Published 2/2023MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHzLanguage: English | Size: 8.33 GB | Duration: 7h 1m

Get the basics RIGHT on Functions, Operations with Functions and Inverses

What you'll learn

You'll be able to translate the concept of function and its properties to different points of view: Relations, procedures, diagram, tables and graphs.

You'll be able to understand what are 1-1, onto and bijective functions logically and intuitively.

See change of variables and function transformation under the light of functions composition and image of sets.

Get a solid foundation of function Inverses.

What is a square root? We'll see in detail using the notion of inverse.

Requirements

A basic knowledge of functions at the high-school level is mandatory.

Having college calculus under your belt will bring the greatest benefits.

Description

After 5 years of tutoring high-school and college students in all sort of classes in Mathematics and Physics I realized the many missing fundamental concepts these students lack and what they struggle with. As a result I created a lecture series to address all those issues. This is Part I of that lecture serie and is related with Functions.I cover the traditional topics in the subject of functions, here are some of the issues we'll address:What are functions? We'll give different points of view such as relations, procedures.Functions viewed as labelers will motivate the notions of 1-1, onto or bijective functions.What operations can be made with functions? Sum, multiplication, division, composition, restriction. We'll see these in detail. These are very simples but they contain many important concepts in mathematics, we will find them.Use composition of functions as a means to understand change of variables, moreover when combined with image of sets, allow us to better understand function transformations. This is one of the subjects that students have more difficulties, both high-school and college. It is now that you'll make sense of them.What is the inverse function? This is intimately connected with bijective functions. And what about those that are not bijective, what should we do? We'll discuss in detail examples of both.Together with this lecture videos you'll find a pdf file. The videos complement the sections of the pdf, which also has the exercises with solutions. On the title of each video you find the corresponding section of the pdf.

Overview

Section 1: Functions

Lecture 1 Introduction

Lecture 2 Functions as Special Relations (Sec 1.1)

Lecture 3 Example 1 of Functions (Sec 1.1.1 )

Lecture 4 Example 2 of Functions (Sec 1.1.1)

Lecture 5 Commentary on Functions (Sec 1.1.1)

Lecture 6 Four Representations of a Function (Sec 1.1.2)

Lecture 7 Seeing Functions as Procedures (Sec 1.2)

Lecture 8 Example 1 of Procedures (Sec 1.2.1)

Lecture 9 Example 2 of Procedures (Sec 1.2.1)

Lecture 10 Procedures vs Relations (Sec 1.3)

Lecture 11 1-1 vs onto vs bijective Functions (Sec 1.4.1)

Lecture 12 Image of a Set (Sec 1.4.2)

Lecture 13 More Examples of Images of a Set (Sec 1.4.2)

Lecture 14 Preimage of a Set (Sec 1.4.3)

Lecture 15 Examples of Preimages (Sec 1.4.3)

Section 2: Operations with Functions

Lecture 16 Introduction

Lecture 17 Defining Operations Between two Functions (Sec 2.1.1)

Lecture 18 Chag Notation (Sec 2.1.2)

Lecture 19 Domain of the New Functions (Sec 2.1.3)

Lecture 20 What is the Composition of Functions? (Sec 2.2)

Lecture 21 Examples of Compositions (Sec 2.2)

Lecture 22 More Examples of Domain of Composite Functions (Sec 2.2)

Lecture 23 Restrictions of a Function (Sec 2.3)

Lecture 24 Examples of Restrictions (Sec 2.3)

Lecture 25 What is Function Decomposition (Sec 2.4.1)

Lecture 26 What is a Functions Transformation (Sec 2.4.2)

Lecture 27 Example of Horizontal Compression (Sec 2.4.2)

Lecture 28 Horizontal Compression Animation (Sec 2.4.2)

Lecture 29 Horizontal Shift (Sec 2.4.2)

Lecture 30 Horizontal Shift Animation (Sec 2.4.2)

Section 3: Inverse Functions

Lecture 31 Introduction

Lecture 32 Inverse Definition (Sec 3.1)

Lecture 33 Inverse Procedure (Sec 3.1.1)

Lecture 34 Inverse Procedure Analysis (Sec 3.1.1)

Lecture 35 Inverse Function of a Linear Functions (Sec 3.2.1)

Lecture 36 Analysis of the Inverse Procedure (Sec 3.2.2)

Lecture 37 Inverse of the x^3 (Sec 3.2.3)

Lecture 38 Inverses of non-bijective Functions (Sec 3.3.1)

Lecture 39 Inverse of x^2 (Sec 3.3.2)

Lecture 40 Inverse of x^n (Sec 3.4)

Lecture 41 First Property - Part I (Sec 3.4.1)

Lecture 42 First Property - Part II (Sec 3.4.1)

Lecture 43 First Property - Part III (Sec 3.4.1)

Lecture 44 Second Property - Part I (Sec 3.4.1)

Lecture 45 Second Property - Part II (Sec 3.4.1)

Lecture 46 Third Property (Sec 3.4.1)

Lecture 47 Discussion of the Three Properties - Part I (Sec 3.4.2)

Lecture 48 Discussion of the Three Properties - Part II (Sec 3.4.2)

Lecture 49 Discussion of the Three Properties - Part III (Sec 3.4.2)

Lecture 50 Rational Powers (Sec 3.4.3)

College students taking Calculus or Analysis.,Adults which within their profession or retired need or wish to review this material from a mature and yet simple approach.,High-school students who are hungry from more and for answers. You'll find them here.

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