1. Symbolic Toolbox
Dr GUNASEKARAN THANGAVEL Lecturer & Program Co-ordinator Electronics & Telecommunication Engineering EEE Section Department of Engineering Higher College of Technology, Muscat.

2. Can other languages do the following?
integrate sin(x) and give –cos(x)+c as the result?
Differentiate sin(x) and give out cos(x)?
Solve a D2y=-a2y and give
y=A sin(ax)+B cos(ax)?
Factorize x^2-3x+2 and give (x-1)(x-2)?

3. Introduction Symbols will be processed instead of numerics.
Mathematical expressions will be manipulated.
Example:
>>syms x
>>s=x^2-3*x+2;
>>factor(s)
Ans: (x-1)*(x-2)

4. Simplification of mathematical expressions
Collect(s) –collects the coefficients of s
>>syms x
>>s=x^2-3*x+2*x+2*x^2+1
>>collect(s)
Ans: 3*x^2-x+1

5. Expand Expand(s)- performs an expansion of s >>syms x
x^2-4*x+4

6. Simple
Simple(s)- simplifies the form of s to a shorter form ,if possible.
>> syms x
>> s= cos(x)^2+sin(x)^2 ;
>> simple(s)
ans = 1

7. Poly2sym
Converts coefficients of the polynomial into symbolic polynomial
>> s=[1 2 3];
>> poly2sym(s)
ans =
x^2+2*x+3

8. sym2poly
Converts symbolic polynomial into coefficients of the polynomial
>> s=x^2+2*x+3;
>> sym2poly(s)
ans =

9. symadd and symsub Performs symbolic addition and symbolic subtraction.
>> syms x
>> s1=1/(1+x);
>> s2=1/(1-x);
>> symadd(s1,s2)
ans =
1/(1+x)+1/(1-x)
>> syms x
>> s1=1/(1+x);
>> s2=1/(1-x);
>> symsub(s1,s2)
ans =
1/(1+x)-1/(1-x)

10. symmul and symdiv Performs symbolic addition and symbolic subtraction.
>> syms x
>> s1=(1+x);
>> s2=(1-x);
>> symmul(s1,s2)
ans =
(1+x)*(1-x)
>> syms x
>> s1=(1+x);
>> s2=(1-x);
>> symdiv(s1,s2)
ans =
(1+x)/(1-x)

11. Equation solving Solve(f)- solves a symbolic expression
>> syms x
>> f='x^2+4*x+4=0';
>> solve(f)
ans =
[ -2]

12. Differential Equation solving
dsolve(‘ differential equation’, initial conditions)
Example:
dsolve('Dx = -a*x') returns
ans = exp(-a*t)*C1

13. Differential Equation solving…
The independent variable of our choice can be included after the initial conditions
y = dsolve('Dy = -a*y',‘y(0) = 1',‘x') returns
y = exp(-a*x)

14. Differentiation .
DIFF(S) differentiates a symbolic expression S with respect to its free variable
DIFF(S,'v') differentiates S with respect to v.
DIFF(S,n), for a positive integer n, differentiates S n times.

15. Examples . >> syms x >> syms x >> s=sin(x);
>> diff(s)
ans =
cos(x)
>> syms x
>> s=x^3;
>> diff(s,2)
ans =
6*x

16. Integration
int(S) is the indefinite integral of S with respect to its symbolic variable
int(S,a,b) is the definite integral of S with respect to its symbolic variable from a to b

17. Examples indefinite integral and definite integral >> syms x
>> int(sin(x))
ans =
-cos(x)
>> syms x
>> int(sin(x),0,2*pi)
ans =

18. User defined function
It is a good practice to create user defined functions if the program requires to perform same operation with different inputs then and there.
In such cases, the operation will be cast into a user defined function.
That should be stored in separate file with filename same as function name.

19. Syndax function z=name(input arguments) operation Example:
function z=add(a,b);
z=a+b;

20. Thank you .

21. You can find… This ppt is available in the following locations
\\ \c\3dplots\symbolictoolbox.ppt
\\ \zs37\matlabworkshop\symbolictoolbox.ppt

22. Excercise 1.Integrate x from 0 to 1 2.Differentiate x^3-5x^2+2x+8
3.Solve the following differential equation D2y(x)=-a^2y(x)
4.Solve x^2+2x+1