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UCSD BENG 221 - Syllabus

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1 UCSD Department of Bioengineering BENG 221 – Mathematical Methods in Bioengineering Fall 2014 Class: Lectures: Tue & Thu, 11:00am –12:20pm, PFBH 161 Problem Solving Sessions: Fri, 11:00am-11:50am, PFBH 161 Instructor: Professor Gert Cauwenberghs Email: [email protected] Office Hours: Tue 12:30p-1:30p, Wed 5:00p-6:00p, or by appointment Teaching Assistants: Sheng-Hsiou (Shawn) Hsu Email: [email protected] Office Hours: Wed 2-3pm, PFBH 391 Yuchen Wang Email: [email protected] Office Hours: Mon 2-3pm, PFBH 391 URL: http://www.isn.ucsd.edu/courses/beng221 Reading: See Reading Materials on the class web page Grading: Homework 30% Problem Solving 20% Midterm 20% Final Exam 30%2 Homework and Exam Policies ALL parts of the homework must be turned-in and will be graded. All parts of exams must be answered unless otherwise stated. Both the exams and homework must be legible, show good use of English, and be organized. Points will be given or deducted for these qualities accordingly. Late homeworks will not be accepted. Any requests for re-grading must be made in writing to the TAs and will result in re-grading of the entire homework or exam, not just a specific problem, first by the TAs themselves and if following this a dispute remains, by the course instructor. Such re-grading could result in a higher or lower overall grade. The Department of Bioengineering adheres to the UCSD Policy on Integrity of Scholarship. An excerpt of this Policy states that "Students are expected to complete the course in compliance with the instructor's standards. No student shall engage in any activity that involves attempting to receive a grade by means other than honest effort...." In other words, cheating of any kind whatsoever WILL NOT BE TOLERATED in any form in this course and will be punishable to the maximum extent possible as per university rules and policies. The full policy is available in the general catalog (e.g., at http://www.ucsd.edu/catalog/AcadRegu.htm)." Group study and discussion of homework assignments is allowed, but the contributions of others should be clearly documented in writing in the homework. Students are allowed to discuss approaches to problem-solving and design, but are not allowed to obtain or provide written solutions. In cases of suspected academic dishonesty, the case will be referred to the appropriate Dean. Generally, the penalty for academic dishonesty is a failing grade at minimum, with other more severe academic penalties possible.3 Problem Solving and Presentations The problem solving sessions offer an exercise in bioengineering problem formulation and solving, demonstrating creative thinking, effective teamwork, and clear presentation skills. In groups of two students you will: a. Formulate a problem in bioengineering in quantitative mathematical terms; b. Simplify the problem to arrive at an analytical solution, and interpret the solution in terms of the dependence on the parameters; c. Use numerical methods to arrive at an approximate solution to the full problem, and interpret any discrepancies between the numerical solution and the simplified analytical solution; d. Present the problem and solutions during one of the presentation sessions, and answer questions from peer students; e. Write and submit a report, presenting and documenting the problem and solutions. Group assignments, and the scheduling of presentations, are made during the first week of classes. Each group presents once, for a total of two presentations each meeting time. Time your presentations not to exceed a total of 20 minutes, not including questions. Use the whiteboard for your presentations. Computer use is allowed for presentation of numerical results, but not for analytical results. The report is due one week after your presentation, and should include title, presenters’ names, problem statement, simplified solution, numerical validation, conclusion, and references/credits. Use diagrams and graphs to document the problem and the solutions. The report should be submitted by e-mail to the TA in charge, in PDF format. Reports will be posted on the class web page as a service to future students taking the class searching for ideas and inspiration. You may consult anyone on your problem statement and methods, but you must do the problem solving yourselves, working with your group companion. You must also give credit to all sources where these guided your problem statement or solutions. Where these sources are in the open literature, you must cite the publications in print or on-line. Success, and enjoy!4 BENG 221 Mathematical Methods in Bioengineering Fall 2014 CLASS SCHEDULE START OF CLASSES October 2 Introduction. Ordinary differential equations (ODEs), and initial and boundary conditions. Solution of homogeneous and inhomogeneous ODEs. Eigenvalue and eigenvector analysis, and multimode analysis. Linear time-invariant systems, impulse response, and transfer function. October 3 Tutorial and problem solving session. Introduction to Matlab for linear systems, ODEs and PDEs. Analytical and numerical techniques. Solution to example problems, using paper and pencil, and verified by numerical simulation. WEEK 1 October 7 Introduction to PDEs. One-dimensional heat equation, and its equivalents in electrical and chemical transport with applications to biomedical engineering. Flux through membranes. One-dimensional wave equation in an electrical transmission line, with open and short circuit termination. Finite difference PDE approximations. October 9 Solutions to PDEs over bounded and unbounded domains. Separation of variables. Boundary value problem and solution of the x dependent equation. Product solution of the PDEs with specified boundary conditions. Solutions over infinite domains using Fourier transforms. October 10 Problem solving session—student presentations. WEEK 2 October 14 Heat equation. Temperature, thermal energy, and flux. Diffusion of thermal energy, and boundary conditions on temperature and flux. Thermal equilibrium. October 16 Analytical solution to the inhomogeneous heat equation with space varying source and boundary conditions. Decomposition of the solution into a particular steady-state solution, and Fourier series eigenmodes of the homogeneous solution. Fourier series expansions of initial conditions revisited.


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