Advanced Mathematics 2
Gain a better understanding of differential equations, kinematics, vector calculus, and dynamics, with this math course.
Description
This course begins by teaching you how to successfully complete mathematics exams. You will then study differential equations which are mathematical equations that relate a function to its derivatives. You will also study the use of the second derivative, kinematics including how to find displacement from velocity and acceleration, and motion under a constant force and motion under a variable force. This course will then present you with advanced mathematics problems covering chemical concentrations and chemical reactions.
You will then study the resolution of forces which include static friction and angle of friction. You will look into vectors and learn how to find a cartesian equation and use a graphic calculator with parametric equations. You will also learn how to calculate the closest distance to a path. This course will then cover the differentiation and antidifferentiation of vectors including the notations used in vector calculus.
In this modern world where advancedtechnology thrives, deeper knowledge in higherlevel maths is crucial to success in many fields. This Advanced Mathematics course will ensure that your math skills are a cut above your peers, that your next maths exam is a little bit easier, and that this fascinating and important field of study becomes a lot more open to you. Start your next learning journey, today.
Modules
Glossary
Differential equations

Introduction

Order and degree of differential equations

Verifying solutions

Rates of change

Rates of change  chain rule

The rates of change example

First order differential equations  type 1

First order differential equations  type 2

Second order differential equations
Common exam mistakes

Basic algebra exam mistakes

Using correct notation in exams

Dividing by fractions

Negative signs

Applying half remembered rules incorrectly
Successfully completing mathematics exams

Introduction

Look for key words

Check level of accuracy

What form should the answer take?

Don't waste time on work that is not assessed

Use all the information provided in the question

Work out the solution before you look at the answers

Rationalise or realise denominators

Essential skills you need to brush up on before the exams

Decide on the order you answer questions

Timing of questions

Setting out

Don't panic

If you are stuck

Guessing

Learning pattern questions

Learning pattern questions: graphs

Learning pattern questions: complex numbers

Learning pattern questions: differentiation

Learning pattern questions: integration

Learning pattern questions: vectors
Kinematics

Introduction

Finding displacement from velocity

Solving differential equations (rectilinear motion) example

Finding acceleration or velocity from displacement

Constant acceleration  introduction

Constant acceleration  example 1

Velocity time graphs  introduction

Finding the acceleration from the velocity time graph

Finding the distance travelled from a velocity time graph

Velocity time graphs  example

Constant acceleration  example 2
Motion

Introduction

Newton's laws of motions

Forcesweight

Diagram of forces

Basic equation of motion

Resolution of forces

Horizontal and vertical

Equations of motion

Parallel and perpendicular to a plane

Equations of motion

Moving down the slope

Connected masses

Motion under a constant force

Motion under a constant force  example 1

Motion under a constant force  example 2

Motion under a variable force

Motion under a variable force  example 1

Motion under a variable force  example 2

Motion under a variable force  example 3

Momentum and impulse

Momentum and impulse example

Moving up the slope

Motion under a constant force  example 1 continued

Forcesnormal reaction

Forcesfriction

Forcestension
Advanced Mathematics: Problems

Activity

Using differential equations

Newton's laws of cooling

Growth and decline

Chemical concentrations

Water flow from a hole in a tank

Chemical reactions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Euler's method for solution of differential equations

Euler's example 1

Euler's example 2
Resolution of forces
Second derivatives
Vectors 2

The garden activity

Notation used in vector calculus

Differentiation and anti differentiation of vectors

Example 1

Example 2
Vectors

Position vectors as functions of time (Parametric Equations)

Finding cartesian equations from parametric equations

Example 1

Example 2

Collision

Example 3

Using a graphic calculator with parametric equations

Using a graphic calculator with two parametric equations to show a collision

The closest distance to a path

Example 4
Assessment
Learning Outcomes
Upon completion of this course you will effectively learn the most important factors to be considered when answering questions in a maths exam. You will be aware of the most common mistakes in maths exams.
You will gain a good knowledge of first and second order differential equations and second derivatives. You will learn about kinematics including acceleration, distance and velocity. You will understand Newton's laws of motion, Newton's laws of cooling, and Euler's method for solution of differential equations.
This course will teach you the resolution of forces and how to calculate vectors.
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire official Certification, which is a great way to share your achievement with the world. Your Alison Certification is:
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An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
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