Calculus: Complete Course

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 are:Differentiation 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