MATLAB by rudra pratap

2.1 Lesson 1: A Minimum MATLAD Session
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EXERCISES
1. Arithmetic operations: Compute the following quantities:
• 2;1 and compare with (1 - .Js )-1.
• 3 (jl;12 - 1. The square root Vx can be calculated with the command
sqrt (x) or x-o . 5.
• Area = 1rr 2 with r = 1r - 1. (1r is pi in MATLAB.)
2. Exponential and logarithms: The mathematical quantities ex, ln x, and
log x are calculated with exp (x) , log (x) , and log10 (x) , respectively. Calculate
the following quantities:
• e3 , ln(e 3), log10(e3), and log10(10 5 ).
• e"VI63.
• Solve 3x = 17 for x and check the result. (The solution is x = 1f,/37
can verify the result by direct substitution.)
. You
3. Trigonometry: The basic MATLAB trigonometric functions are sin, cos ,
tan, cot , sec, and esc. The inverses, e.g., arcsin, arctan, etc., are call:ulated
with as in, a tan, etc. The same is true for hyperbolic functions.
The inverse function atan2 takes two arguments, y and x, and gives the fourquadrant
inverse tangent. The argument of these functions must be in radians.
Calculate the following quantities:
• sin ' cos 1r, and tan ·
• sin 2 + cos 2 · (Typing sin-2(x) for sin 2 x will produce an error).
• y = cosh 2 x -sinh 2 x, with x = 327r.
4. Complex numbers: MATLAB recognizes the letters i and j as the imaginary
number A. A complex number 2 + 5i may be input as 2+5i or 2+5*i
in MATLAB. The former case is always interpreted as a complex number,
whereat; the latter case is taken as complex only if i has not been assigned
auy local value. The same is true for j. This kind of context dependence, for
better or worse, pervades MATLAB. Compute the following quantities:
• i:+:!. Can you check the result by hand calculation?
• c; . Check the Euler's Formula e i x = cos x + i sin x by computing the
right-haml t;iue too, i.e., compute cot>(7r/4) + ·i sin(7r/4).
• Exet.:ule the commands exp (pi/2*i) and exp (pi/2i). Can you explain
the difference between the two results?