Problem 1: = y Sm[xj Note that if you want to generate the plcture's solutlon curve, you can use DSolve With an mitlal
condition of, say y(0):1."3
Ij3'3'1«"e|:{1f"[x]== -Y[x] ~Sin[x]: Y[01== 1/3}: x]. x]
Hype] > 2e (1+3 ex Cos{x} m3ex SinEx1)}}
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1.4: Separable Equations and Applications
Basic Definitions
The first order differential equation
Recall: If y
dy
dx
H x, y is called separable if H x, y
f x , then the differential of y is dy
f' x
dy
dx
gx hy.
f ' x dx, so we can represent the derivative
1.3: Slope Fields and Solution Curves
Basic Definitions
Consider the differential equation
dy
f x, y . This represents the slope through the point (x, y).
dx
A direction (or slope) field is generated by drawing a short line segment through each point (x,
1.2: Integrals as General and Particular Solutions
Basic Definitions
Consider a first order differential equation,
The general solution is y x
fx
x
dy
dx
f x where the right hand side does not depend upon y x .
C where C is some constant.
dy
For the first
1.1: Differential Equations and Mathematical Models
Basic Definitions
An ordinary differential equation is an equation that relates an unknown function, one independent variable, and one or more of
the functions derivatives.
A partial differential equatio
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Math 306 Test 2
Printed Name:
H indicates a By Hand problem where technology is not allowed. One exception is the
Apart command which may be used at any time.
T indicates a Technology problem where you: use Mathematica or a calculator. You
may
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Math 306 Test 1
Printed Name:
Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit!
This test has a total of 150 points.
H indicates a By Hand problem where technology is not allowed. One exception is the A
Math 306 Lab 1 Eulers Method
Printed Name:
Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit!
This lab will investigate Eulers Method for approximating the solutions to dierential equations. As an example
Dierential Equations
Class:
Instructor:
Oce Hours:
MATH 306 010
1:00 PM 2:15 PM, TR
Keith E. Emmert
MWF: 1:30 2:30 PM
TR: 2:30 3:30 PM
or by appointment
Class Room:
Math 208
Oce:
Web Page:
Email:
Phone:
Math Room 330
http:/faculty.tarleton.edu/Emmert
emme
Math 306 Test 3
Printed Name:
Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit!
The Printed Name question is worth 5 points.
H indicates a By Hand problem where technology is not allowed.
T indicates a
Math 306 Test 2
Printed Name:
Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit!
The Printed Name question is worth 5 points.
H indicates a By Hand problem where technology is not allowed.
T indicates a
Math 306 Test 1
Printed Name:
Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit!
The Printed Name question is worth 5 points.
H indicates a By Hand problem where technology is not allowed.
T indicates a
Dierential Equations
Class:
Instructor:
Oce:
Oce Hours:
MATH 306 010
1:00 PM 1:50 PM, MWF
Keith E. Emmert
Math Room 330
MWF: 10:00 - 10:50 AM, 2:00 - 3:00 PM
or by appointment
Class Room:
Math 209
Web Page:
Email:
Phone:
www.math.tarleton.edu/Faculty/Emme