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Contents
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| 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: |
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| 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. |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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