tests. Notch impact test. Fatigue test. Radiation tests. Elastic-wave tests. Electrical and magnetic tests. Optical tests. Other tests.

**MAK738 Applied Elasticity (3 0 3) 6 ECTS**

Stress analysis. Stress and strain relations. 2D problems in elasticity. Beam deflection. Torsion of prismatic beam. Axial symmetric problems. Plates and shells.

**MAK739 Fracture Mechanics (3 0 3) 6 ECTS**

Basic concepts. Stress at a crack tip. Stress intensity factor. The Griffith criterion. Fracture types. Mechanisms of fracture and crack growth. Yield condition. Fracture criteria and fracture toughness. Ductile and brittle fracture. The elastic crack-tip stress field. The Airy stress function. The crack tip plastic zone. Determine size of the crack tip plastic zone. The energy principle. The energy release rate. The criterion for crack growth. The crack resistance (R curve). The J integral. Plane strain fracture toughness. The standard test. Plane stress and transitional behaviour. Concept of plane stress. The thickness effect. Elastic-plastic fracture. The crack tip opening displacement. The possible use of the CTOD criterion. Parameters affecting the critical CTOD. J and CTOD relation. Measurement of JIc and Jr. Fatigue crack propagation. Crack growth and the stress intensity factor. Factor affecting crack propagation. Fracture resistance of materials. Fracture in corrosive environments. Test methods for fracture mechanics. Calculation methods for material lifetime and crack length.

**MAK740 Energy and Variational Methods in Mechanics (3 0 3) 6 ECTS**

Variation calculation. Principles of virtuel work and energy. Ritz method. Weighted residual methods.

**MAK741 Damage Mechanics****(3 0 3) 6 ECTS**

Introduction to continuum damage mechanics (Formulation of the ısotropic unified damage law, formulation of the anisotropic damage law, tensor equations). Brittle failures (Weibull model, sensitivity analysis, crack propagation). Ductile failures (validation of the damage law, sensitivity analysis, neuber method, crack arrest). Low cycle fatigue. High cycle fatigue. Numerical analysis of damage mechanics (uncoupled analysis, coupled analysis, locally-coupled analysis).

**MAK742 Computational Fluid Dynamic****(3 0 3) 6 ECTS**

Computational fluid dynamics. Finite volume and finite difference solutions in fluid mechanics.

**MAK744 Mass Transfer (3 0 3) 6 ECTS**

Basic concepts. Fick`s law, definitions of concentration, velocity, mass flux relations. Diffusion coefficients for binary gas systems. Molecular diffusion for binary gas systems. Diffusion coefficients for binary liquid systems. Equation of continuity for binary mixtures. Steady-state mass transfer. Mass transfer with heterogeneous chemical reaction, mass transfer with homogeneous chemical reaction.

**MAK748****Tensor Analysis (3 0 3) 6 ECTS**

Fundamentals of vectors and vectoral analysis. Tensor notion and algebraic operations with tensors. Coordinate transformation. Covariant and covariant vector fields. Covariant and covariant tensor fields. Symmetric and asymmetric tensor. Metric tensor. Christoffel symbols. Permutation symbol. Applications of covariant derivative, gradient, divergence, and rotational tensor analysis to engineering problems.

**MAK750 Vibration Analysis of Continuous Systems (3 0 3) 6 ECTS**

Continuous systems. Smooth and curved beams. Frame systems. In-plane and out-plane vibrations. Elastic potential energy. Kinetic energy equations. Finite element method. Shape functions. Natural frequency. Forced frequencies and structural solutions. Vibration mode shapes. Programming for finite element solutions.

**MAK751 Plates and Shells (3 0 3) 6 ECTS**

Linear elastic plates. Membrane and bending theory of shells. Approximate treatment of edge effects. Differential geometry of surfaces. Linear and nonlinear plate and shell theories in curvilinear coordinates. Anisotropic and laminated shells. Stability and post-buckling behaviour. Collapse analysis. Analysis by using finite element methods.

**MAK752****Theory of Plasticity (3 0 3) 6 ECTS**

Systematic product development. Manufacturing, ergonomics, aesthetic, design for environment. Modern product development techniques and CAD software. Data transfer formats. Modern production techniques (erosion, rapid prototyping etc.), CNC based machine tools and CAM software. Data formats for CAD (IGES, step, etc.). Post-processing transform for CL data. Analyze samples for designing and manufacturing pilot product. Pilot product prototype development and manufacturing. Industrial applications.

**MAK753****Continuum Mechanics (3 0 3) 6 ECTS**

Introduction to Elasticity and Viscoelasticity. Tensor Analysis ( Notation and Summation Convention, Cartesian Tensor, Tensor Equations). Stress Tensor ( Equations of Equilibrium, Stres Deviations, Stres Tensor in General Coordinates). Analysis of Strain. Conservation Laws (Gauss Theorem, Equation of Continuity, Equation of Motion, Other Field Equation). Linear Elasticity (Boundary Value Problems, Saint Venant’s Theory of Torsion, Bending of Beams). Two Dimensional Problems in Elasticity. Finite Deformation ( Strain Tensors, Lagrange’s and Kirchhoff’s Stres Tensors, Equation of Motion in Lagrangian Description, Rate of Deformation, Elasticity, Hyperelasticity and Hypoelasticity)

**MAK754 Fatigue of Materials (3 0 3) 6 ECTS**

Definition of fatigue and mechanism. Types of fatigue loading. Fatigue strength of materials and determine experimentally. Fatigue strength diagrams. Applications and classical method against fatigue in designing. Short-life fatigue.

**MAK755 Mechanical Behaviour of Materials (3 0 3) 6 ECTS**

Crystal structure defects. Dislocations. Mechanisms of plastic deformation. Strengthening mechanisms for metals. Damage and fracture.

**MAK756 Tribology (3 0 3) 6 ECTS**

Geometric characteristics and quality of surfaces, dry friction, friction theories, boundary friction, abrasion and mechanism, lubricators, lubrication systems, liquid friction zone systems, Reynolds differential equation, radial and axial sliding bearings, externally pressurized bearings, fluid films between rolling elements, elasto-hydradynamics, dynamically loaded bearings, thermo-hydrodynamics, hydrodynamic instability.

**MAK757 Applications of Finite Element Method in Machine Designing (3 0 3) 6 ECTS**

Fundamentals of finite elements. 1D, 2D and 3D modelling of solid objects. Bar element, beam element, plane element, axial symmetric element, contact element and thermal element properties. Gear systems, clinch joints, force fitting joints, welding joints, adhesive joints, screwed joints, cylinder under pressure, beam systems. Loading and boundary conditions, fatigue, crack propagation, thermal stress, residual stress and multiplication problems.

**MAK758 Experimental Stress Analysis (3 0 3) 6 ECTS**

Fundamentals of mathematical theory of elasticity, strain measurement methods, elementary factors for sensor selection, sensor selection and selection procedure, sensor applications, strain sensor circuits, error sources in strain measurement, warning levels in strain measurement, correction factors for measurements, application examples.** **

**MAK760 Drying Technology (3 0 3) 6 ECTS**

Drying technique, humidity of dryer fluid, huminity of drying product, qualitative description of drying, non hygroscopic product drying, static calculation of drying, dynamic calculation of drying, fundamentals of industrial drying.

**MAK762****Reliability and Life Prediction in Machine Elements (3 0 3) 6 ECTS**

Strength, safety and life-time calculations of construction elements with reliability concept and with take into consideration of statistical methods. Design construction elements in most realistic way that grounds on strength limit of materials intended reliability.** **

**MAK797 M. Sc. Seminar (0 2 0) 3 ECTS**

It is anticipated that the student prepares a seminar project on a subject determined in collaboration with his/her advisor, presents this project in a proper way before the previously defined deadline and hands over the final seminar report to his/her advisor.

**MAK798 M.Sc. Field of Specialization (2 0 0) 15 ECTS**

This is a theorical course offerred in semestre, semestre break and summer terms followed by appointment of the advisor for M.Sc. students. It provides M.Sc. students to obtain scientific ethic and discipline.

**MAK799 M.Sc. Thesis Research (0 1 0) 15 ECTS**

This is a practical course offerred in year, semestre, semestre break and summer terms followed by appointment of the advisor for M.Sc. students.

## Content of Courses for Mechanical Engineering PhD Program

**MAK801 Exergy Analysis (3 0 3) 6 ECTS**

I. and II. law of Thermodynamics for open and close systems; Steady-State Steady Flow (SSSF) systems, Uniform State Uniform Flow (USUF) systems. Exergy; Exergy analysis for close and open systems, optimization principles for systems. Exergy analysis for different heat processes; Entropy generation, irreversibility (exergy loss).

**MAK802 Two Phase Flows and Heat Transfer (3 0 3) 6 ECTS**

Two phase flows and flow models. Determine friction pressure losses in two phase flows. Heat transfer in two phase flows. Stagnant boiling. Forced convection boiling and post - dryout heat transfer. Industrial applications.

**MAK803 Combustion (3 0 3) 6 ECTS**

Chemical thermodynamics, theoretical and actual combustion processes. Adiabatic flame temperature. Chemical equilibrium, equilibrium constant. Equilibrium constants of simultaneous reactions. Chemical kinetics. Conservation equations for multicomponent reactive systems. Detonation and deflagration waves for premixed gases. Premixed laminar flames. Turbulent flames. Combustion experiments. Shock tubes. Soot formation.

**MAK804 Boundary Layer Theory (3 0 3) 6 ECTS**

Boundary layer theory; boundary layer equations and solutions for inner and outer flows in laminar, transient and turbulent flow cases. Drag and friction coefficients.

**MAK805 Drying Technique (3 0 3) 6 ECTS**

Drying technique and industrial applications: humidity and moisture of drying product, humidity of dryer fluid, physical statements and definitions of drying principles. Computation of drying in static conditions (thermodynamics). Computation of drying in dynamic conditions (heat and mass transfer). Drying apparatuses (machines).** **

**MAK806 Heat Convection (3 0 3) 6 ECTS**

Fundamental equations of heat transfer. Continuity, momentum and energy balances. Boundary equations. Energy equations. Forced convection in turbulent flow. Steady-state turbulent flow equations. Friction factor in turbulent flow. Time dependent convection in a channel. Heat transfer in natural convection. Heat transfer of high velocity flow.

**MAK807 Design of Thermal Systems (3 0 3) 6 ECTS**

Fundamental definitions and notions for designing. Working thermal systems. Design of heat exchangers. Multi-effect evaporator design. Choosing fluid equipment. Optimization techniques. Research models. Sample applications.

**MAK808 Computational Fluid Dynamics (CFD) (3 0 3) 6 ECTS**

Computational fluid dynamics. Finite volume and finite difference solutions in fluid mechanics.** **

**MAK809 Analytical Methods in Space Mechanisms (3 0 3) 6 ECTS**

Deriving valid rotation and translation matrix components for plane and space. Transformations of 3D rigid body. Position, velocity and acceleration analysis of space mechanisms. Synthesis problems for space mechanisms. Skew algebra. Robotic kinetics applications.

**MAK810 Hydraulics of Transient Unsteady Flows in Pipelines (3 0 3) 6 ECTS**

Definition of water hammer. Unsteady flow in pressurized pipelines. Fundamental equations of unsteady flows. Rigid water column theory. Elastic theory. Solutions with characteristic method. Water hammer in complex pipelines. Analyze water hammer cause of pumps and turbines. Problems of unsteady flows in pipelines. Water hammer control devices and methods.** **

**MAK811 Advanced Vibration Analysis (3 0 3) 6 ECTS**

Notions and descriptions for vibrations. Superposition principle. Impact factors. Matrix form of Lagrange equations. Coordinate transforms, dependency, equations of motion. Natural methods for disjoint systems. Eigenvalue problems. Orthogonality of eigenvectors. Modal matrix. Normal coordinates, expansion theorem. Matrix iteration method. Deriving secondary eigenvectors. Rayleigh ratio. Dunkerley equation. Vibrations of continuous systems. Boundary value formulation. Orthogonality of eigenfunctions. Vibrating strings and vibration of beams. Approximated method at natural modes and frequencies calculations. Random vibration approach.** **

**MAK812 Engineering Mathematics II (3-0-3) 6 ECTS**

Differential equation systems. Operator methods. Canonical solutions. Modelling of vibration problems with many degrees of freedom. Approximate solution methods. Differential equations of Bessel and Bessel functions. Legendre polynomials. Gauss equation. Gamma functions. Laplace transforms. Partial differential equations. One and two dimension wave equations. Boundary value problems in vibration in continuous media. Boundary value problems in heat transfer.

**MAK813 Advanced Control Theories (3-0-3) 6 ECTS**

Fundamentals of mathematics and techniques. Industrial control problems. Linearization of non-linear systems. State-space modelling techniques. Unsteady systems and Z-transforms, presentation of unsteady equations in state-space. Solutions of state equations. Analysis and modelling techniques for control systems on time and frequency plane.

**MAK814 Robotic Technology (3-0-3) 6 ECTS**

History and classification of robotics. Robotic elements. Principles of robot control. Robot kinematics. Linear and inverse kinematics. Robot dynamics and Lagrange formulation. Industrial applications of robots.

**MAK816 Artificial Intelligence Applications in Mechanical Engineering (3-0-3) 6 ECTS**

Artificial intelligence conception, its aim and techniques. Structures of expert systems. Inference mechanisms. Forward and back chaining methods. Information arrangement and databases. Techniques of expressing information. Rules, objects, systematic networks. Expert system shells and their usages. Expert system applications. Selection programs. Design programs. Analyzing and studying on available programs. Expert system development workings. Logic of genetic algorithms (GA). Genetic structure. Crossing. Mutation. Application areas of genetic algorithms. Logic of artificial neural networks (ANN). Techniques and structures of ANN. Perceptron. Hopfield network techniques. Application areas and program development works on perceptron. Uncertainties and modelling and applications. Fuzzy sets. Notion of fuzzy logic and its applications.

**MAK817 Plates and Shells (3 0 3) 6 ECTS**

Linear elastic plates. Membrane and bending theory of shells. Approximate treatment of edge effects. Differential geometry of surfaces. Linear and nonlinear plate and shell theories in curvilinear coordinates. Anisotropic and laminated shells. Stability and post-buckling behaviour. Collapse analysis. Analysis by using finite element methods.

**MAK818 Plasticity Theory (3 0 3) 6 ECTS**

Stress-strain relations. Yield criteria and the general behaviour of materials beyond proportional limit. Approximate theories on the theory of plastic flow; applications to problems of bending, torsion, plane strain and plane stress. Plastic theory for materials with isotropic hardening, kinematic hardening and time dependence. Theories based on crystal slip. Variational theorems. Range of validity of total deformation theories. Theory of generalized stresses. Limit analysis of shells. Plastic response to impact loads. Minimum weight design.

**MAK819 CAD/CAM Integrated Product Development and Manufacturing (3 0 3) 6 ECTS**

Systematic product development. Manufacturing, ergonomics, aesthetic, design for environment. Modern product development techniques and CAD software. Data transfer formats. Modern production techniques (erosion, rapid prototyping etc.), CNC based machine tools and CAM software. Data formats for CAD (IGES, step, etc.). Post-processing transform for CL data. Analyze samples for designing and manufacturing pilot product. Pilot product prototype development and manufacturing. Industrial applications.

**MAK820 Tensor Analysis (3 0 3) 6 ECTS**

Fundamentals of vectors and vectoral analysis. Tensor notion and algebraic operations with tensors. Coordinate transformation. Covariant and covariant vector fields. Covariant and covariant tensor fields. Symmetric and asymmetric tensor. Metric tensor. Christoffel symbols. Permutation symbol. Applications of covariant derivative, gradient, divergence, and rotational tensor analysis to engineering problems.

**MAK821 Advanced Engineering Materials (3-0-3) 6 ECTS**

Metal matrix composites. Al-Li alloy applications. Directional hardening and mechanical alloying materials. Metallic glass. Polymer materials.

**MAK822 Dynamics of Mechanical Systems (3-0-3) 6 ECTS**

Fundamental numerical techniques, matrix methods and solutions. Time response notion, modelling and numerical solutions. Analyzing some elementary mechanisms with time response method. Review of virtual work and its applications. Deriving Lagrange’s equations of motion and its various examples of mechanic system applications. Analyzing with Lagrange equation. Revising static and dynamic equilibrium methods. Moment equilibrium for elementary mechanisms that have force equilibrium. Equilibrium effects of initial moment. Numerical works for equilibrium. Notion of elastic bar. Elastic bar’s planar motion and modelling. Stiffness matrix. Elastic member model. Modelling of elastic systems and solution methods.

**MAK823 Mechanical Behavior of Materials (3-0-3) 6 ECTS**

Definition of mechanical behavior of materials. Principles of plastic deformation of metals. Crystal structures. Defects of crystal structures. Edge, screw and mixed dislocations. Dislocation network, partial dislocations and array of dislocations. Non screw dislocations. Macroscopic strain as a result of dislocation movement. Stress field around of dislocations. Dislocation energy. Forces on dislocations. Linear stresses of dislocations. Forces between dislocations. Dislocation intersection and step formation. Dislocation increment. Dislocation accumulations at obstacles. Orowan dislocation.

**MAK824 Advanced Characterization Techniques (3-0-3) 6 ECTS**

Scanning electron microscopy (SEM). Transmission electron microscopy (TEM). Atomic force microscopy (AFM). X-ray diffraction (XRD). X-ray photoelectron spectroscopy (XPS). Secondary ion mass spectrometry (SIMS).

**MAK825****Non-traditional Manufacturing Processes****(3-0-3) 6 ECTS**

Classification of non-traditional manufacturing processes. Ultra-Sonic Machining (USM), Abrasive Jet Machining (AJM), Chemical Machining, Electro-Chemical Machining (ECM), Electrical Discharge Machining (EDM), Laser Beam Machining (LBM), Electron-Beam Machining (EBM), Plasma Arc Machining (PAM), explosive forming, electromagnetic forming and other non-traditional manufacturing processes.

**MAK826 Gas Dynamics (3-0-3) 6 ECTS**

Fundamental definitions and conservation equations. Compressible flow, shock wave and Mach number. Isentropic flow. Shock waves. Flow in constant area duct with friction. Flow in constant area duct with heat transfer. Hypersonic flow. Numerical methods for steady hypersonic flow.

**MAK828****Fatigue of Materials****(3-0-3) 6 ECTS**

Definition of fatigue and its mechanism. Characteristics of fatigue load, reasons of fatigue fractures and factors of fracture. Appearance of fatigue cracks. Forms of fatigue crack formations. Examples of fatigue cracks under different loadings. Determining fatigue strength. Fatigue symbols. Definitions of fatigue strengths. Cyclic fatigue strength. Fatigue life. Representation of fatigue strength with Smith diagrams. Fatigue strength diagrams for different materials. Fatigue strength of joint elements. Corrosion fatigue. Corrosion fatigue of materials that have surface protection processes. Notch sensitivity. Fatigue notch factor. Fatigue notch factors of various shafts and bars and their calculations. Stress raisers and reducers. Effects of dimension and surface shape to fatigue strength. Impact effect and safety factor. Design of machine elements. Excessive loads and combined stress. Numerical examples and calculations.

**MAK850 Dynamics of Continuous Systems (3 0 3) 6 ECTS**

Conclusion of multi-freedom systems. The definition of continuous systems. Elastic membrane. The lateral vibrations of thin and thic beams. The longitudional vibrations of beams. Torsional and bending vibrations of shafts. Mod shapes and natural frequencies. Free and forced vibrations. Receptance and mobility.

**MAK897 Ph. D. Seminar (0 2 0 ) 3 ECTS**

It is anticipated that the student prepares a seminar project on a subject determined in collaboration with his/her advisor, presents this project in a proper way before the previously defined deadline and hands over the final seminar report to his/her advisor.

**MAK898 Ph.D. Field of Specialization (3-0-0) 15 ECTS**

This is a theorical course offerred in year, semestre, semestre break and summer terms followed by appointment of the advisor for Ph.D. students. It provides Ph.D. students to obtain scientific ethic and discipline.** **

**MAK899 Ph.D. Thesis Research (0-1-0) 15 ECTS**

This is a practical course offerred in year, semestre, semestre break and summer terms followed by appointment of the advisor for Ph.D. students.