% In class 19-Feb-2008 clear, clc, home fprintf('The date and time: %s \n', datestr(now))
The date and time: 19-Feb-2008 13:33:09
% Techniques by which math problems are formulated and solved on a computer. % % Engineers apply numirical methods in cases that involve for example: % Lare systems of equations % Non-linearities % Complicated Geometries % non-analytic solutions avaliable % Graphical solutions % In all of these cases algorithms must be generated. % % Steps in solving these types of problems in 4 steps % 1) State problem clearly % 2) Develope a mathematical model % 3) Solve equations which result as a consequence of 2) % 4) Carefully interpret the numerical results in 3) % % If an algorithm fails; it may be due to errors. % Tpes of errors: % Human errors: syntax errors. % ex: typing sine instead of sin % Hint: type exist to see if function exist. exist('fuction') % Run-time errors: Logic errors. % ex: tpe a > b instead of b > a % Approximations errors 3 types % 1. Machine Precision % controled by matchines % 2. Round off errors % controled by matchines % ex: 1.234567 round to 3 decimals 1.235 % 3. Truncation errors % dropping the last terms in the Talior series expantion % % To illistrate the acceptance of errors we consider the terms: % 1) Absolute error = Teacher: below *100 % |(True value) - (Calculated vaue)| % 2) Relative error = Teacher: below w/out *100 % (Absolute error)/(True value)*100 % % Read for Thursday Ch.5 and Ch.8
% Purpose: to demonstate Symbolic Opporations. syms x b % declare variables x and b symbolic y = x^2 intigrate_x = int(x) intigrate_y = int(y) disp('Pretty form of the above') pretty(int(x)) pretty(int(y)) diff(sin(x^2)) % The version of Matlab we are using can't do partial differentiation. [x,y] = solve('x^2 + x*y + y = 3','x^2 - 4*x + 3 = 0') % this program converst the strings to numbers, solves the system % using gaussian elimination, then returns the answers in symbolic form.
y =
x^2
intigrate_x =
1/2*x^2
intigrate_y =
1/3*x^3
Pretty form of the above
2
1/2 x
3
1/3 x
ans =
2*cos(x^2)*x
x =
1
3
y =
1
-3/2