Mathematics (MAM1005H)

85% PASS

For every natural number n we define n-dimensional space as the set Rn of all ordered n-tuples x1 x2  xn where xi  R for i  1 2  n. One-dimensional space R1 corresponds with the set of real numbers R. For n  2 we usually denote the ordered n-tuple x1 x2     xn by x, the ordered n-tuple a1 a2     an by a, and so on. If x  x1 x2  xn, we say that xi is the i’th coor...

This unit contains a brief summary of concepts, definitions, notation, and results that you are assumed to be familiar with SETS RELATIONS AND FUNCTIONS

THESE ARE THE RULES FOR CALCULUS DIFFERENTIATION

Providing worked examples of inequalities; introduction to absolute values; relationship between absolute values and inequalities; sketching inequalities and absolute values (graphical representation)

Introduction to Inverse Functions: Discussion of exponential and logarithmic functions as examples of inverse functions; using Vertical Line Test to check if functions are one-to-one or one-to-many; strategy for finding the inverse function; sketching of inverse functions

Introducing the concept of shifting functions to produce new functions (new from old); how to shift functions; graphical and algebraic representations; combinations of functions algebraically and graphically; compositions of functions and examples

Compares the derivative at a point with that of the derivative over a distance; provides the definition of the derivative (the formula for finding the derivative of any function; provides graphical examples illustrating the derivative at a point and the derivative over a distance; provides and works through in-depth examples of finding derivative using first pricniples