Course  Materials


MATLAB Handouts
0 Syllabus of textbook Zill.

1. MATLAB handout on Graphs and Functions(SPENNELL).

2. MATLAB Handout on Symbolic Capabilities(SPENNELL).

3. solve y'+py=q by linode1 and by dsolve.

31. solve y'+py=q problems are in a file for p and q.

4. Exact equations the Long method of solution Mdx+Ndy=0.

5. Solve Bernoulli y'+p y =q y^(n).

6. a y''+b y'+c y = 0 ; y=linode20(a,b,c).

7. Reduction of order y''+py'+qy=0. y1 is a solution Find y2=ROO(p,q,y1).

8. a y''+b y'+c y = q1(x); variation is used in y=linode22(a,b,c,q1).

9a. ax^2 y''+bxy'+c y = q1(x); Variation is used in yy=cauchy_euler(a,b,c,q1).

9b. ax^2 y''+aplusb xy'+c y = q1(x); Variation is used in yy=aplusb_cauchy_euler(a,aplusb,c,q1).

10. Variation and reduction of order:Find y2 and yp of y''+py'+qy=r. y=varROO(p,q,r,y1).

11. yp=u y1+v y2 . Method of Variation of parameters y''+py'+qy=r. yy=variation(p,q,r,y1,y2).

12a. 3rd order Method of Variation of parameters y''' + p1 y'' + p2 y' + p3 y = r. yy=var3(y1,y2,y3,r,x).

12b. 4th order Method of Variation of parameters y''''+p1y'''+p2y''+p3y'+p4y=r. yy=var4(y1,y2,y3,y4,r,x).

12c. Nth order Method of Variation of parameters D^n y +p1 D^(n-1) y+...+qy=r. yy=varvec(y,r,x).

13.a Laplace transform of ay''+by'+cy=q1. y(0)=y0,y'(0)=yprime0 y=lapode22(a,b,c,q1,y0,yprime0).

13b. Volterra integral equation solved by Laplace transform .y = g + koy

14. Numerical Euler method to print and plot y versus t of y'=f(t,y) with y(a)=ya.R=Euler11{'f',a,b,ya,M)

15. Numerical Euler method to print compare and plot y versus t of y'=f(t,y) with y(a)=ya. R=Euler22{'f',a,b,ya,M)

16. Numerical RK4-Euler-EXACT sample problem plot comparison. y'=f(t,y) with y(a)=ya. R=n2rk4{'f',a,b,ya,M)
17. SYSTEMS+2nd ORDER). RK4-IVP y'=f(t,x,y) x'=g(t,x,y) with y(a)=ya. x(a)=xa R=rk42IVP{'f','g',a,b,xa,ya,M)
18. SYSTEMS+2nd ORDER). RK4-IVP y'=f(t,x,y'') with y(a)=ya. y'(a)=xa R=rks4{f,a,b,Za,M)
19. SYSTEMS+2nd ORDER). BVp rks. for y'=f(t,x,y'') with y(a)=ya. y(b)=yb L=Linsht{f1,f2,a,b,Za,M)
20. sample excercises on cauchy euler.
21. sample excercises on volterra + laplace transform
Copyright ©1998 Beverly J. Volicer and Steven F. Tello, UMass Lowell.  You may freely edit these pages for use in a non-profit, educational setting.  Please include this copyright notice on all pages.