University of London - B.Sc. Management Maths Notes

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MT105a Study Notes – J.Fenech

Chapter 1/2 – Basics
1. Basic notations 1.1. Sum of: ∑ 1.2. Product of: ∏ 2. Sets       A = {1,2,3} describes the set A containing members 1, 2, and 3. A={n | n is a whole number and 1≤n≤3} x  A denotes that x is a member of set A S  T denotes that S is a subset of T A  B is the set whose members belong to either set A, set B or both i.e. A  B = {x | x  A or x  B} A  B is the intersection of 2 sets where A  B = {x | x  A and x  B}  denotes an empty set

3. Functions Given two sets A and B, a function from A to B is a rule which assigns to each member of A precisely one member of B.

A function is a one-way relationship: the function number, (x).

takes a number x as input and it returns another

An inverse function takes as input a number y and returns the number x such that ( ) ( ) Not all functions have an inverse. Ex.  ( ) A composite function is one where two functions that; ( ) ( ( )) 4. Powers Rules ( )

is given by

are applied consecutively to obtain h such

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MT105a Study Notes – J.Fenech

Chapter 3 – Differentiation
1. Definition The derivative is a measure of the instantaneous rate of change of a function 1.1. Derivative from first principles ( ) ( )

1.2. Alternative notation ( ) 1.3. Standard Derivatives Table

2. Differentiation Rules 2.1. Sum Rule ( ) ( ) ( ) ( ) ( ) ( )

2.2. Product Rule

( )

( ) ( )

( )

( ) ( )

( ) ( )

2.3. Quotient Rule ( )

( ) ( )

( )

[ ( ) ( ) ( ) ( )] ( )

2.4. Chain Rule or Composite function rule ( ) ( ( )) ( ) ( ( )) ( )

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MT105a Study Notes – J.Fenech 3. Differentiation by taking logarithms 4. Local Maxima and Minima Derivatives are very useful for finding the maximum and minimum values of a function In particular;  If ’(x) > 0 then is increasing at x  If ’(x) < 0 then is decreasing at x 4.1. First derivative test At a point c for which ’(c) =0, is neither increasing nor decreasing. C is the...
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