LECTURE NOTES: MAT 501
ERROS IN NUMERICAL ANALYSIS
2.1INTRODUCTION
In the practice of numerical analysis it is important to be aware that computer solutions are
not exact mathematical solutions. The computer works with a number of significant figures,
so
LECTURE NOTES: MAT 501
SOLUTION OF SETS OF LINEAR EQUATIONS
3.1 Introduction
Simple techniques can be applied to solve small number of simultaneous equations for
example when they are three or less. Graphical method, Cramers Rule and the elimination of
un
NUMERICAL INTEGRATION
Q1. Evaluate the following integral
a)
b)
c)
d)
e)
f)
Analytically.
Using single application of the trapezoidal rule.
Composite trapezoidal rule, with n=2 and 4.
Single application of Simpsons 1/3 rule.
Simpsons 3/8 rule.
Determine t
TAYLORS SERIES AND NUMERICAL DIFFERENTIATION
Question 1
Use Taylor series expansions to approximate
() = 0.1 4 0.15 3 0.5 2 0.25 + 1.2
Also fine the true error for each approximation. Plot the polynomials in a graph.
Question 2
Use Taylor series expansion
SOLUTION OF LINEAR SETS OF EQUATIONS
Q1. For the following sets of equations
a) Compute the determinant
b) Use Crammers rule to solve for the xs
c) Substitute your results back into the original equation to check our results.
Q2 Given the following equati
LECTURE NOTES: MAT 501
TWO POINT BOUNDARY VALUE PROBLEMS
7.1 Introduction
In this section, solutions of 2nd order ODEs will be obtained by the Finite Difference Method
(FDM) particularly for two point boundary value problems. The students are referred to
LECTURE NOTES: MAT 501
NUMERICAL INTEGRATION
4.1 Introduction
Newtons formula or the Newton Gregory forward formula for interpolation will be used in
this chapter. The version of this formula for equally spaced data points is given below.
is the truncati