Bsc in mechanical engineering Study guides, Class notes & Summaries

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

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