This is a practice exam for the differential equations FLOT Mathematics. Can also be used for courses with differential equations. Approved by a teacher on FLOT Mathematics.
Contains:
Assignment on Newton's Cooling Law
Assignment differential field command
Assignment on Euler's Method
Assi...
Maths 214 Advanced Calculus notes for A1 (2024)
Instructors solutions
All for this textbook (6)
Written for
Differential Equations
All documents for this subject (31)
Seller
Follow
robintonjes
Content preview
Differential equations
Oefententamen
Formulas to be used:
( )
dP P (t ) K K −P0
=k∗P ( t )∗ 1− ⇒ P ( t )= with A=
dt K 1+ A∗e
−kt P0
Assignment 1
You microwaved a warm bowl of soup. After removing the bowl from the microwave, it has a
temperature of 80 degrees Celsius. Let the bowl cool for 15 minutes and then measure the
temperature again. The temperature of the bowl after fifteen minutes is 67 degrees Celsius. The
temperature of the outside environment is 21 degrees Celsius. The differential equation of the
dT
cooling process is is =k (T omgeving −T ). T is in degrees Celsius and t is in minutes
dt
1. Show that
ln ( 4659 ) t is a solution to this differential equation.
T ( t )=59 e 15
+21
2. Calculate how long it takes till the temperature drops to 37 degrees Celsius.
, Assignment 2
In the pictures on the right you see a
directional field with the differential equation
. y ' ( x )=−xy+ x
1. On the worksheet, draw a solution
with the condition y ( 0 )=4 .
2. Solve the differential equation with
the condition y ( 0 )=0.
3. Calculate y (1) using Euler's method.
The initial condition is . y ( 0 )=0 Take
as step-sized Δ h=0,5 .
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller robintonjes. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R68,64. You're not tied to anything after your purchase.