Objectives
Construct mathematical models for linear and non-linear engineering systems Apply existing numerical methods for a range of engineering systems Make use of MATLAB/Spreadsheets for the numerical solutions of engineering problems
Week 1
MECH201
MECH201 ENGINEERING ANALYSIS
Lecture Notes
(Week 3)
Tutorial quiz 1 : Next week - Week 4
9.20-10.30am (Week 1 to 3 inclusive)
(open book ONLY for TUT QUIZ)
1
Review of Matrix Notation
and Algebra
2
Matrix notation
Matrix element
Matrix symbol
n-by-m matri
MECH201 Week 5
Optimisation & Curve
fitting
1
Multi-Dimensional
Unconstrained Optimization
2
Description of multidimensional
unconstrained optimization
Find x
Maximize or minimize f(x)
3
Method 1 Random search
This method repeatedly evaluates the function
MECH201 ENGINEERING ANALYSIS
Lecture Notes
(Week 4)
Optimization
1
Difference between roots and optima
Roots:
Optima:
f ( x) = 0
f ( x) = 0
f ( x) < 0
f ( x) = 0
f ( x) > 0
Maximum
Inflection point
Minimum
2
Example falling parachutist
You are an engineer
MECH201 ENGINEERING ANALYSIS
Lecture Notes
(Week 1)
Coordinator and Lecturer: Dr Guillaume Michal
Lecturer : Prof. Kiet Tieu
Office: Bld8.123
Email: [email protected]
Consultation time: 2:00pm-4:00pm on Tuesday
Text book
Chapra, S. C. & Canale R. P., Num
MECH201 Week 8
Numerical Integration
Lecturer: Guillaume Michal
Office: B8. G14
Email: [email protected]
Week 8: Numerical Integration
An integral part of
engineering
Mathematical
background
Tabulated data vs
equations
Methods of integration
Multipl
MECH201 ENGINERING ANALYSIS
Lecture Notes
(Week 2)
1
NOTICE
NOT all tutorial solutions will be uploaded. You
need to attend tutorials, and seek assistance
from tutors:
Yuankun Zhang [email protected] (Group 1
and 3)
SamWassim Khamiss [email protected]
MECH201 Week 11
Ordinary Differential Equations II:
Boundary value and Eigenvalue Problems
Lecturer: Guillaume Michal
Office: B8. G14
Email: [email protected]
Week 10: ODE I
Boundary value and Eigenvalue problems
Recap of RK
Boundary value
problems
Ei
Objectives
MECH201 Understanding what roots problems are and where they occur in engineering and science Knowing how to determine a root graphically Knowing how to solve a roots problem using bracketing methods Knowing how to solve a roots problem with op
Outline
Week 3 What are linear algebraic equations Matrix algebra overview Solving linear algebraic equations
- graphics methods - direct methods:
Gauss elimination LU decomposition Thomas methods
Week 3 Week 3
Linear Algebraic Equations
Linear Algebraic
Background
Week 4
Both root location and optimization involve guessing and searching for a point on a function Root location involves searching for zeros of a function or functions, while optimization involves searching for either the minimum or the maxi
Objectives
Week 5
Curve Fitting & Interpolation
Use least-square regression to fit a straight line to measured data Use polynomial regression to fit polynomials to the measured data
Week 5
Week 5
Curve Fitting
There are two approaches for curve fitting:
1 REVISION
1.1 Polynomial Approximation and Interpolations
Given a set of points (xi, yi), where i = 0, 1, 2, 3, n, a polynomial of n degree can be fitted. The polynomial is in the form:
y(x ) =
Aj x j
j =0
n
so that x = xi, y = yi.
This give rises to n+
The central difference scheme is more accurate than the other twos as it is of order x2. See figures 23.1 to 23.3 for higher order representation of derivative of a function. The higher order or accuracy can be achieved by using more points in the neighbo
5 EIGENVALUE PROBLEMS
5.1 The engenvalue and eigenvectors
Section 27.2.1 Eigenvalue or characteristic value problems are used in a wide variety of engineering contexts involving vibrations, elasticity, and oscillating systems. Let us consider a set of non
8 PARTIAL DIFFERENTIATION A REVISON
Consider an analytic function which has two depend variables: x and y. That is z = f(x,y).
(f/y)dy z = f(x,y) y
(f/x)dx
A B
C
x
Figure 8.1 A 3-D profile.
If z is the vertical axis, the x-axis is in the East-West directi
10 THE PARABOLIC PARTIAL DIFFERENTIAL EQUATION
10.1 Heat conduction through a wall
Section 30.1 The following problem for heat conduction through a wall of infinite plan area turns out to be an identical mathematical problem as the previous problem: the f
10.6 The Crank-Nicolson Scheme - an Implicit method
In the computation using the implicit method half of the spatial differentiation in the "future time" and thus have to be solved by iteration. The FDA is expressed as:
Ti , j +1 Ti , j t = 2 x
T 2Ti , j
MECH201 ENGINERING ANALYSIS
Lecture Notes
(Week 2)
1
NOTICE
NOT all tutorial solutions will be uploaded. You
need to attend tutorials, and seek assistance
from tutors:
Yuankun Zhang [email protected] (Group 1
and 3)
SamWassim Khamiss [email protected]