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Syllabus ( BSB 611 )


   Basic information
Course title: Foundations of Mathematical Modelling in Biology
Course code: BSB 611
Lecturer: Prof. Dr. Hasan SADIKOĞLU
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 1/2, Fall
Level of course: Third Cycle (Doctoral)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: none
Professional practice: No
Purpose of the course: The focus is the solution of linear/nonlinear equations as well as the solution of ordinary differential equations. The foundations of modelling and application to biological systems will be aimed throughout the course.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Construct mathematical models and solve them

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts in the field of Bioinformatics and Systems Biology
    2. Link the concepts belonging to the different disciplines and interpret & analyze scientific research in these disciplines.Question and find out innovative approaches

    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. Define and manipulate advanced concepts in the field of Bioinformatics and Systems Biology
    2. Apply modelling approaches to cellular networks.

    Method of assessment

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

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts in the field of Bioinformatics and Systems Biology
    2. Apply modelling approaches to cellular networks.
    3. Find out new methods to improve his/her knowledge.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
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 Exam
Week 11: 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:
Recommended readings: 1. Brian Ingalls, "Mathematical Modeling in Systems Biology: An Introduction", The MIT Press, 2013
2. Erwin Kreyszig, “Advanced Engineering Mathematics”, 10th Edition, John Wiley and Sons, New York, 2011.
3. Richard G. Rice, Duong D. Do. “Applied mathematics and modeling for chemical engineers”, John Wiley and Sons, New York, 1995.
4. 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 Up
Method of assessment Week number Weight (%)
Mid-terms: 10 30
Other in-term studies: 0
Project: 0
Homework: 2,4,6,8,10,12 30
Quiz: 0
Final exam: 16 40
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 6 14
Practice, Recitation: 0 0
Homework: 5 6
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 7 2
Mid-term: 3 1
Personal studies for final exam: 12 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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