Advanced Higher Mathematics of Mechanics (Course Code: C802 77)

SCQF Level 7 (32 SCQF credit points)

Why study Mathematics of Mechanics?

Mechanics is the branch of mathematics concerned with the study of forces that act on bodies and any resultant motion that they experience, and is widely used in physics and technology. Mechanics uses mathematics to enable us to model real-life situations and equip us with the skills we need to interpret and understand how things work, simplify and solve problems, identify limitations and draw conclusions.

You will learn of the range and power of mathematics and the importance of mathematical applications to society in general. This course encourages independent thinking and demands an enquiring approach, developing your questioning skills, logical reasoning, analysis, problem solving skills, creativity and the ability to communicate explanations concisely.

What do I need to get in?

This is at the discretion of the school/college but you would normally be expected to have attained one of the following:

What will I study?

The course comprises three areas of study.

Linear and Parabolic Motion

The general aim of the unit is to develop advanced knowledge and skills in algebra and calculus to be applied to the mechanics of linear and parabolic motion.

You will:

• interpret the effects of forces on a body and will use mathematical models in problems involving motion in a straight line under the influence of either constant force or variable force where acceleration is dependent on time. A vector approach is encouraged in the study of the relative motion of bodies, the effects of winds and currents, collision courses and closest approach
• explore the motion of projectiles in a vertical plane. Newton’s Laws of Motion are used to develop an understanding of equilibrium, friction and resulting motion, with particular emphasis on Newton’s Second Law to consider one-dimensional motion on horizontal and inclined planes.

Force Energy and Periodic Motion

The general aim of the unit is to develop advanced mathematical knowledge and skills to be applied to the mechanics of force, energy and periodic motion.

You will:

• interpret the effects of both constant and variable forces on a body
• use mathematical models in problems where the acceleration is dependent on displacement or velocity, and where interpretation and solution of problems involving first order differential equations is required
• develop the principles of momentum and impulse and those of work, power and energy, and include the work–energy principle and the use of conservation of energy.

Mathematical Techniques for Mechanics

You will:

• be introduced to the modelling of practical problems using differential equations, including those with separable variables and those with an integrating factor. Partial fractions are introduced
• widen your skills in calculus to include parametric and implicit differentiation as well as integration using substitution, using partial fractions and by parts.

How will I be assessed?

Course Assessment

The course assessment consists of one component totalling 90 marks:

• Component 1 – Question paper (90 marks).

The question paper will be set and marked by SQA.

The grade awarded is based on the total marks achieved across course assessment.

The course assessment is graded A-D.

What can I go on to next?

Further study, training or employment in: