## Mathematics 2E: Mechanics MATHS2034

**Academic Session:**2023-24**School:**School of Mathematics and Statistics**Credits:**10**Level:**Level 2 (SCQF level 8)**Typically Offered:**Semester 2**Available to Visiting Students:**Yes

### Short Description

This course provides an introduction to the mathematical modelling of mechanical phenomena, for example, the motion of a golf ball moving under the influence of gravity. The main mathematical tools used in this course are vector algebra and the analysis of solutions of differential equations. It is an essential course for intending honours students.

### Timetable

2 x lectures per week. Fortnightly tutorials.

### Requirements of Entry

Mathematics 1 at at least grade D3.

### Excluded Courses

None

### Co-requisites

Mathematics 2A: Multivariable Calculus

Mathematics 2B: Linear Algebra

### Assessment

One degree examination (80%) (1 hour 30 mins); coursework (20%).

**Main Assessment In:** April/May

**Are reassessment opportunities available for all summative assessments?** No

Reassessment will not be available for continuous assessment. Immediate feedback will be given to students at the assignment deadline, and it is not practical to set multiple versions of each of these exercises.

In total 80% of the assessment can be repeated for students not reaching the threshold grade.

Note that students are required to submit 75% of the assessments in order to receive a grade for the course. Accordingly, students who have a substantial period of illness and have all feedback exercises and tutorial group work MV'ed, will not be in danger of failing to receive credits.

### Course Aims

The aim of this course is to provide an introduction to the kinematics and dynamics of a single point mass particle. Equations of motion are constructed via the application of Newton's laws. The Lagrangian formalism of mechanics is introduced.

### Intended Learning Outcomes of Course

By the end of this course, students will be able to:

■ Predict functional dependence based on dimensional analysis.

■ Calculate the tangent vector and arc-length of a parametric curve and sketch such curves; use plane, cylindrical and spherical polar coordinates to describe particle motion; fluently apply the terms velocity, speed, acceleration, displacement and distance travelled to describe the motion of a point particle and connect these concepts to properties of parametric curves.

■ Mathematically model suitable particle mechanics systems using vectors and differential equations as appropriate, and solve the resulting equations to determine the motion of the particle.

■ Define the terms linear momentum, impulse and force and apply these in calculations; given a description of a mechanical system, construct a model of this system and provide predictions of future states of the system.

■ Define and apply the concepts of energy, work and power in given physical situations; compute projectile motion and motion governed by Hooke's Law; use plane polar coordinates to model and solve elementary mechanics systems.

■ Determine appropriate Lagrangians, and derive and solve the equations of motions for simple mechanical systems subject to the principle of least action.

■ State the definitions, results and formulae presented in lectures; apply and adapt these to solve suitable problems.

### Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.