ENCH620
Methods of Engineering Analysis
Fall 2013
Class Handouts & Lecture Notes
Class Syllabus
Policy on Academic Integrity
Homework
09/03
Link to CHBE250, Computer Methods
Mathcad
Pop quiz
09/05
Ax=b
,
matrix review
What is a function?
09/10
Getting Started with Matlab
09/12
f(x)=0
:
Iteration
f(x)=0
:
Algorithms (Bisection, Chord, Secant, Newton's Method)
09/17
Function approximation
-- Taylor's series
Function approximation
-- Lagrange interpolation polynomial
09/19 Lagrange interpolation polynomial
09/24 Cubic spline. Difference (forward, backward, central)
09/26 Integration,
Trapezoidal Rule & Simpson's Rule
Gauss quadrature
Gaussian Elimination
& matrix inverse:
Ax=b
&
A
^{-1}
.
LU decomposition
Gauss-Seidel iteration, Jacobi iteration
10/01 Regression,
Intercept and slope equations
,
Multivariate regression (Part 1, Linear least squares regression)
(Part 2, Multiple least squares regression)
10/03 Goodness of fit (sse, r
^{2}
), number of terms, nonlinear regression
10/08 Exam #1
10/10
ODE by Euler, Runge-Kutta
, finite element
10/15
Vector Analysis
,
linear vector space
,
10/17
Scalar|dot|inner product
, length|magnitude|norm,
angle
, Gram-Schmidt orthogonalization process
10/18 Projection
10/22 Application of vector projection (regression & function approximation, approximation of solution to ODE, method of weighted residuals)
10/24 vector
10/29 vector
10/31
Linear transform
11/05 Linear transform,
rotation in 3D Cartesian coordinates
11/07 Exam #2
11/12
Eigenvalue-eigenvector
11/14
Eigenvalue-Eigenvector of 2nd Derivative Operator
1st-order ODE via eigenvalue-eigenvector, exp(A*t),
Jordan normal form
11/19 Localized stability analysis of 1st-order ODE dx/dt=A*x via eigenvalue-eigenvector
11/21
PDE by separation of variables
(another application of eigenvalue-eigenvector)
11/26 PDE by separation of variables
11/03 optimization (static)
11/05 optimization (dynamic)
11/10 perturbation method
11/12 perturbation method
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Methods of Engineering Analysis
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Nam Sun Wang
Department of Chemical & Biomolecular Engineering
University of Maryland
College Park, MD 20742-2111
301-405-1910 (voice)
301-314-9126 (FAX)
e-mail:
nsw@umd.edu
©2013 by Nam Sun Wang