Chapter 7
First Order Ordinary Differential
Equation
7.1 Introduction
Ordinary differential equation (ODEs): Equation involving only one independent
variable and one or more dependent variables, together with their derivatives with respect
to the independ
Chapter 1 Introduction to MATLAB
1.1 What is MATLAB?
MATLAB = MATrix LABoratory, the language of technical computing, modeling
and simulation, data analysis and processing, visualization and graphics, and
algorithm development.
1.2 MATLAB System
The MATLA
Chapter 3 Multiple Integration
This chapter provides only a very brief introduction to the major topic of multiple
integration. Uses of multiple integration include the evaluation of areas, volumes, masses,
total charge on a surface and the location of a
Chapter 4
Solving a System of Linear Equations
4.1 Introduction
A system of linear equations arises in problems that include several (possibly many)
variables that are dependent on each other. A system of m linear equations in n unknowns
can be written as
Chapter 6 Numerical Differentiation and
Integration
6.1 Numerical Differentiation
When a function is given as a simple mathematical expression, the derivative can be
determined analytically. When analytical differentiation of the expression is difficult o
Chapter 4 Sequences and Series
4.1 Sequence Review
Sequence: a set of elements (numbers or letters or a combination of both). The elements
of the set all follow the same rule (logical progression). The number of elements in the
set can be either finite or
1.
ENGR 3425 Assignment #2 Solution
2 2
L+_y_=1
9 5
The standard eqn for ellipse is
(xxor + 02on _1
2 b2
a
Thus the center is at (x0, yo) > (O, 0), and a=3, b=\/§ .
0:ch2 b2 =V9~5=2
The foci are at (xo-c, yo) and (xo+c, yo) > (-2, O) and (2, 0).
The
Chapter 8 Higher Order Ordinary Differential
Equation
8.1 General Form
Of the second (and higher) order ordinary differential equations (ODE), only linear
equations with constant coefficients will be considered in this chapter:
Where P and Q are constant
Chapter 2 Errors in Numerical Methods
Numerical methods are mathematical techniques used for solving mathematical
problems that cannot be solved or are difficult to solve analytically.
Solutions to a math problem can be classified into two types: 1) Analy
Chapter 5
Curve Fitting and Interpolation
5.1 Basic Concepts
Consider a set of (x, y) data pairs (points) collected during an experiment,
Curve fitting: is a procedure to develop or evaluate mathematical formulas (functions or
equations) that best fit the
Memorial University of Newfoundland
Faculty of Engineering and Applied Science
Engineering 3425 - Mathematics for Civil Engineering 1
Assignment #5
l. (l)Ifu=x2y+yzz+zzx,prove that ux +uy +uz =(x+y+z)2.
ux =2xy+zz, uy =1:2 +2yz, u, =y2 +22x,
Thus,
ux
Chapter 2 Conic Sections and Polar Coordinates
2.1 Conic Sections
2.1.1 Definition
All members of the family of curves known as conic sections can be generated, (as the
name implies), from the intersections of a plane and a double cone. The resulted conic
Chapter 3 Solving Nonlinear Equations
3.1 Introduction
The nonlinear function of unknown variable x is in the form of
where n could be non-integer. Root is the numerical value of x that satisfies f ( x) 0 .
Graphically, the root is the point where the fun