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Engr 0012 (04-1) LecNotes 15-01

Declaring/using a function for evaluation. String Function. Inline Function. m-file Function. Declaration. Declaration. Declaration. str = ' 2* x +2 '; fcn = inline( str); negf = inline[' -( ',str,' ) ' ];. fcn = ' 2* x +2 '; negf = [' -( ',fcn,' ) ' ];. function [y] = fcn(x)

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Engr 0012 (04-1) LecNotes 15-01

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  1. Declaring/using a function for evaluation String Function Inline Function m-file Function Declaration Declaration Declaration str = '2*x+2'; fcn = inline(str); negf = inline['-(',str,')' ]; fcn = '2*x+2'; negf = ['-(',fcn,')' ]; function [y] = fcn(x) y = 2*x+2; function [y] = negf(x) y = -fcn(x); Calculating “y-values” Calculating “y-values” Calculating “y-values” xvec = linspace(-5,5,8); yvec = feval(fcn,xvec); xvec = linspace(-5,5,8); yvec = feval(fcn,xvec); x = linspace(-5,5,8); y = eval(fcn,x); Displaying function - any declartion domain = [-10 10]; fplot(fcn,domain); Finding roots - any declaration xroot = fzero(fcn,where); Engr 0012 (04-1) LecNotes 15-01

  2. Declaring/using a function for evaluation String Function m-file Function Inline Function Finding minima Finding area between (lb,ub) - any declaration Finding minima Finding maxima Finding maxima Finding minima Finding maxima xmax = fminbnd(negf,lb,ub); ymax = feval(fcn,xmax); xmin = fminbnd(fcn,lb,ub); ymin = feval(fcn,xmin); xmax = fminbnd(negf,lb,ub); ymax = feval(fcn,xmax); xmin = fminbnd(fcn,lb,ub); ymin = feval(fcn,xmin); area = quad(fcn,lb,ub); or area = quadl(fcn,lb,ub); xmax = fminbnd(negf,lb,ub); x = xmax; ymax = eval(fcn,x); xmin = fminbnd(fcn,lb,ub); x = xmin; ymin = eval(fcn,x); Engr 0012 (04-1) LecNotes 15-02

  3. Declaring/using a function for evaluation String Function m-file Function Inline Function Finding area - traps Plotting cumulative area - any declaration Finding area - traps Finding area - traps ntraps = 100; xtrap = lb:(ub-lb)/ntraps:ub; x = xtrap; ytrap = eval(fcn,x); area = trapz(xtrap,ytrap); % calc cumarea from xmin to xpt xpts = xmin:(xmax-xmin)/500:xmax; for i = 1:1:length(xpts) cumarea(i) = quad(fcn,xpts(1),xpts(i)); end % plot cumulative area hold on plot(xpts,cumarea,'g-') ntraps = 100; xtrap = lb:(ub-lb)/ntraps:ub; ytrap = feval(fcn,xtrap); area = trapz(xtrap,ytrap); ntraps = 100; xtrap = lb:(ub-lb)/ntraps:ub; ytrap = feval(fcn,xtrap); area = trapz(xtrap,ytrap); Engr 0012 (04-1) LecNotes 15-03

  4. Calculating a derivative forward difference backward difference central difference definition of derivative approximations of the derivative - for small x Engr 0012 (04-1) LecNotes 15-04

  5. Calculating a derivative implementation in MATLAB specify x evaluate function at x+x evaluate function at x-x estimate derivative Engr 0012 (04-1) LecNotes 15-05

  6. Declaring/using a function for evaluation Inline Function String Function m-file Function Plotting derivative Plotting derivative Finding derivative at xpt Finding derivative at xpt Finding derivative at xpt Plotting derivative delx = (xmax-xmin)/10000; fx_p = feval(fcn,xpt+delx); fx_m = feval(fcn,xpt-delx); der = (fx_p-fx_m)/(2*delx); % calc derivative at xpts xpts = xmin:(xmax-xmin)/ 500:xmax; fx_p=feval(fcn,xpts+delx); fx_m=feval(fcn,xpts-delx); der =(fx_p-fx_m)/(2*delx); % plot derivative hold on plot(xpts,der,'b--') % calc derivative at xpts xpts = xmin:(xmax-xmin)/ 500:xmax; x = xpts+delx; fx_p = eval(fcn,x); x = xpts-delx; fx_m = eval(fcn,x); der =(fx_p-fx_m)/(2*delx); % plot derivative hold on plot(xpts,der,'b--') % calc derivative at xpts xpts = xmin:(xmax-xmin)/ 500:xmax; fx_p=feval(fcn,xpts+delx); fx_m=feval(fcn,xpts-delx); der =(fx_p-fx_m)/(2*delx); % plot derivative hold on plot(xpts,der,'b--') delx = (xmax-xmin)/10000; fx_p = feval(fcn,xpt+delx); fx_m = feval(fcn,xpt-delx); der = (fx_p-fx_m)/(2*delx); delx = (xmax-xmin)/10000; x = xpt+delx; fx_p = eval(fcn,x); x = xpt-delx; fx_m = eval(fcn,x); der = (fx_p-fx_m)/(2*delx); Engr 0012 (04-1) LecNotes 15-06

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