CHAPTER 1 INTRODUCTION TO NUMERICAL METHODS In engineering, it is often necessary to solve complicated mathematical problems. Many of these problems do not have known analytical solutions. Numerical solutions are usually needed in these situations. This c
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 4 This tutorial focuses on methods of fitting and interpolating given data points. Consider the following data points: x y 1 1.2 2 1.8 4 2.9 5 3.
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 5 This tutorial investigates Matlab implementation of the Gaussian elimination method. The result is application to linear systems of n equations
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 6 Numerical differentiation is often needed to treat problems that involve iterative solutions. Consider the following characteristic equation th
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 7 The spectrum of a light bulb or the sun follows the following formula:
f ( x) =
x3 , e x 1
where x is a normalized frequency. The curve is plot
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 8 A RLC resonant circuit can be solved using a second-order ordinary differential equation (ODE). We consider the following circuit with R = 20 ,
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 9 The cooling a copper rod is investigated using the heat equation. The rod is uniformed heated to 100C before t =0. It is then put into contact
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Assignment 1 Deadline: 5:00pm, 1 Feb 2008 (Room G6354) Please put down your name, university ID and the time-slot of your tutorials. 1. Evaluate the follo
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Assignment 2 Deadline: 5:00pm, 22 Feb 2008 (Room G6354) Please put down your name, university ID and the time-slot of your tutorials. 1. Consider the equa
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Assignment 3 Deadline: 5:00pm, 27 Mar 2008 (Room G6354) Please put down your name, university ID and the time-slot of your tutorials. 1. An unknown electr
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Assignment 4 Deadline: 5:00pm, 18 Apr 2008 (Room G6354) Please put down your name, university ID and the time-slot of your tutorials. 1. In a piece of sem
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 3 There are many useful specialized functions in engineering. These special functions typically have complicated expressions, but are standard so
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 2 In this tutorial, we examine the manifestation of numerical errors in the real computations. Round-off errors and truncation errors are conside
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 1 The last tutorial demonstrated the basic Matlab operations and script execution. This tutorial is a bit more advanced. It is about matrix index
CHAPTER 2 NUMERICAL ERRORS All numerical calculations are prone to numerical errors. This chapter examines two important sources of error: round-off error and truncation error. Round-off errors are related to the discrete representation of numbers in comp
CHAPTER 3 ROOT FINDING This chapter is about different root searching techniques. Given a function f(x), we are interested to look for its root (i.e. f() = 0). The general idea is to revise the value of x through a repeated process. The goal is for x to a
CHAPTER 4 CURVE FITTING AND INTERPOLATION When a number of data points (xi, yi), for i = 1, 2, , m, are given; there are two approaches to use an analytic function to approximate the x-y relationship. The first approach is to use a simple curve to fit the
CHAPTER 5 LINEAR SYSTEMS A linear system with n unknowns x1, x2, x3, represented by the equation: Ax = b , where
a11 a12 L a1n M a21 O A= M O is an nn matrix, a ann n1
,
xn can be
-(1)
However, for simplicity, we focus on the case of n = 3. As a result,
CHAPTER 6 NUMERICAL DIFFERENTIATION Differentiations on simple functions should usually be performed analytically. However, there are situations that we must rely on numerical differentiation methods. For example, the function may come from experimental m
CHAPTER 7 NUMERICAL INTEGRATION Numerical integrations are basically techniques of finding the area under a curve by summations. Considering a function f(x), its integral:
The area under the curve is given by the integration:
f ( x)dx = e x dx
2
2 2 = e
CHAPTER 8
NUMERICAL ORDINARY DIFFERENTIAL EQUATIONS
(ODE) This chapter is about solving for a function of time y(t) when its time-derivative is given, namely,
The following problem of charging and discharging a capacitor will be considered as an example t
CHAPTER 9
NUMERICAL PARTIAL DIFFERENTIAL EQUATIONS
(PDE) A classic example of partial differential equations (PDE) is the heat equation that governs the temperature distribution as time evolves. For a uniform one-dimensional object, the equation takes the
CHAPTER 10 OPTIMIZATION Optimization refers to the techniques that minimize (or maximize) an objective quantity of a problem. The objective is generally represented as a real function f(x), where the independent vector variable x comprises of all the cont
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Midterm Formula Sheet The following formulae may or may not be useful in the midterm. The same formula sheet will be provided during the midterm test.
f (
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Project: Optical Wave Propagation Deadline: 5:00 pm, 5 May 2008 (Room G6354) Please put down your name, university ID, and the time-slot of your tutorials
City University of Hong Kong Electronic Engineering Semester B 2007-2008 EE3108 Engineering Analysis Tutorial 0 The course EE3108 relies heavily on the use of Matlab. This tutorial serves as a warm-up exercise for new users of Matlab. Follow the steps bel