A-Level Further Maths: Core Pure 2

Posted By: ELK1nG

A-Level Further Maths: Core Pure 2
Published 8/2025
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 8.57 GB | Duration: 15h 22m

Master the Core Pure 2 content from A-level Further Maths, and practice on real past paper exam questions.

What you'll learn

Complex Numbers: De Moivre's Theorem, Complex Series

Series: Method of Differences, Maclaurin Series

Methods in Calculus: Improper Integrals, Mean Value of a Function, Inverse Trig Integration

Volumes of Revolution

Polar Coordinates

Hyperbolic Functions

Differential Equations: 1st Order, 2nd Order, Coupled and Modelling

Requirements

A good understanding of A-Level Maths and AS Level Further Maths (or equivalent)

Key prior knowledge: calculus (with polynomials, exponentials, logs and trig), basic knowledge of complex numbers.

Description

A-Level Further Maths: Core Pure 2 is a course for anyone studying A-Level Further Maths.This course covers all the content in the second Core Pure paper. The course has been modelled around the Edexcel exam board, but it matches all the content in OCR as well. It's also a great option for anyone looking to learn more advanced pure mathematics.The main sections of the course are:- Complex Numbers - we expand what we know about complex numbers, looking at exponential form, De Moivre's Theorem, and how to use complex numbers to evaluate trigonometric series.- Series - we will learn how to use the method of differences, as well as how to find the Maclaurin Series of a function.- Methods in Calculus - we look at a range of new methods, such as evaluating improper integrals, finding the mean value of a function, as well as using inverse trig functions in calculus.- Volumes of revolution - we apply the technique learned in Core Pure 1 to much more advanced functions.- Polar Coordaintes - we'll learn how to represent beautiful curves using polar coordinates, and how to differentiate and integrate polar curves.- Hyperbolic Functions- we'll explore the fascinating world of hyperbolic functions, learn the similarities and differences between hyperbolic functions and trig functions, and learn how to differentiate and integrate them.- Differential Equations - we'll learn how to solve 1st and 2nd order differential equations, and and see how to use these to model a range of real world problems.What you get in this course:Videos: Watch as I explain each topic, introducing all the key ideas, and then go through a range of different examples, covering all the important ideas in each. In these videos I also point out the most common misconceptions and errors so that you can avoid them.Quizzes: Each sub-section is followed by a short quiz for you to test your understanding of the content just covered. Most of the questions in the quizzes are taken from real A-Level past papers. Feel free to ask for help if you get stuck on these!Worksheets: At the end of each chapter I have made a collection of different questions taken from real A-Level past papers for you to put it all together and try for yourself. At the bottom of each worksheet is a full mark-scheme so you can see how you have done.This course comes with:· A 30 day money-back guarantee.· A printable Udemy certificate of completion.· Support in the Q&A section - ask me if you get stuck!I really hope you enjoy this course!Woody

Overview

Section 1: Introduction

Lecture 1 Introduction

Section 2: Complex Numbers

Lecture 2 Exponential Form of a Complex Number

Lecture 3 Multiplication and Division of Complex Numbers in Exponential Form

Lecture 4 Optional - Justification of Exponential Form

Lecture 5 De Moivre's Theorem - Intro

Lecture 6 Applications of De Moivre's Theorem - Part 1

Lecture 7 Applications of De Moivre's Theorem - Part 2

Lecture 8 Applications of De Moivre's Theorem - Part 3

Lecture 9 Applications of De Moivre's Theorem - Part 4

Lecture 10 A Clever Trick with Exponentials

Lecture 11 Sums of Series of Complex Numbers - Part 1

Lecture 12 Sums of Series of Complex Numbers - Part 2

Lecture 13 Sums of Series of Complex Numbers - Part 3

Lecture 14 Sums of Series of Complex Numbers - Part 4

Lecture 15 Roots of Unity

Lecture 16 Sums of Roots of Unity

Lecture 17 Finding the Roots of Any Complex Complex

Lecture 18 Polygons

Lecture 19 Complex Numbers - Exam Problems

Section 3: Series

Lecture 20 The Method of Differences - Part 1

Lecture 21 The Method of Differences - Part 2

Lecture 22 The Method of Differences - Part 3

Lecture 23 Higher Derivatives

Lecture 24 Maclaurin Series - Derivation

Lecture 25 Maclaurin Series - Part 1

Lecture 26 Maclaurin Series - Part 2

Lecture 27 Standard Results for Maclaurin Series

Lecture 28 Maclaurin Series - Exam Problems

Section 4: Methods in Calculus

Lecture 29 Introduction to Improper Integrals

Lecture 30 Limit Notation in Improper Integrals

Lecture 31 Convergent vs Divergent Integrals

Lecture 32 The Mean Value of a Function - Derivation

Lecture 33 Calculating the Mean Value of a Function

Lecture 34 The Mean Value of a Transformed Function

Lecture 35 Derivatives of Inverse Trig Functions

Lecture 36 Differentiating Inverse Trig Functions with the Chain Rule

Lecture 37 Functions that Integrate to Inverse Trig Functions - Part 1

Lecture 38 Functions that Integrate to Inverse Trig Functions - Part 2

Lecture 39 Integrating Inverse Trig Functions

Lecture 40 Partial Fractions with Inverse Trig Integrals - Part 1

Lecture 41 Partial Fractions with Inverse Trig Integrals - Part 2

Section 5: Polar Coordinates

Lecture 42 Introduction to Polar Coordinates

Lecture 43 Converting Between Polar and Cartesian

Lecture 44 Sketching Polar Curves

Lecture 45 Differentiating Polar Curves - Part 1

Lecture 46 Differentiating Polar Curves - Part 2

Lecture 47 Integrating Polar Curves - Derivation

Lecture 48 Integrating Polar Curves - Part 1

Lecture 49 Integrating Polar Curves - Part 2

Lecture 50 Polar Coordinates - Exam Problems

Section 6: Hyperbolic Functions

Lecture 51 Introduction to Hyperbolic Functions

Lecture 52 Why is it Hyperbolic?

Lecture 53 Graphs of sinh(x), cosh(x) and tanh(x)

Lecture 54 Solving Simple Hyperbolic Equations

Lecture 55 Inverse Hyperbolic Functions

Lecture 56 Graphs of Inverse Hyperbolic Functions

Lecture 57 Proving Hyperbolic Indentities - Part 1

Lecture 58 Proving Hyperbolic Indentities - Part 2

Lecture 59 Solving Hyperbolic Equations - Part 1

Lecture 60 Solving Hyperbolic Equations - Part 2

Lecture 61 Differentiating Hyperbolic Functions

Lecture 62 Differentiating Inverse Hyperbolic Functions - Part 1

Lecture 63 Differentiating Inverse Hyperbolic Functions - Part 2

Lecture 64 Integrating Hyperbolic Functions - Part 1

Lecture 65 Integrating Hyperbolic Functions - Part 2

Lecture 66 Integrating Hyperbolic Functions - Part 3

Lecture 67 Hyperbolic Functions - Exam Problems

Section 7: Differential Equations

Lecture 68 Families of Curves

Lecture 69 Integrating Factors - Developing Intuitions

Lecture 70 Optional - Integrating Factor Derivation

Lecture 71 Integrating Factors - Part 1

Lecture 72 Integrating Factors - Part 2

Lecture 73 2nd Order Differential Equations - Distinct Rela Roots

Lecture 74 2nd Order Differential Equations - Complex and Repeated Roots

Lecture 75 2nd Order Differential Equations - Boundary Conditions

Lecture 76 Non-Homoegeneous 2nd Order Differential Equations - Part 1

Lecture 77 Non-Homogeneous 2nd Order Differential Equations - Part 2

Lecture 78 Non-Homogeneous 2nd Order Differential Equations - Part 3

Lecture 79 Non-Homogeneous 2nd Order Differential Equations - Part 4

Lecture 80 Modelling With 1st Order Differential Equations

Lecture 81 Differential Equations With No "t"

Lecture 82 Simple Harmonic Motion

Lecture 83 Damped Harmonic Motion - Part 1

Lecture 84 Damped Harmonic Motion - Part 2

Lecture 85 Forced Harmonic Motion

Lecture 86 Coupled Differential Equations - Part 1

Lecture 87 Coupled Differential Equations - Part 2

Lecture 88 Differential Equations - Exam Questions

People studying A-Level Further Maths,People who want to learn some more advanced pure mathematics