Problems

Exercise 1

Generate a list of square numbers from 1 to 100, use the “/@” construction. Replace the head of the list to obtain the sum of squares.

Exercise 2

Construct a 4 x 4 Vandermonde matrix and obtain its determinant.

Exercise 3

Expand (1 + a + ((x))^10), collect in terms of x and Simplify each coefficient.

Exercise 4

Generate the sum (∑_(i=1)^5)((Subscript[a, i])/(Subscript[b, i])) and make it have a common denominator.

Problem 1

Define a function “MyLog” which works as follows:

MyLog[a b c 5] = MyLog[a] + MyLog[b] + MyLog[c] + MyLog[5] +

Problem 2

Define a function which computes the mean of a list

Problem 3

Implement a function “FirstAndLast”, which returns the first and last element of the input.

Problem 4

Expand (1 + a + ((x))^10) and produce a list of terms with only odd powers of x.

Problem 5

Do a series expansion of the exponential function up to the third order and plot it against the real function.

Problem 6

Plot a 3d parabola.

Problem 7

Plot the real and imaginary parts of (Sqrt[(x^2)-1]) on the complex plane. Make sure that it has only 1 cut going from -1 to 1.

Problem 8

Use only patterns to transform 
		M, a, p, {}, l, e, S, {y, {r}}, u, p 
to 
			M, a, p, l, e, S, y, r, u, p.

Problem 9

Define a function that symmetrises the arguments.

Problem 10

Write a function that deletes duplicates in a list.

Problem 11

Write a function to sort a list.

Problem 12

Write a function to implement the function Riffle.

Problem 13

Implement Sum though recursion.

Problem 14

Implement a function “ExtractKth[erpr,k]” which will keep every kth element of a structure.

Problem 15

Given a list of functions, find the multiplier in the power x of any terms at any level.