BIM_107_w10-Syllabus

BIM_107_w10-Syllabus - Bio-Mathematical Methods BIM 107...

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Unformatted text preview: Bio-Mathematical Methods BIM 107 Winter 2010 Location: Olson 118 Meeting Times: M 12:10-2:00 pm (sections 01 and 02 combined) Location: SciLab 2060 Meeting Times: W (Section 01) 12:10-2:00 pm or F (Section 02) 12:10-2:00 pm Instructor: Subhadip Raychaudhuri Office: 2521 GBSF Building Phone: 530 754 6716 Email: raychaudhuri@ucdavis.edu Illustrative Readings: Numerical Methods in Biomedical Engineering By Stanley M. Dunn, Alkis Constantinides, and Prabhas V. Moghe Publisher: Elsevier Academic Press, 2006. (Copies should be on reserve in the shields library!) Instructor Office Hours: Section 01: W 1:10-2:00 pm (SciLab 2060) Section 02: F 1:10-2:00 pm (SciLab 2060) TA Office Hours: TBA Topical outline: Applications of linear systems and differential equations to biomedical problems. Topics include vectors and matrices, eigenvalues and eigenvectors, singular value decomposition, Monte Carlo Simulations, ordinary and partial differential equations. Students will be introduced to numerical solution techniques in MATLAB. Grading: Letter grade based on – Homeworks: 30% (HW1 – 5 points, HW2 - 5 points, HW3 – 10 points, HW4 – 5 points, HW5 – 5 points) Midterm: 30% (Monday, February 1st, 12:10-2:00 pm) Final: 40% (Wednesday, March 17th, 6:00-8:00 pm) Schedule of Lectures Date Chapter Assignment 1 1/4 HW 1 2 1/6 or 1/8 3 1/11 4 1/13 or 1/15 1/18 Vectors and Matrices – Biomedical Applications Numerical Calculation in MATLAB Singular Value Decomposition Introduction to Programming in MATLAB Holiday – No Lecture 5 1/20 or 1/22 Monte Carlo Simulation 6 1/25 7 1/27 or 1/29 Monte Carlo – Master Equation and Random Walk Monte Carlo Simulation 8 2/1 Midterm Exam 9 2/3 or 2/5 10 2/8 11 2/10 or 2/12 2/15 Biomedical Applications of Monte Carlo Simulation Biomedical Applications of Monte Carlo Simulation Ordinary Differential Equations (ODEs) Holiday – No Lecture 12 2/17 or 2/19 Numerical solution of ODEs 13 2/22 14 2/24 or 2/26 15 3/1 16 3/3 or 3/5 17 3/8 Laplace Transform Method, Numerical Solution of ODEs Numerical and MATLAB ODE solution Partial Differential Equations (PDEs) PDEs & MATLAB plot of PDE solutions Numerical solution of PDEs 18 3/10 or 3/12 19 3/15 Numerical and MATLAB Solutions of PDE Final Review 3/17 Final Exam Due HW 2 HW 1 HW 3 HW 2 HW 4 HW 3 HW 5 HW 4 HW 5 Exam Topics: Midterm Exam - Vectors and Matrices, SVD, MATLAB programming (30 points) Final Exam – ODE and PDE (40 points) Biomedical Applications: (will be discussed in class lectures) Vectors and Matrices, SVD –gene expression data analysis Monte Carlo simulation – random walk of cell surface receptors, apoptotic cell death signaling and diseases ODE –receptor-ligand binding and estimation of kinetic rate constants PDE – signaling in T and B (immune) cells (Additional applications: imaging data analysis, drug delivery in polymeric materials) ...
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