TMS3133 Numerical Methods
Learning Unit 5
Numerical Dieren<a<on &
Integra<on
Contents
Numerical Dieren.a.on
First Deriva.ve
Example
Solu.on
Example
Solu.on
Lab work
Create functions in Matlab to answer the question
TMS3133 Numerical Methods
Learning Unit 6
System of Linear Equa>ons
REVIEW
Linear Algebraic Equa>ons and
Matrices
Overview
A matrix consists of a rectangular array of
elements represented by a single symbol
(
TMS3133 Numerical Methods
Learning Unit 7
LU Factoriza<on
Itera<ons Methods
LU Factoriza<on
Deni<ons
Procedure
Types of factoriza<on
DooliDle Method
To illustrate the direct computa<on of LU,
consider n x n
TMS3133 Numerical Methods
Learning Unit 8
Numerical Linear Algebra
(Eigenvalue Problem)
Dynamics of Three Coupled Bungee
Jumpers in Time
Is there an underlying pattern?
MathemaHcs
Up until now, heterogeneous systems:
[A] cfw_x
TMS3133
Numerical Methods
Assignment 2
Semester 1 2015/2016
Due date: 18th Dec at 4pm
ode45 in Matlab was written to solve initial-value problems (IVPs). Hence, it cannot be directly use
TMS3133 Numerical Methods
Lecture 4
Interpola:on and Approxima:on
What is Curve FiAng?
Fitting data into a curve
Need techniques to fit
curves to such data to
obtain intermediate
estimates
TWO approaches in curve fitting:
Curve FiAng
W
TMS3133 Numerical Methods
Lecture 3
Numerical Techniques in Solving
Nonlinear Equa;ons
Contents of Learning Unit
What is Nonlinear Equa;on?
Solving Nonlinear Equa;on
Means the same with nding the root of
nonlinear e
TMS3133
Numerical Methods
Numerical Computa7on
Lecture Objec7ves (1/2)
Understanding the dis7nc7on between accuracy and
precision.
Learning how to quan7fy error.
Learning how error es7mates can be used to decide
wh
TMS3133
Numerical Methods
Lecture 1
Introduc8on to the course
What is the course about?
This course provides the study and applica2on
of numerical methods, which gives the
transi2on from the mathema2cal model of
TMS3133 Numerical Methods
Semester 1 2015/2016
Tutorial Sheet 1
6. Indicate in the Table below the first three points that will be plotted with the following MatLab
sentences:
x
c
cf
TMS3133 Numerical Methods
Semester 1 2015/2016
Tutorial Sheet 2
4. Solve the problems 1 3 above using the Bisection Method by hand. Do your
calculations in 3 decimal places.
5. Solve the problems 1 3 abov