Module FOUN0267: MATHEMATICAL APPLICATIONS 2

Department: Foundation Year

FOUN0267: MATHEMATICAL APPLICATIONS 2

Prerequisites

• None.

Corequisites

• Numerical Skills and Research Methods for Scientists (FOUN0331) or Numerical Skills and Research Methods for Social Scientists (FOUN0321)

Excluded Combination of Modules

• None.

Aims

• to introduce and develop a knowledge of matrices and their applications.
• to introduce and develop a knowledge of first and second order differential equations and their applications.
• to improve confidence in algebraic and trigonometric manipulation.
• to develop students' abilities to apply mathematics to problems based on physical situations.

Content

• Matrices 2x2 and nxm, addition, subtraction and multiplication, determinant, transpose and inverse. Applications to simultaneous equations.
• addition, subtraction and resolution of co-planar vectors.
• displacement, speed, velocity and acceleration.
• equations of motion (e.g. v = u + at).
• independence of motion in two directions at right angles (e.g. projectiles).
• use of F = ma.
• calculation of moments, conditions for equilibrium.
• conservation of momentum.
• Hooke's law, Young's modulus.
• First Order Differential equations including separating variables.
• Second Order Differential equations.

Learning Outcomes

• By the end of this module the student will have acquired the skills to be able to:
• apply mathematics to a variety of problems based on physical situations.
• use matrices in a number of mathematical situations.
• understand and use first and second order differential equations in a range of situations as appropriate to the syllabus.
• confidently manipulate a range of algebraic and trigonometric expressions as required in problems appropriate to the syllabus.

• By the end of the module students will:
• be able to communicate effectively in writing
• be able to apply number in the tackling of numerical problems
• be able to demonstrate problem solving skills

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Theory, initial concepts and techniques will be introduced during lectures.
• Much of the learning, understanding and consolidation will take place through the use of structured worksheets during tutorials and students' own time.
• Manipulative skills and ability to use and apply mathematics will be tested by: a coursework portfolio containing students' solutions to questions or tasks set by the tutor on a weekly basis, an invigilated test and an end of module exam.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Weekly self-testing units

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University