Linear Differential Equations and the Integrating Factor
Linear Differential Equations
A differential equation is called linear if it can be written in the form
+ () = ().
Ex 1:
+ 2 = is linear and would have () = 2 and () = .
Ex 2:
+ 2 = sin() is NOT lin
Modeling Diff Eq Practice
1.
is the solution of the differential equation
initial condition
.
2. A population is modeled by the differential equation
the population decreasing?
3.
. Find the solution that satisfies the
is the family of solutions of the di
Math 272 Integration - Lab 2
Integrate each by using symbolic techniques only. Do not use tables or calculators. Show all
work on your paper. Clearly label each problem.
1
(2 x 3)dx
2
dx
2 x 8 x 10
1 x2
2
2
3
3 sin (2 x) cos (2 x)dx
4
9
10
x tan 1 ( x)dx
MAT 272 Lab 4
Twelve differential equations are listed below: some are separable, some are linear, and some are
neither. For each one classify it (separable, linear, or neither), and if it is separable or linear solve the
equation symbolically.
MAT 272
1.
Test 4
Review
Does each of the following geometric series converge or diverge? If any converges, state the sum.
1
4 2
a)
n
b)
2+
n 1
3
(1)n 4
n 3
c)
2.
n
Does each of the following p-series converge or diverge?
1
n 1
a)
n3
c)
4n
n 1
5
MAT 272 Test 1 Practice
These problems are not a comprehensive list of all possible problems to be seen on the test. They are
meant as extra practice and reinforcement of the concepts.
2x 4
1.
dx
2
x 1
2.
3x e
dx
2
x 9
4.
sin (2 x) cos (2 x)dx
6.
MAT 272 Final Exam Practice Problems SP16
1. Find the arc length of the graph of y = 2x over the interval [0,1]. Show that the answer agrees
with the formula for the distance between two points.
2. Find the area of the surface formed by revolving the grap
Phyllis Allen
Time (hours)
Amount of yeast (grams)
0
10
5
119
10
513
15
651
Amount of yeast (grams)
700
600
500
Amount of yeast (grams)
400
Amount of yeast (grams)
300
200
100
0
0 5 10 15 20 25 30 35
Time (hours)
My data is in the shape of a curve that re
Wake Technical
Mathematics & Physics Department
Spring
Community College
Mathematics & Sciences Division
2017
Course Syllabus
MAT 121:
Section:
Algebra/Trigonometry I
LECTURE
2
LAB
2
CREDIT
3
Description:
This course provides an integrated approach to tec
Instructions for Student
changed its method of reporting if the method (payments received) used for 2016 is
different from the reporting method used for 2015 (amounts billed). You should be aware
of this change in figuring your education credits.
Box 4. S
In Excel lab 2 we'll start again by putting our name in cell A1.
Wrap text if you need to,
and then changing our view to page layout view.
Now we can get started.
We want to graph functions using Excel.
Our first function as a linear function
and there ar
MAT 121
Checklist for the week of January 19th January 25th
NOTE: Test 1 is scheduled for Tuesday Wednesday, January 31st February 1st next
week. You will take all tests in one of the four testing centers of your choice (on the Western
Wake campus, Main C
Practice 3 Solution
1. Write a query that produces the following for each employee:
<employee name> earns <salary> monthly but wants <3 times salary>. Label the column
Dream Salaries. Sort the rows in descending of Dream Salary.
Example, Ward earns 1250 m
[Silence]
Excel Lab 1 is an introduction to Excel,
before we get started what we need to do is change our view to the page layout view.
This will help you see all the page breaks,
while you are working
so that your graphs and tables don't hang off the pag
It seems some of you are having a little difficulty with the more complicated
conversions. This particular conversion comes off of your review sheet. With
something like this where you're converting something per something to
something else per something
Section 2.6: Continuity
There are two types of continuity:
Type # 1: _
Type # 2: _
Type # 1: _
In other words: f(x) is continuous at a point where x = a if there are no holes, gaps, or jumps in the graph of
f(x) at x = a (you can trace the curve without l
Section 2.2: Definitions of Limits
Quick Review from MAT 171
Using the graph to the left, find
the following:
h(1)
h(2)
h(4)
h(5)
Example: Use the graph of g(x) in the figure to find the
following values or state that they do not exist.
Use the graph of f
Section 2.5: Limits at Infinity
If f(x) become arbitrarily large as x becomes arbitrarily large, when we write:
lim () =
Following limits are defined similarly:
lim () =
lim () =
lim () =
A few helpful rules:
Examples: Determine the following limits
l
Section 2.1: The Idea of Limits
Types of Velocity can sometimes be thought of as _ or _
Type # 1: _
This is velocity that is calculated over an interval of time.
To find average velocity, we use a common formula you learned in MAT 171: _
The position of a
Section 2.3: Techniques for Computing Limits
Law
Linear
Functions
Explanation
For linear functions f(x) = mx +b,
Example
(3 + 8)
2
lim f ( x) f (a) m(a) b
x a
Polynomial
Functions
If p(x) is a polynomial and a is in the domain of p(x), then
lim p( x) p(a
MAT 171 Review: Rational Functions
What is a rational function?
A rational function is a function that can be written in the form _ where P(x) and Q(x)
are _. Also Q(x)0.
Recall from MAT 171, you learned many different characteristics of a rational functi
Unit Conversions with Google
There are many tools available for converting units without having to memorize conversion facts or risk
calculation errors. One of the simplest and most readily available of these tools is Google's converter.
Example: Marty ha
Practice for Test 1 Key
1. 7.5 c
2. a. 49.2 f
c. 37.16 m2
b. 0.5284 gal
d. 2515.31 yd
e. 946.4 mL
f. 804.672 m
3. American Corn
4. 0.02857g/cm3
5. a. 124.7 mg/dose b. 2.494 mL/dose
6. a. 249.43 mg/dose
b. 2.49 mL/dose
7. a. -9
b. -28.1%
10. a. 3/6
11 a. 1
Practice for Test 1
2A, 2B, 12C 3A, 3B, 3E, 7A, 7C
MAT 143
Name _
Basic Conversions
1. A fly spray concentrate is to be mixed at a rate of 3 fl. oz. per quart of water. You wish to make 5
gallons of spray. How many cups of concentrate should you use?
2. C
Buying a New Car: Financing Options Lab
Research:
a)
b)
c)
d)
e)
Vehicle Chosen:
Type of vehicle sought (sedan, motorcycle, SUV, pickup, etc.): Jeep Wrangler
2016
Prioritized list of features with most important listed first. Mark required
features with a
Exercises (Show work for full credit)
1. Determine the vector function that represent the velocity and position of the baseball from
the pitcher to the plate. (25 pts)
We have v i=120,3,4> , s = 40 rps , and c = 0.005 ft /s2
r i ( 60,0,6 ) ft
We know
a s