Published 5/2024
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 7.15 GB | Duration: 20h 4m

From Beginner to Expert - Calculus Made Easy, Fun and Beautiful

What you'll learn
Differentiation
Integration
Differential Equations
Optimization
Chain Rule, Product Rule, Quotient Rule
Limits
Maclaurin and Taylor Series

Requirements
A good basic foundation in algebra.
Knowledge of trigonometry useful but not essential
Knowledge of exponentials and logarithms useful but not essential

Description
This is course designed to take you from beginner to expert in calculus. It is designed to be fun, hands on and full of examples and explanations. It is suitable for anyone who wants to learn calculus in a rigorous yet intuitive and enjoyable way.The concepts covered in the course lie at the heart of other disciples, like machine learning, data science, engineering, physics, financial analysis and more.Videos packed with worked examples and explanations so you never get lost, and many of the topics covered are implemented in Geogebra, a free graphing software package.Key concepts taught in the course areifferentiation Key Skills: learn what it is, and how to use it to find gradients, maximum and minimum points, and solve optimisation problems.Integration Key Skills: learn what it is, and how to use it to find areas under and between curves.Methods in Differentiation: The Chain Rule, Product Rule, Quotient Rule and more.Methods in Integration: Integration by substitution, by parts, and many more advanced techniques.Applications of Differentiation: L'Hopital's rule, Newton's method, Maclaurin and Taylor series.Applications in Integration: Volumes of revolution, surface areas and arc lengths.Alternative Coordinate Systems: parametric equations and polar curves.1st Order Differential Equations: learn a range of techniques, including separation of variables and integrating factors.2nd Order Differential Equations: learn how to solve homogeneous and non-homogeneous differential equations as well as coupled and reducible differential equations.Much, much more!The course requires a solid understanding of algebra. In order to progress past the first few chapters, an understanding of trigonometry, exponentials and logarithms is useful, though I give a brief introduction to each.Please note: This course is not linked to the US syllabus Calc 1, Calc 2 & Calc 3 courses, and not designed to prepare you specifically for these. The course will be helpful for students working towards these, but that's not the aim of this course.

Overview
Section 1: Introduction
Lecture 1 Introduction
Lecture 2 What's in the Course?
Section 2: Introduction to Calculus
Lecture 3 What is Calculus
Lecture 4 Intuitive Limits
Lecture 5 Terminology
Lecture 6 The Derivative of a Polynomial at a Point
Lecture 7 The Derivative of a Polynomial in General
Lecture 8 The Derivative of x^n
Lecture 9 The Derivative of x^n - Proof
Lecture 10 Negative and Fractional Powers
Lecture 11 Getting Started with Geogebra
Section 3: Differentiation - Key Skills
Lecture 12 Finding the Gradient at a Point
Lecture 13 Tangents
Lecture 14 Normals
Lecture 15 Stationary Points
Lecture 16 Increasing and Decreasing Functions
Lecture 17 Second Derivatives
Lecture 18 Optimisation - Part 1
Lecture 19 Optimisation - Part 2
Section 4: Integration - Key Skills
Lecture 20 Reverse Differentiation
Lecture 21 Families of Functions
Lecture 22 Finding Functions
Lecture 23 Integral Notation
Lecture 24 Integration as Area - An Intuitive Approach
Lecture 25 Integration as Area - An Algebraic Proof
Lecture 26 Areas Under Curves - Part 1
Lecture 27 Areas Under Curves - Part 2
Lecture 28 Areas Under the X-Axis
Lecture 29 Areas Between Functions
Section 5: Applications of Calculus
Lecture 30 Motion
Lecture 31 Probability
Section 6: Calculus with Chains of Polynomials
Lecture 32 f(x)^n - Spotting a Pattern
Lecture 33 Differentiating f(x)^n - An Algebraic Proof
Lecture 34 The Chain Rule for f(x)^n
Lecture 35 Using the Chain Rule for f(x)^n
Lecture 36 Reverse Chain Rule for f(x)^n
Lecture 37 Reverse Chain Rule for f(x)^n - Definite Integrals
Section 7: Calculus with Exponentials and Logarithms
Lecture 38 Introduction to Exponentials
Lecture 39 Introduction to Logarithms
Lecture 40 THE Exponential Function
Lecture 41 Differentiating Exponentials
Lecture 42 Differentiating Chains of Exponentials - Part 1
Lecture 43 Differentiating Chains of Exponentials - Part 2
Lecture 44 The Natural Log and its Derivative
Lecture 45 Differentiating Chains of Logarithms
Lecture 46 Reverse Chain Rule for Exponentials
Lecture 47 Reverse Chain Rule for Logarithms
Section 8: Calculus with Trigonometric Functions
Lecture 48 Radians
Lecture 49 Small Angle Approximations
Lecture 50 Differentiating Sin(x) and Cos(x)
Lecture 51 OPTIONAL - Proof of the Addition Formulae
Lecture 52 Differentiating Chains of Sin(x) and Cos(x)
Lecture 53 Reverse Chain Rule for Trig Functions
Lecture 54 Integrating Powers of Sin(x) and Cos(x)
Section 9: Advanced Techniques in Differentiation
Lecture 55 The Chain Rule
Lecture 56 The Product Rule - An Intuitive Approach
Lecture 57 Using the Product Rule
Lecture 58 Algebraic Proof of the Product Rule
Lecture 59 The Quotient Rule
Lecture 60 Derivatives of All Six Trigonometric Functions
Lecture 61 Implicit Differentiation
Lecture 62 Stationary and Critical Points
Section 10: Advanced Techniques is Integration
Lecture 63 Integrating the Squares of All Trigonometric Functions
Lecture 64 Integrating Products of Trigonometric Functions
Lecture 65 Reverse Chain Rule
Lecture 66 Introduction to Partial Fractions
Lecture 67 Integrating with Partial Fractions
Lecture 68 Integration by Parts - Part 1
Lecture 69 Integration by Parts - Part 2
Lecture 70 Integration by Parts - Part 3
Lecture 71 Integration by Substitution - Part 1
Lecture 72 Integration by Substitution - Part 2
Lecture 73 Integration by Substitution - Part 3
Lecture 74 Integration by Substitution - Part 4
Lecture 75 Area of a Circle - Proof with Calculus
Lecture 76 Reduction Formulae - Part 1
Lecture 77 Reduction Formulae - Part 2
Section 11: Advanced Applications in Differentiation
Lecture 78 Connected Rates of Changes
Lecture 79 Newton's Method
Lecture 80 L'Hopital's Rules - Part 1

Lecture 81 L'Hopital's Rule - Part 2
Lecture 82 Maclaurin Series - Part 1
Lecture 83 Maclaurin Series - Part 2
Lecture 84 The Leibnitz Formula
Lecture 85 Taylor Series
Section 12: Advanced Applications in Integration
Lecture 86 Volumes of Revolution Around the X-Axis - Part 1
Lecture 87 Volumes of Revolution Around the X-Axis - Part 2
Lecture 88 Volumes of Revolution Around the Y-Axis
Lecture 89 Surface Areas of Revolution - Part 1
Lecture 90 Surface Areas of Revolution - Part 2
Lecture 91 Arc Lengths
Section 13: Alternative Coordinate Systems
Lecture 92 Parametric Equations - Introduction
Lecture 93 Converting Parametric Equations into Cartesian Equations
Lecture 94 Differentiating Parametric Equations
Lecture 95 Integrating Parametric Equations
Lecture 96 Volumes of Revolution with Parametric Equations
Lecture 97 Surface Areas and Arc Lengths of Parametric Equations
Lecture 98 Polar Coordinates - Introduction
Lecture 99 Converting Between Polar and Cartesian Form
Lecture 100 Differentiating Polar Curves
Lecture 101 How to Integrate Polar Curves
Lecture 102 Integrating Polar Curves
Section 14: First Order Differential Equations
Lecture 103 What is a Differential Equation?
Lecture 104 Separating Variables - Part 1
Lecture 105 Separating Variables - Part 2
Lecture 106 Separating Variables - Modelling - Part 1
Lecture 107 Separating Variables - Modelling - Part 2
Lecture 108 Integrating Factors
Section 15: Second Order Differential Equations
Lecture 109 Homogeneous Second Order Differential Equations - Part 1
Lecture 110 Homogeneous Second Order Differential Equations - Part 2
Lecture 111 Homogeneous Second Order Differential Equations - Part 3
Lecture 112 Non-Homogeneous Second Order Differential Equations
Lecture 113 Boundary Conditions
Lecture 114 Coupled Differential Equations - Part 1
Lecture 115 Coupled Differential Equations - Part 2
Lecture 116 Reducible Differential Equations - Part 1
Lecture 117 Reducible Differential Equations - Part 2
Data scientists,People studying calculus,Engineers,Financial analysts,Anyone looking to expand their knowledge of mathematics

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