• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

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. Apply mathematical analysis and modeling methods for bioengineering design and production processes.

   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. Apply mathematical analysis and modeling methods for bioengineering design and production processes.

   Method of assessment

   1. Written exam
   2. Homework assignment

Contents
Week 1:	Vectors, Matrix Theory (Determinant, Rank)
Week 2:	- Solution of linear equation systems: Gaussian Elimination method, Gauss-Jordan Elimination method, LU Decomposition, Inverse of a matrix by elimination - Eigenvalues: Matrix Rotation & Definition, Eigenvalues
Week 3:	- Eigenvectors - Black Box Modeling of systems: Definition & Derivation of Error Function
Week 4:	Black Box modeling of systems: Derivation of Equations, R2, Quadratic Models Quiz I
Week 5:	- Linear transformation of nonlinear models, Enzyme Kinetics - Newton-Raphson for 1-unknown nonlinear systems
Week 6:	Numerical derivatives, Nonlinear Model parameter estimation (Newton-Raphson)
Week 7:	- Basics of (Ordinary) Differential equations (first order, linear and nonlinear, homogenous and nonhomogenus), - Analytical Solution of 1st Order ODEs - Taylor Series Transformation Quiz II
Week 8:	Midterm Exam Introduction to numerical methods for solving ODEs
Week 9:	Numerical methods in solving nonlinear ordinary differential equations: Euler, Heun methods
Week 10:	- Numerical methods in solving nonlinear ordinary differential equations:Runge-Kutta method - Solution of System of ODEs, Solution of Higher-Order ODEs - Stiffness Quiz III
Week 11:	- Equilibrium points (steady-state), Stability Analysis, Phase Plane Diagrams - Stability analysis by Eigenvalues
Week 12:	- Bifurcation Points - Modeling Changes (ODE-based Models): Introduction - Modeling Changes: Bioengineering & Biology problems I
Week 13:	Modeling Changes: Bioengineering & Biology problems II Quiz IV
Week 14:	- Control in Bioengineering - Bioreactor balance problems and solutions
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:	8	25
Other in-term studies:		0
Project:		0
Homework:	3,6,9,12	20
Quiz:	4,7,11,14	20
Final exam:	16	35
	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:	1	4
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)