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 s
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. Conside
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
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 solut
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
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
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 h
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
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 an
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 an
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 an
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 typi
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 computati
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 tu
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 re
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
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.
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
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.
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
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 dis
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
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
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 form
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 n
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