as maths c3 coursework

Extracts from this document. C3 Coursework – Numerical SolutionsDecimal SearchThere a numerous ways to solve a problem and in finding the unknown. Some methods give you the exact and precise answer but usually are harder and more complex. The Decimal search method enables you to get a very close approximate to the real solution but more easily. The way this method works is by looking between two numerical values (for example 1 and 2) and then As a demonstration in applying this method, I will be attempting to solve this equation using the Decimal Search method and going through the method step by step:Below is what this function looks when plotted on a graph:We know that the solution for F(x) = 0 is the point on the X axis where the sign changes from a positive to a negative. So if we zoom in a little bit further, from this graph we can tell where the solution lies, somewhere between 0 and 10Now that we know the solution is roughly between these two values, I will use excel to solve the problem with firstly taking increments in x, the size of 1. So when I substitute the incremented values of x between -10 and 0 into the equation, I get the following results:F(x)-13-56-125-226-365-548You can tell that the sign changed between -3 and -4. So I set these as my initial values. The fact that the solution lies between -3 and -4 can also be seen in the graph:So next, I check with increments of 0.1 in x. I again substitute the values in to the equation and tabulate the results and look for where the sign change occurs.
How to complete the Change in Sign domain for the Core 3.
Discussion in 'Mathematics' started by bonusfeature, Nov 25, 2007. Hello, I am doing this coursework and I am a little bit unsure about how to state my error for decimal search. I have established that the root lies between -2.28682 and -2.28683. Do I say that the solution is -2.2868 +/- 0.00005, since that was the root from my previous search that I have now established it is closer to? Or can I say that it is -0.286825 +/- 0.000005, as this will cover all values in my range? Thanks in advance for any help, BF. Hello, I am doing this coursework and I am a little bit unsure about how to state my error for decimal search. I have established that the root lies between -2.28682 and -2.28683. Do I say that the solution is -2.2868 +/- 0.00005, since that was the root from my previous search that I have now established it is closer to? Or can I say that it is -0.286825 +/- 0.000005, as this will cover all values in my range? Thanks in advance for any help, BF. Thanks for that Calum. Can anyone tell me why it isn't -0.286825 +/- 0.000005? Surely that covers all the possible values in my range? We allow our students to use either. In fact, in your case I would say it's more sensible if you're doing the change of sign method to say it's -2.286825 +/- 0.000005 because the method gives you an interval at the end. However, for Newton-Raphson and rearrangement (i.e. the fixed point methods) they tend to converge on an actual value - so for these give them to a certain number of decimal places e.g. 1.05142 to 5dp WARNING: I think you have to give these to at least 5sf but check the coursework guide. NOTE: for the fixed point iterations you must check your result by trying e.g. for the above result: f(1.051415) f(1.051425) One should be positive and one negative, thus confirming your result to the number of decimal places given. Hmm I've written an essay, can you tell I've been.