       ## Syllabus ( BENG 314 )

 Basic information Course title: Mathematical Modelling & Control in Bioengineering Course code: BENG 314 Lecturer: Assoc. Prof. Dr. Tunahan ÇAKIR ECTS credits: 6 GTU credits: 3 () Year, Semester: 3, Spring Level of course: First Cycle (Undergraduate) Type of course: Compulsory Language of instruction: English Mode of delivery: Face to face Pre- and co-requisites: BENG 215, MATH 215 Professional practice: No Purpose of the course: Ders, doğrusal/doğrusal olmayan denklem çözümlerinde adi diferansiyel denklemlerin çözümlerinde izlenen matematiksel yöntemler, modellemenin temelleri ve biyolojik sistemlere uygulanması konuları üzerinde durarak öğrencilere matematiksel modelleme becerileri kazandırmayı amaçlamaktadır
 Learning outcomes Upon successful completion of this course, students will be able to:

1. construct mathematical models and solve them

### Contribution to Program Outcomes

1. Acquire knowledge on biological, chemical, physical and mathematical principles which constitute the basis of bioengineering applications
2. Understand design and production processes in bioengineering applications.
3. Apply mathematical analysis and modeling methods for bioengineering design and production processes.
4. Find out new methods to improve his/her knowledge.

### Method of assessment

1. Written exam
2. Homework assignment
2. grasp the logic behind differential equations and the approaches for their numerical solutions, and apply the approaches

### Contribution to Program Outcomes

1. Acquire knowledge on biological, chemical, physical and mathematical principles which constitute the basis of bioengineering applications
2. Apply mathematical analysis and modeling methods for bioengineering design and production processes.

### Method of assessment

1. Written exam
2. Homework assignment
3. apply modelling methods to biological systems

### Contribution to Program Outcomes

1. Acquire knowledge on biological, chemical, physical and mathematical principles which constitute the basis of bioengineering applications
2. Convert biological, chemical, physical and mathematical principles into novel applications for the benefit of society,
3. Understand design and production processes in bioengineering applications.
4. Apply mathematical analysis and modeling methods for bioengineering design and production processes.
5. Design processes for the investigation of bioengineering problems, collect data, analyze and interpret the results.

### Method of assessment

1. Written exam
2. Homework assignment
 Contents Week 1: Analytic and Numerical Derivative, Series and Sequences, Taylor and MacLaurin series, Error and Error Analysis Week 2: Vectors, Matrix Theory (Determinant, Rank, Eigenvalues, Eigenvectors) Week 3: Solution of linear equation systems: Gauss method, Gauss-Jordan method Week 4: Gauss-Seidel method, LU method Week 5: Optimization (linear and nonlinear), Black Box modeling of systems, Parameter estimation Week 6: Least squares method: Curve fitting (Enzyme kinetics, Population growth), Linear equation system (steady-state CSTR series, modeling of a separation system) Week 7: Ordinary differential equations (first order, linear and nonlinear, homogenous and nonhomogenus), and the solution methods Week 8: Second order ordinary differential equations (linear, homogenous and nonhomogenous) Week 9: Numerical methods in solving nonlinear ordinary differential equations (Euler, Heun, Runge-Kutta methods) Week 10: Midterm ExamModelling of Lumped parameter systems Week 11: Examples of modelling of Lumped parameter systems: liquid tank, mixed tank heater, isothermal CSTR, nonisothermal CSTR, systems with multiple reactions Week 12: Solution of differential equations with finite difference method Week 13: Stability analysis, phase diagrams, bifurcation analysis Week 14: Introduction to partial differential equations- Overview Week 15*: - Week 16*: Final Exam Textbooks and materials: 1. Brian Ingalls, "Mathematical Modeling in Systems Biology: An Introduction", The MIT Press, 2013 Recommended readings: 1. Erwin Kreyszig, “Advanced Engineering Mathematics”, 10th Edition, John Wiley and Sons, New York, 2011.2. Richard G. Rice, Duong D. Do. “Applied mathematics and modeling for chemical engineers”, John Wiley and Sons, New York, 1995.3. William E. Boyce, Richard C. Di Prima, “Elementary Differential Equations and Boundary Value Problems”, 10th Edition, John Wiley and Sons, New York, 2012. * 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: 10 30 Other in-term studies: 0 Project: 0 Homework: 3,6,9,12 30 Quiz: 0 Final exam: 16 40 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: 3 14 Practice, Recitation: 0 0 Homework: 7 4 Term project: 0 0 Term project presentation: 0 0 Quiz: 0 0 Own study for mid-term exam: 7 2 Mid-term: 2 1 Personal studies for final exam: 14 1 Final exam: 3 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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