# Mathematics 2C: Topics In Applied Mathematics MATHS2005

**Academic Session:**2019-20**School:**School of Mathematics and Statistics**Credits:**10**Level:**Level 2 (SCQF level 8)**Typically Offered:**Semester 2**Available to Visiting Students:**Yes**Available to Erasmus Students:**Yes

#### Short Description

This course provides an introduction to the mathematical modelling of mechanical and biological

phenomena, for example, the motion of a golf ball moving under the influence of gravity or the effect of predation on a population of prey. The main mathematical tools used in this course are vectors and the solution of differential equations.

#### Timetable

Lectures are on Wednesdays and Fridays at 10.00 am or Wednesdays and Fridays at 12.00 noon. Fortnightly tutorials on Mondays.

#### Requirements of Entry

Mathematics 1R or 1X at Grade D and Mathematics 1S or 1T or 1Y at Grade D and a pass in the Level 1 Skills Test.

#### 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

#### Course Aims

This course has two main components. First it provides an introduction to the modelling of populations using difference and differential equations, the solution of the equations arising in such models and their qualitative analysis. Second it provides an introduction to the kinematics and dynamics of a single point particle. Equations of motion are constructed via application of Newton's laws.

#### Intended Learning Outcomes of Course

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

■ analyse the dimensions of quantities and make predictions of parameter dependence based on dimensional analysis;

■ derive and analyse single-population dynamical systems, including the exponential and logistic models with predation;

■ analyse the stability of equilibrium points in first order autonomous differential equations and to construct simple bifurcation diagrams for single-population dynamics systems;

■ calculate the tangent vector and arc-length of a parametric curve and to sketch such curves;

■ use plane, cylindrical and spherical polar coordinates to describe particle motion;

■ explain the terms velocity, speed, acceleration, displacement and distance travelled in connection with the motion of a point particle and to connect these terms to properties of parametric curves;

■ formulate problems in particle mechanics in mathematical terms using vectors and/or 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 use them in calculations;

■ construct and solve problems using: kinematics; Newtons Laws; concepts of energy, work and power; collisions and impulse; projectile motion and motion governed by Hooke's Law;

■ construct and solve problems in elementary mechanics using plane polar coordinates;

■ formulate problems in particle mechanics in mathematical terms using vectors and/or differential equations as appropriate, and solve the resulting equations to determine the motion of the particle;

■ learn and apply formulas which are taught in the course.

#### 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.