# BME 230A Applied Engineering Mathematics I (2015-2016)

#### BME 230A Applied Engineering Mathematics I

**BME 230A Applied Engineering Mathematics I (Credit Units: 4)** Analytical techniques applied to engineering problems in transport phenomena, process dynamics and control, and thermodynamics. Graduate students only. . (Design units: 0)

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1. Model and solve biomedical engineering problems with ordinary differential equation.

2. Model and solve biomedical engineering problems with a system of differential equations.

3. Model and solve biomedical engineering problems with partial differential equations (wave equation, Laplace equation, and diffusion equation).

Ordinary differential equation, linear algebra

- Introduction and classification of differential equations, modeling of linear and nonlinear differential equations.
- Linear differential equations of second and higher order, superposition principle, linear dependence and independence, Wrongskian determinant.
- Homogeneous linear differential equations, basis functions, Nonhomogeneous linear differential equations, variation of parameters method.
- System of differential equations. Matrix eigenvalue problems, eigenvalue, eigenvector, basis of eigenvector, matrix diagonalization. Homogeneous and nonhomogeneous linear systems. Modeling of linear systems.
- Linear system equation with nonconstant coefficient. Power series method. Method of Frobenius.
- Special function: Legendre equation and functions; Bessel equation and functions.
- Sturm-Liouville Problems: regular, singular and periodic S-L problems. Orthogonal functions and eigenfunction expansion. General Fourier expansion.
- Partial differential equations. Modeling of wave equation, heat transfer equation, and Laplace equation. * Separation of variable method.
- Partial differential equations in Cartesian coordinates.
- Partial differential equations with cylindrical and spherical coordinates.

Meets for 3 hours of lecture each week for 10 weeks.

Optional.

None.

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- Homework: 20%
- Midterm: 30%
- Final: 50%
- 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