HAB719 - MATHEMATICAL MODELLING IN BIOMECHANICS
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| MATHEMATICAL MODELLING IN BIOMECHANICS | HAB719 | Any Semester/Year | 3 | 2 | 4 | 10 |
| Prequisites | None | |||||
| Course language | Turkish | |||||
| Course type | Elective | |||||
| Mode of Delivery | Face-to-Face | |||||
| Learning and teaching strategies | Lecture Discussion Question and Answer Demonstration Experiment Drill and Practice Project Design/Management | |||||
| Instructor (s) | SERDAR ARITAN | |||||
| Course objective | Covers the use of mathematical modelling in understanding problems in biomechanics; scientific method, Newtonian mechanics, translations and rotations in sport; computer simulation models, determining model parameters; | |||||
| Learning outcomes |
| |||||
| Course Content | Covers the use of mathematics and numerical analysis methods that can be used in the mathematical modelling based on Biomechanical research. Brief introduction to models that widely used in Biomechanics and basics of the modelling. | |||||
| References | McMahon, T., Muscles, Reflexes and Locomotion. Princeton University Press, 1984. ISBN: 978-0-691023-76-2 Ross, S.L., Differential Equations, Third Edition, Wiley, 1984. ISBN : 978-0-471032-94-6 Chapra, S.C., Applied numerical methods with MATLAB for engineers and scientists. Third Edition. McGraw-Hill, ISBN 978-0-07340-11-0 Gran, R.J., Numerical Computing with Simulink, Volume I: Creating Simulations. SIAM, 2007. ISBN : 978-0-89871-637-5 | |||||
Course outline weekly
| Weeks | Topics |
|---|---|
| Week 1 | Introduction to the course, What is biomechanical modelling? |
| Week 2 | Introduction to Mathematical Modelling; Vectors in 2D and 3D; Matrices and Determinants |
| Week 3 | Least Squares; Regression; Interpolation and extropolation. Application: Model fitting in LSE |
| Week 4 | Classification of ODEs;First order one variable ODE. Application : Modelling population dynamics. |
| Week 5 | Second order ODEs;uncoupled second order two variables ODE. Application: Free-Shot in Basketball. |
| Week 6 | Coupled second order two variables ODE. Application : Lancaster and Lotka-Voltera Models |
| Week 7 | Mid Term |
| Week 8 | Introduction to analytical ODE solvers in Matlab; Using symbolic toolbox and MuPad in Matlab. |
| Week 9 | Introduction to numerical analysis in Matlab. Application : Scalars,vectors and arrays in Matlab. Input/Output command, control commands, looping and simple graphics in Matlab. |
| Week 10 | Introduction to numerical ODE solvers programming in Matlab. Application : Euler, improved Euler and Runge-Kutta methods. |
| Week 11 | Modelling dynamics systems by using Simulink. Simulink's interface and library. |
| Week 12 | Developing a visual algorithms by using Simulink. Using Simmechanics toolbox and its libraries. |
| Week 13 | Using Control System Toolbox in Matlab that provides algorithms and tools for systematically analyzing, designing, and tuning linear control systems. |
| Week 14 | Using Stateflow that is a control logic tool used to model reactive systems via state machines and flow charts within a Simulink model. Modelling by using Stateflow which uses a variant of the finite-state machine notation. |
| Week 15 | Preparation for the final exam |
| Week 16 | Final Exam |
Assesment methods
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | ||
| Laboratory | ||
| Application | ||
| Field activities | ||
| Specific practical training | ||
| Assignments | ||
| Presentation | ||
| Project | ||
| Seminar | ||
| Midterms | ||
| Final exam | ||
| Total | ||
| Percentage of semester activities contributing grade succes | ||
| Percentage of final exam contributing grade succes | ||
| Total | ||
WORKLOAD AND ECTS CALCULATION
| Activities | Number | Duration (hour) | Total Work Load |
|---|---|---|---|
| Course Duration (x14) | 0 | ||
| Laboratory | 0 | ||
| Application | 0 | ||
| Specific practical training | 0 | ||
| Field activities | 0 | ||
| Study Hours Out of Class (Preliminary work, reinforcement, ect) | 0 | ||
| Presentation / Seminar Preparation | 0 | ||
| Project | 0 | ||
| Homework assignment | 0 | ||
| Midterms (Study duration) | 0 | ||
| Final Exam (Study duration) | 0 | ||
| Total Workload | 0 | 0 | 0 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition level* | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest