Mathematics

Discusses important features of the derivative: Differences between average velocity and instantaneous velocity in terms of derivatives; practical applications of the derivative; class test revision example

Basic introduction to the concept of the Derivative: Finding the derivative by first principles/ by the definition; graphing of original function and derivative; how to interpret original function from derivative and vice versa

These lecture notes cover: Revision of first and second derivatives; examples of first and second derivatives; common applications through word problems; graphing of first and second derivatives and how to find one from the other; and linear approximation

Concise introduction to functions: definition of a function; examples of functions; ways of representing functions; sketching graphs of functions graphically; identifying functions using the Vertical Line Test (VLT)

Concise summary for both beginners and intermediate students, covering: Limits - finding the limit of a function by first order principles; finding the limit near a point; and one sided limits; Continuity - definition of continuity; evaluating functions for signs of continuity; Differentiability - determining whether a function is differentiable or not; relationship between differentiability and continuity

Introduction to and revision on Co-Ordinate Geometry: description of distance midpoint formula; definition and formula of straight lines; formula for parallel and perpendicular lines; formula for circles and graphical representations; also includes worked examples for each section

This is a bulk compilation of all the MAM1000W summarised chapters I have uploaded.