# BME 230B Applied Engineering Mathematics II (2013-2014)

#### 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. This course will provide graduate students in Biomedical Engineering with the knowledge and understanding for analyzing and simulating biomedical systems.

2. Define computational problems in BME. (EAC a, EAC b, EAC d)

3. Understand numerical techniques typically encountered in biomedical research. (EAC a, EAC b)

4. Formulate solutions as algorithms. (EAC a, EAC b, EAC e, EAC i, EAC j)

5. Translate algorithms into a computational tool. (EAC b)

6. Use tools for solving computational problems. (EAC b)

7. Document the problem identification, design and solution. (EAC e, EAC i, EAC j)

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 I
- Applied Statistics: Functional MRI
- Basic Statistics II, Least Square Estimation
- Solving Linear Algebraic Equations
- Shape Analysis by Spherical Harmonics
- Nonlinear Least Squares Estimation
- Nonlinear Least Squares Example
- Interpolation and Extrapolation
- Compartment Models
- Image Registration
- Solving Partial Differential Equations I
- Solving PDEs: Three Examples
- Motion Estimation
- Finite Element Analysis I
- Finite Element Modeling II
- Clinical Simulation using FEA

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

Homework involves writing simple programs (e.g., R, Python, 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