Please download the free software at
http:/math.exeter.edu/rparris for additional explorations.
1
Area
of
Polar Regions
by
Prof. Velimor D. Almonte
Objective:
Upon completing this lesson, you
will be able to find the area of
regions bounded by polar cur
MATH022
Areas of Plane Regions
Objectives
At the end of the period, you should be able to:
Find the area of the region bounded by a
curve, the coordinate axis.
Find the area of the region bounded by two
curves.
Apply definite integration in finding area
2009 Calculus Hustle
1. Find the absolute maximum of = 4 3 + 5 2 + 8 + 3 on the interval [-1,2].
2. Find the derivative of ( )4x.
2
3. What is the volume of a solid above the x-axis upper bounded by + 4 from x=0 to x = 5 rotated
120o around the y axis?
4.
6/24/2013
2
A statistic is a characteristic or
measure obtained by using the data
values from a sample.
A parameter is a characteristic or
measure obtained by using the data
values from a specific population.
Data Description:
Summarizing Data Sets
1
6/2
Objectives
Define and derive Laplace transform
formulas.
Perform Laplace transformation of functions.
Perform inverse transformation of functions.
Apply Laplace transformation in solving
linear differential equations.
The Laplace transform method is
Dierential Equations
BERNOULLI EQUATIONS
Graham S McDonald
A Tutorial Module for learning how to solve
Bernoulli dierential equations
q Table of contents
q Begin Tutorial
c 2004 [email protected]
Table of contents
1.
2.
3.
4.
5.
6.
Theory
Exercis
02
JANUARY 6, 2010
COURSE SYLLABUS
COLLEGE / DEPARTMENT
:
COLLEGE OF ARTS AND SCIENCE
COURSE CODE
COURSE TITLE
:
:
MATH025
DIFFERENTIAL EQUATIONS
PRE-REQUISITE
CO-REQUISITE
CREDIT UNIT(S)
CLASS SCHEDULE
:
:
:
:
MATH023
None
Three (3) units
1.5 hours per m
General Linear Equation
The general linear differential equation of order n is an
equation that can be written in the form
dny
d n 1 y
dy
bn x n bn 1 x n 1 . . . b1 x b0 x y Rx
dx
dx
dx
If the value of the function R(x) is zero for all x, then the
equa
MATH025-A16
First Term 2013-2014
Assignment No. 2
Due: June 29, 2013 (Saturday)
Determine the type of each of the following differential equations. Then solve the
equations. Solution to the DE must be in explicit form, if possible.
1.
y' e 2 x y
2.
(cos x
1.
A dead body is discovered at 3:00 P.M. on Monday in a storage room where the air temperature is 10C.
The temperature of the body at the time of discovery is 26.7C and 20 minutes later, is 25.6C. ( a) Find
the temperature of the body at any time t. (b)
MATH025
Differential Equations
Casiano DC. Jaurigue
Objectives
Define differential equation (DE) and other
terminologies that describe a DE.
Distinguish between ordinary differential
equation (ODE) and partial differential equation
(PDE).
Identify the ord
MATH025
Differential Equations
First-Order
Differential Equations
Objectives
Recognize the equation type and use the
appropriate technique to solve equation
Solve first-order linear DE using
separation of variables.
Solve first-order linear homogeneous DE
nth-Order Linear Homogeneous Differential Equations with Constant Coefficients
The Method of Undetermined Coefficients
Variation of Parameters
The Laplace Transform
Find the Laplace transforms of the given function.
Inverse Laplace Transforms
Solutions of
MATH025-A16
First Term 2013-2014
Assignment No. 4
Due: August 13, 2013 (Tuesday)
1.
Solve the linear homogeneous differential equation
32
DD 5 D 3 1D 2 D 5y 0 .
2.
Find the general solution to a fourth-order linear homogeneous differential equation
for y
Applications of
First-Order Differential Equations
GROWTH AND DECAY PROBLEMS
Let N(t) denote the amount of substance (or population) that is
either growing or decaying. If we assume that dN/dt, the time rate of change
of this amount of substance, is propo
HYPERBOLIC AND
INVERSE HYPERBOLIC FUNCTIONS
Combinations of e x and e x that appear mostly in
applications of mathematics like in engineering and
physics are called hyperbolic functions.
sinh 2 x 2 sinh x cosh x
cosh 2 x cosh 2 x sinh 2 x
2 cosh 2 x 1
2
The Method of U ndetermined Coefficients
The general solution to the linear differential equation L(y) = R(x) is
given by y y h y p where y p denotes one solution to the
differential equation and y h is the general solution to the associated
homogeneous e
Higher-Order Linear
Differential Equations
Linear Equation with Constant Coefficients
Any linear homogeneous differential equation with constant
coefficients, n
n 1
a0
dy
dy
dy
a1 n 1 . . . an 1 an y 0
dx n
dx
dx
may be written in the form
f Dy 0
where