# BME 230B Applied Engineering Mathematics II (2012-2013)

#### BME 230B Applied Engineering Mathematics II

**BME 230B Applied Engineering Mathematics II (Credit Units: 4)** Advanced engineering mathematics for biomedical engineering. Will focus on biomedical system identification. Includes fundamental techniques of model building and testing such as formulation, solution of governing equations (emphasis on basic numerical techniques), sensitivity theory, identifiability theory, and uncertainty analysis. Graduate only. (Design units: 0)

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1. Define computational problems in BME.

2. Understand numerical techniques typically encountered in biomedical research.

3. Formulate solutions as algorithms.

4. Translate algorithms into a computational tool.

5. Use tools for solving computational problems.

6. Document the problem identification, design and solution.

Math (Linear Algebra, Differentiation, Integration, Solution of PDEs), Basic Statistics, Computer Literacy (experience in solving mathematical problems on a computer)

- Introduction, Mathematical Preliminaries
- Basic Statistics
- Least Squares Estimation
- Solving Linear Algebraic Equations
- Nonlinear Least Squares Estimation
- Interpolation and Extrapolation
- S Interpolation and ExNumerical Solution of Ordinary Differential Equations
- Compartment Models
- ExNumerical Solution of Partial Differential Equations
- Finite Element Modeling

Meets for 3 hours of lecture and 1 hour of discussion each week for 10 weeks.

Homework involves writing simple programs (e.g., spreadsheet, C, Matlab, etc.)

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- Homework: 50%
- Midterm: 25%
- Final: 25%
- Total: 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 0.0 credit units

Engineering Science: 0.0 credit units

Engineering Design: 0.0 credit units