Mathematics A Graphical Approach (Intermediate) (updated 6/2022)

An Intuitive Graphical Introduction to Mathematics

What you'll learn

High School Mathematics

Graphs and Functions

Lines and Circles

Trigonometry

Calculus (Differentiation Integration)

Polynomials and Quadratics

Exponential and Logarithmic Functions

Vectors

Differential Equations

Learn in an Intuitive Fun Graphical Way

Requirements

If you are stressing about mathematics then this it not your fault. Let me take the stress and worry about learning mathematics from your shoulders and replace it with CALM FUN LEARNING

Description

Do you want to learn mathematics in an intuitive fun way. Then why not learn mathematics the easy way using simple graphics to introduce all the main concepts before moving onto the equations. We will cover a broad range of introductory topics and it will all be introduced firstly in an intuitive graphical manner to help build up confidence before we start to write down the equations and finally move onto examples. We will use a free online graphical calculator called DESMOS which will allow you to learn  in an intuitive fun graphical way. All the simulations are in the resources section so you can go online to the graphical calculator and recreate everything for yourself.If you are stuck at calculus (integration and differentiation) or with trigonometry then this is a perfect course to really get a great graphical understanding of what is going on. Rather than plug numbers into formulas without knowing what is going on , why not OWN the subject ? You can do this with an Intuitive Graphical Introduction to Mathematics.I have used this graphical approach to tutor students in basic mathematics for many years and have perfected the graphical approach that really adds value to your understanding and MAKES MATHEMATICS MAKE SENSE.Most importantly. You have direct access to me so if you get stuck then get in touch and I will help you out.You won't find another mathematics course like this one !!!

Overview

Section 1: Introduction

Lecture 1 Introduction

Section 2: The Straight Line

Lecture 2 Straight Lines y=x

Lecture 3 Practice Video y = x

Lecture 4 Straight Line y=mx

Lecture 5 Practice Video y=mx

Lecture 6 Equation of a Straight Line (y=mx+c)

Lecture 7 Practice Video y=mx+c

Lecture 8 Drawing Lines

Lecture 9 Straight Line y-b=m(x-a)

Lecture 10 Practice Video y-b=m(x-a)

Lecture 11 Straight Lines 2 Points

Lecture 12 Guess a Line

Lecture 13 Straight Line Perpendicular

Lecture 14 Practice Video Perpendicular

Lecture 15 Triangles and Lines

Lecture 16 Practice Video Triangles and Lines

Lecture 17 Co-linear Lines

Lecture 18 Practice Video Co-linear Lines

Lecture 19 Practice Video Distance Between 2 Points

Lecture 20 Distance Between 2 Points

Lecture 21 General Equation of a Straight Line

Section 3: Graphs and Functions

Lecture 22 Composition of Functions

Lecture 23 Practice Video Composition of Functions

Lecture 24 Manipulating Functions (Intuition)

Lecture 25 Manipulating Functions (Mathematics)

Lecture 26 Practice Video Manipulating Functions

Lecture 27 Inverse of a Function

Lecture 28 Practice Video Inverse Functions

Lecture 29 Composition with Inverse Functions

Lecture 30 Practice Video Composition with Inverse Functions

Section 4: Trigonometry

Lecture 31 What is Trigonometry

Lecture 32 Opposite Adjacent and Hypotenuse (SOHCAHTOA)

Lecture 33 Tangent Function

Lecture 34 Practice Video Tangent Function

Lecture 35 Sine Function

Lecture 36 Practice Video Sine Function

Lecture 37 Cosine Function

Lecture 38 Practice Video Cosine Function

Lecture 39 Trigonometric Functions

Lecture 40 Practice Video Sin Cos Tan

Lecture 41 Inverse Trigonometric Functions

Lecture 42 Practice Video Inverse Trigonometric Functions

Lecture 43 All Sinners Take Care

Lecture 44 Two Angles One Value

Lecture 45 Practice Video Two Values

Lecture 46 Common Angles

Lecture 47 Practice Video Common Angles

Lecture 48 Compound Angles

Lecture 49 Practice Video Compound Angles

Lecture 50 Trigonometric Identities

Lecture 51 Practice Video Trigonometric Identities

Lecture 52 Radians

Lecture 53 Practice Video Radians

Section 5: Differentiation

Lecture 54 What is Differentiation

Lecture 55 Differentiation Intuition

Lecture 56 Finding the Derivative

Lecture 57 Practice Video Finding Derivatives

Lecture 58 Equation of a Tangent

Lecture 59 Practice Video Equation of a Tangent

Lecture 60 Stationary Points

Lecture 61 Practice Video Stationary Points

Lecture 62 Curve Sketching

Lecture 63 Practice Video Curve Sketching

Lecture 64 Optimisation (Intuition)

Lecture 65 Optimisation (Solution)

Lecture 66 Practice Video Optimisation

Lecture 67 Differentiating Trigonometric Functions

Lecture 68 Leibniz Notation

Lecture 69 Practice Video Leibniz Notation

Lecture 70 Practice Your Differentiation

Section 6: Integration

Lecture 71 What is Integration

Lecture 72 Fundamental Theorem of Calculus (Intuition)

Lecture 73 Fundamental Theorem of Calculus (Mathematics)

Lecture 74 Anti Differenetiation

Lecture 75 Definite and Indefinite Integral

Lecture 76 Practice Video Indefinite Integration

Lecture 77 Practice Video Definite Integration

Lecture 78 Area Between Curves

Lecture 79 Practice Video Area Between Curves

Lecture 80 Integrating Trigonometric Functions

Section 7: Polynomials

Lecture 81 What is a Polynomial

Lecture 82 Finding the Value of a Polynomial

Lecture 83 Practice Video Find the Value of a Polynomial

Lecture 84 Synthetic Division

Lecture 85 Practice Video Synthetic Division

Lecture 86 Remainder Theorem

Lecture 87 Practice Video Remainder Theorem

Lecture 88 Factor Theorem

Lecture 89 Practice Video Factor Theorem

Lecture 90 Function from Graph

Lecture 91 Practice Video Function from Graph

Lecture 92 Graph from Function

Lecture 93 Practice Video Graph from Function

Section 8: Quadratic Functions

Lecture 94 Quadratic Functions

Lecture 95 Factorising Quadratics

Lecture 96 Practice Video Factorise Quadratics

Lecture 97 Quadratic Graph from Function

Lecture 98 Practice Video Graph from Function

Lecture 99 Quadratic Function from Graph

Lecture 100 Practice Video Function from Graph

Lecture 101 Completing the Square

Lecture 102 Practice Video Completing the Square

Lecture 103 Quadratic Formula

Lecture 104 Practice Video Quadratic Formula

Lecture 105 The Discriminant

Lecture 106 Practice Video Discriminant

Section 9: The Circle

Lecture 107 Equation of a Circle

Lecture 108 Practice Video 1 Circle

Lecture 109 Practice Video 2 Circle

Section 10: Vectors

Lecture 110 What is a Vector ?

Lecture 111 Addition , Multiplication , Subtraction of a Vector

Lecture 112 Practice Video Vectors Add , Mult , Sub

Lecture 113 Unit Vector and Position Vector

Lecture 114 Practice Video Unit and Position Vectors

Lecture 115 Three Dimensional Vectors

Lecture 116 Practice Video 3 Dimensional Vectors

Lecture 117 Scalar Product (Multiplying Two Vectors)

Lecture 118 Practice Video Scalar Product

Lecture 119 Scalar Product Component Form

Lecture 120 Practice Video Scalar Product Component Form

Lecture 121 Angle Between Vectors

Lecture 122 Practice Video Angle Between Vectors

Lecture 123 Perpendicular Vectors

Lecture 124 Practice Video Perpendicular Vectors

Section 11: Exponential and Logarithmic Functions

Lecture 125 What are Exponential Functions ?

Lecture 126 Exponential Growth and Decay

Lecture 127 What is a Logarithmic Function

Lecture 128 Laws of Logarithms

Lecture 129 Exponential Function to Base e

Lecture 130 Exponential , Logarithms and Data

Section 12: Wave Equation

Lecture 131 Wave Equation

Section 13: Introduction to Differential Equations

Lecture 132 What is a Differential Equation

Section 14: A Journey Into Mathematics and Physics

Lecture 133 Reading Mathematics and Doing Mathematics ?

Lecture 134 Goodbye

Section 15: Video Appendix

Lecture 135 Scalar Product Component Form

High School Students,Those who may be stressed or having a bad mathematics time