Module FOUN0257: MATHS APPLICATIONS 1

Department: Foundation Year

FOUN0257: MATHS APPLICATIONS 1

Prerequisites

• None.

Corequisites

• None.

Excluded Combination of Modules

• Maths Applications Combined

Aims

• To extend and develop knowledge of the six trigonometrical functions and inverses.
• 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 extend knowledge of Cartesian coordinates in two dimensions to include equations of circles and lines.
• to introduce the concept of polar coordinates.
• to extend and develop knowledge of complex numbers.
• to develop a knowledge of vectors and their applications in two and three dimensions
• to introduce the concept of linear programming

Content

• trigonometrical functions of angles, real numbers and graphs.
• Cartesian equations in two and three dimensions of straight lines, perpendicular lines and circles.
• complex numbers: +, -, x, /, complex conjugate, polar form, Argand diagrams, De Moivre's theorem.
• vectors in two and three dimensions including: use of column and unit vectors, addition, subtraction and multiplication by scalar.
• Scalar (dot) and vector (cross) product and their applications.
• vector equations of lines and planes.
• Matrices 2x2 and nxm, addition, subtraction and multiplication, determinant, transpose and inverse. Applications to simultaneous equations.
• First Order Differential equations including separating variables.
• Second Order Differential equations.
• Linear Programming

Learning Outcomes

• Define the 6 trigonometrical functions (SSK 1)
• State the rules for addition, subtraction and multiplication of matrices and for finding inverses. (SSK2)
• State the standard forms for general solutions of second order differential equations (SSK3)
• Give standard Cartesian equations for circles and lines (SSk4)

• By the end of the module the student will have acquired the skills to be able to:
• select and use trigonometric and techniques as required in problems appropriate to the syllabus. (SSS1)
• confidently manipulate a range of Cartesian and vector equations in two dimensions. (SSS2)
• understand and use complex numbers in a range of situations as appropriate to the syllabus. (SSS3)
• use matrices in a number of mathematical situations. (SSS4)
• understand and use first and second order differential equations in a range of situations as appropriate to the syllabus (SSS5)
• reduce problems to a series of equations and inequalities and solve using linear programming techniques. (sss6)

• By the end of the module the student 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
• Test 1 covers SSK2, SSS4, KS1, KS2
• Test 2 covers SSK1. SSK4, SSS1, SSS2, KS1, KS2
• Examinations covers SSK3, SS3, SSS5, SSS6, KS1, KS2
• Portfolio covers SSK1-4, SSS 1-6, KS1, KS2,

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.
• Ability to recall, select and use knowledge will be tested by: a coursework portfolio containing students solutions to questions or tasks set by the tutor on a weekly basis, mid-module invigilated test and an end of module invigilated test.

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