You are Here: Home >< Maths

# Trouble With Partial Differentiation Watch

1. I am stuck with the start of this question:

The water table height in the region between two rivers equilibrates over a long time to the water level in the rivers. The axis OX measures the lateral distance between the two rivers, with x = 0 corresponding to the left river and x = L corresponding to the right river. The water table height at position x at time t is given by h(x, t), measured with respect to ground level. The water table
height obeys a diusion-like equation:

dh/dt = k(d^2*h)/(d*x^2) (The d is actually the partial squiggly d thing)

The river level was initially -H, however this changes instantaneously to a level of h(0; t) = h(L; t) = 0.

How do I find the initial conditions h(x,0)? (and in terms of a Fourier sine series?)

I'm stuck as the next part talks about seperating the variables to find h(x,t), does this mean I do not seperate variables in the first part? If so, what is the method for that? And how does that affect the second part?

Annoying as after these parts the majority of the question is routine

Thanks

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 20, 2010
Today on TSR

### Oxford grad sues for £1m

Claims damages because he didn't get a first

### 'No evidence of shots fired' at Oxford Circus

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.