Equation Editor Templates

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MAT 330 In this course, you are expected to show your work for your assignments. To do so, you must show the formulas and equations used. Equation Editor (Equation Tools/Equation Rion! from "icrosoft #\$ce is one free tool you can use. %or tutorials, use the following resour resources& ces& "icrosoft 'ord ))* and )+)& http&//o\$ce.microsoft.com/enus/wor osoft.com/enus/wordhelp/where dhelp/whereisequationeditor isequationeditor http&//o\$ce.micr -))+)00.aspx http&//www http&//www.youtue.com/watch1234 .youtue.com/watch123456en"7s87 56en"7s87 •

"icrosoft for "ac& Insert9#4ect9"icrosoft Insert9#4ect9"icr osoft Equation http&//grok.lsu.edu/article.aspx1articleid3:;) http&//www.dummies.com/howto/c .dummies.com/howto/content/writingandediti ontent/writingandediting ng http&//www equationsino\$ce)++form.html • •

<elow are some premade templates that were created using Equation Editor that you may =nd helpful when completing your homework.

Derivatives: 2

d  y 2 dx

dy dx ' '

y + y + y

Integrals:

∫ f   (( x ) dx

b

∫ f  ( (  xx ) dx a

>i?erential >i?erenti al equations&

 general form& n

n−1

d  y  dy  d  y an ( x ) n  + a ❑n−1 ( x ) n−1  + … + a ❑1 (  xx ) + a ❑0 ( x )  y = F ( x ) dx dx dx

@arious di?erential equations&

dy =e ax dx

ax

y ' = e

2

d  y  dy  + p ( t )  + q ( t ) y =f ( t ) 2 dt  d t

2

x dx + 2  ydy =0

dy =g ( x ) p ( y ) dx

n initial 2alue prolem&

' '

y + A y + Cy = Df ( t )

y ( 0 )= A , y ( 0 )= B '

AewtonBs law of cooling&

dT   = k ( M −T ) dt

"odel for heating/cooling of a uilding&

dT   = K   [[ M   M ( t )−T   (( t ) ] + H  ( ( t ) + U ( t ) dt

 <ernoulli equation& dy + 2 y = x y−2 dx

Exact equations&  M (  xx , y ) dx + N   ((  xx , y ) dy =0 ∂ M  ∂ N   = ∂y ∂x

F (  xx , y )=  M  ( (  xx , y ) dx + g ( y ) ∂ F   = N (  xx , y ) ∂y

F ( x , y )=  N   ((  xx , y ) dy + h ( x )

Cinear =rstorder equations& dy + P ( x ) y =Q ( x ) dx

P ( x ) dx   ( x  x ) =e∫

 (  xx )

dy + P ( x )  ( x ) y =  ( x ) Q ( x ) dx d  x )  [   ( x )  y ]=  (  xx ) Q ( x dx

5opulation models&

dp  = k p , p ( 0 )= p 0 dt

dp  = k 1 p− k 2 p2 , p ( 0 )= p0 dt

AewtonBs laws& !

' '

d"  = F (t , " ) dt  '

! y =−ky − b y + F ext  ext ( t )

%arada aradayCenD yCenD la law& w&  d%   # \$= \$ dt  •

\$

RC circuit&

d%  + &% = # ( t ) , %  ( ( 0 )= % 0 dt

R8 circuit&

&

dq  q  + = # (t ) , q ( 0 )= q0 dt  C

econdorder linear #>E with constant coe\$cients and auxiliary equation with complex roots&

a y + b y + y =0 ( y ( t 0 ) = y 0 y ' ( t 0 )= y 1 ' '

' '

a y + b y + y =0 2

a ) + b) +  = 0 ) 1=* + + ) 2= * −+  y (t )= 1 e

*t

cos

*t  ( t   t )+  e -+nt  2

"iscellaneous equations&

. ( x )=a x + bx 2

∫ h ( y ) dy =∫ g ( x ) dx

dx =∫ e ∫ dy dx

ax

dy =−2 dx  y −1

dy =−2 dx  y −1

# &= &%

1

#C =  q C

dx

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