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

BME 230A Applied Engineering Mathematics I

(Not required for any major.)
Catalog Data:

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)

Required Textbook:
. Edition, , 1969, ISBN-13 978-0470458365.

Recommended Textbook:
None
References:

None.

Coordinator:
Zhongping Chen
Relationship to Student Outcomes
No student outcomes specified.
Course Learning Outcomes. Students will:

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).

Prerequisites by Topic

Ordinary differential equation, linear algebra

Lecture Topics:
  • 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.
Class Schedule:

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

Computer Usage:

Optional.

Laboratory Projects:

None.

Professional Component

None.

Design Content Description
Approach:

None.

Lectures:
Laboratory Portion:
Grading Criteria:
  • Homework: 20%
  • Midterm: 30%
  • Final: 50%
  • Total: 100%
Estimated ABET Category Content:

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

Prepared:
August 6, 2014
Senate Approved:
April 25, 2014
Approved Effective:
2014 Fall Qtr