ENCH620
Methods of Engineering Analysis
Fall 2016
Class Handouts & Lecture Notes
Class Syllabus
Policy on Academic Integrity
Homework
08/30
Mathcad
What is a function?
Pop quiz
09/02
Ax=b
,
matrix review
09/06
Getting Started with Matlab
09/08
f(x)=0
:
Iteration
f(x)=0
:
Algorithms (Bisection, Chord, Secant, Newton's Method)
09/13
Function approximation
-- Taylor's series
Function approximation
-- Lagrange interpolation polynomial
09/15 Lagrange interpolation polynomial, Cubic spline. Difference (forward, backward, central)
09/20 Integration,
Trapezoidal Rule & Simpson's Rule
Gauss quadrature
09/22
Gaussian Elimination
& matrix inverse:
Ax=b
&
A
^{-1}
.
LU decomposition
Gauss-Seidel iteration, Jacobi iteration
09/27 Regression,
Intercept and slope equations
,
Multivariate regression (Part 1, Linear least squares regression)
(Part 2, Multiple least squares regression)
09/29 Goodness of fit (sse, r
^{2}
), number of terms, nonlinear regression
10/04 Exam #1
10/06
ODE by Euler, Runge-Kutta
, finite element
10/11
Vector Analysis
,
linear vector space
,
10/13
Scalar|dot|inner product
, length|magnitude|norm,
angle
, Gram-Schmidt orthogonalization process, Projection
10/18 Application of vector projection (regression & function approximation, approximation of solution to ODE, method of weighted residuals)
10/20 vector
10/25 vector
10/27
Linear transform
11/01 Linear transform,
rotation in 3D Cartesian coordinates
11/03
Eigenvalue-eigenvector
11/08 Exam #2
11/10
Eigenvalue-Eigenvector of 2nd Derivative Operator
1st-order ODE via eigenvalue-eigenvector, exp(A*t),
Jordan normal form
11/15 Localized stability analysis of 1st-order ODE dx/dt=A*x via eigenvalue-eigenvector
11/17
PDE by separation of variables
(another application of eigenvalue-eigenvector)
11/22 PDE by separation of variables
11/24 Thanksgiving Day
11/29 optimization (static)
12/01 optimization (dynamic)
12/06 perturbation method
12/08 perturbation method
12/19 4-6pm Final Examination (Exam #3)
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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
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nsw@umd.edu
©2016 by Nam Sun Wang