## Description

Mathematica

Problem Sheet 3

Building Functions

1. Build a function which takes a value x as an argument and gives the value of

a) ex sin(x) b) ln(ex ex)

2. Build a function which takes two values x and y as arguments and gives the

value of a) sin(x2 y2) b) tan1 y

x

Numerical Computation: Sums & Products

1. Find the summation of the following series:

a) 1 23 456…………….100

b) 12 22 32 42 52 62 ……………..n2

c) 1357…………….99

d) 1 ……………… up to

2. Find the summation of the following series:

1(1 2) (1 23) (1 23 4) ………..(1 23…..7) 3. Find the product of the following series:

a) 12 22 32 …..62

b) 2(24)2462468

4. Build a function called FormulaOfSummation[] which takes a number x as an argument and provide the formula to compute the summation of the following series up to n’th term.

1x 2x 3x 4x 5x 6x ……………..nx

Try to find FormulaOfSumation[1], FormulaOfSumation[2] and

FormulaOfSumation[3]

Numerical Computations: Equation Solving

1. Find the solution of the following equations:

a) x2 9x 2 0

b) ax2 bxc 0

c) ax3 bx2 cxd 0

d) x5 16×4 7×3 17×2 11x5 0

e) sincos1x2 x1 2. Solve the equations.

a) 5×2 6y2 9, x y 1

b) x yz 9,x 4y 4,2x3yz 9

3. Solve the equation ln(x) sin(x) 2

A y ln(x) sin(x) 2vs. x graph is plotted above. The x coordinate of the points where the curve cuts the x axis are the roots of the equationln(x) sin(x) 2. We can see there are roots near x = 4, 6, 9, 13 and 15. Find root near x=4

4. Solve the equations: sin(xy) sin xcosy, cos(xy) sin xcosy for x and y The curves representing the two equations are shown below. The thick curve is for the first equation and the thin curve is for the second equation. The coordinates of the point of intersection will be the solutions of the two equations. We can see there is a solution near x=0.6, y= 1.4. Find the approximate solutions.

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