EXERCISE 1 An operator is a mathematical instruction to carry out some operation on a function, such as a multiplication or a differentiation. Operators will be denoted by the symbol ^, or A^,B^, when referring to a series of operators. Examples of simple operators are the multiplication by x,^=x, or the differentiation with respect to x,^=d/dx. An operator ^ acting on a function f gives another function f : f=f Let us now consider the a function h that is the linear combination of the functions f and g : h=af+bg where a and b are two constants. If the following relationship is satisfied ^h=h=a^f+b^g then ^ is a linear operator. (1) Consider the following operations and show which one is a linear operation and which is a non-linear operation. Justify your answer. a) dxd b) xdxd c) Integration