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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 advanced-technology thrives, deeper knowledge in higher-level 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
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Introduction
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Order and degree of differential equations
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Verifying solutions
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Rates of change
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Rates of change - chain rule
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The rates of change example
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First order differential equations - type 1
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First order differential equations - type 2
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Second order differential equations
Common exam mistakes
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Basic algebra exam mistakes
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Using correct notation in exams
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Dividing by fractions
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Negative signs
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Applying half remembered rules incorrectly
Successfully completing mathematics exams
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Introduction
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Look for key words
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Check level of accuracy
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What form should the answer take?
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Don't waste time on work that is not assessed
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Use all the information provided in the question
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Work out the solution before you look at the answers
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Rationalise or realise denominators
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Essential skills you need to brush up on before the exams
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Decide on the order you answer questions
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Timing of questions
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Setting out
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Don't panic
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If you are stuck
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Guessing
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Learning pattern questions
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Learning pattern questions: graphs
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Learning pattern questions: complex numbers
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Learning pattern questions: differentiation
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Learning pattern questions: integration
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Learning pattern questions: vectors
Kinematics
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Introduction
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Finding displacement from velocity
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Solving differential equations (rectilinear motion) example
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Finding acceleration or velocity from displacement
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Constant acceleration - introduction
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Constant acceleration - example 1
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Velocity time graphs - introduction
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Finding the acceleration from the velocity time graph
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Finding the distance travelled from a velocity time graph
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Velocity time graphs - example
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Constant acceleration - example 2
Motion
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Introduction
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Newton's laws of motions
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Forces-weight
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Diagram of forces
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Basic equation of motion
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Resolution of forces
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Horizontal and vertical
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Equations of motion
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Parallel and perpendicular to a plane
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Equations of motion
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Moving down the slope
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Connected masses
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Motion under a constant force
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Motion under a constant force - example 1
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Motion under a constant force - example 2
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Motion under a variable force
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Motion under a variable force - example 1
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Motion under a variable force - example 2
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Motion under a variable force - example 3
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Momentum and impulse
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Momentum and impulse example
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Moving up the slope
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Motion under a constant force - example 1 continued
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Forces-normal reaction
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Forces-friction
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Forces-tension
Advanced Mathematics: Problems
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Activity
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Using differential equations
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Newton's laws of cooling
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Growth and decline
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Chemical concentrations
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Water flow from a hole in a tank
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Chemical reactions
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Example 1
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Example 2
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Example 3
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Example 4
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Example 5
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Example 6
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Euler's method for solution of differential equations
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Euler's example 1
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Euler's example 2
Resolution of forces
Second derivatives
Vectors 2
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The garden activity
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Notation used in vector calculus
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Differentiation and anti differentiation of vectors
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Example 1
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Example 2
Vectors
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Position vectors as functions of time (Parametric Equations)
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Finding cartesian equations from parametric equations
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Example 1
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Example 2
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Collision
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Example 3
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Using a graphic calculator with parametric equations
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Using a graphic calculator with two parametric equations to show a collision
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The closest distance to a path
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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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