MATLAB by rudra pratap

50 Tutorial Lessons
EXERCISES
1. Some basic symbolic manipulations: Define the following function symbolically
f(x) = (x2 - 4x)(x2 - 4x + 1) - 20.
(a) Expand f(x) using expand.
(b) Show that (x2 - 4x + 4) is a factor of f by dividing f with this factor.
(c) Factorize f using the symbolic function factorize and verify the factor
you used in (b).
(d) Find the roots of one of the two factors. (Hint: Take one of the factors
as an expression and use solve to find two roots x1 and x 2 ).
(e) Substitute one of the roots for x, say x =
x1, in f and simplify the
expression to show that j(x1) = 0.
2. Computation with symbolic vectors: Define r = [x yjT where x and y
are declared as real variables. Compute
(a) rrT (the outer product of r) .
(b) J0 1 rrT dx.
(c) f0 1 f0 1 rrT dxdy.
(d) Determinant of J; J0 1 rrT dxdy.
3. Solving simultaneous linear equations: Solve the following set of simultaneous
linear algebraic equations.
X+ 3y - Z 2
x-y+z 3
3x - 5y 4.
4. Solving simultaneous linear equations: Solve the following nonlinear
algebraic equations simultaneously.
3x 3 + x 2 - 1 0
x4 - 10x 2 + 2 0.
5. Integrals: Find the following integrals:
(i) 100 e-xdx, (ii) 100 e-x2 dx , and (iii) lxo e-x2 sin(x)dx.
6. Solving differential equations: Use function dsolve to solve the following
differential equations along with the given initial conditions.
(a) + x2 = 0, x(O) = xo.
(b) + w2y = 0, y(O) = Yo and (0) =
Vo .
[First, use on-line help on dsol ve to see how to enter the differential equation
and the initial conditions as input to the function. Please note that this
function requires the differential operator ft to be denoted by D. Therefore,
the first differential equation will be written as Dx + x-2 = 0].