Module FOUN0341: MATHS APPLICATIONS (COMBINED)

Department: Foundation Year [Queen's Campus, Stockton]

FOUN0341: MATHS APPLICATIONS (COMBINED)

Pre-requisites

Corequisites

Excluded Combinations

Aims

• To introduce and develop a knowledge of matrices and their applications.
• To extend knowledge of Cartesian coordinates in two and three dimensions to include equations of circles, lines and planes.
• To develop a knowledge of vectors and their applications in two and three dimensions to include equations of lines and planes.
• To introduce and develop knowledge of the six trigonometrical functions and inverses.
• To introduce and develop understanding of trigonometric identities and their uses.
• To introduce the concept of polar coordinates.
• To introduce and develop knowledge of complex numbers.
• 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

• Cartesian equations: lines, normals, circles, planes.
• Vectors : column and unit vectors, addition, subtraction and multiplication by scalar. Scalar(dot) and vector(cross) product and applications. Equations of lines and planes. Resolution.
• Trigonometry: six ratios, inverse functions, use of identities, solution of equations, Radian measure. Polar coordinates.
• Complex numbers: +, -, x, /, conjugate, polar form, Argand diagrams, De Moivre's theorem.
• Motion: velocity , acceleration, equations with constant acceleration, projectiles, variable acceleration/force, F=ma. Conservation of momentum, impulse.
• Hooke's law, SHM.
• First Order Differential equations including separating variables.
• Second Order Differential equations.
• Integration by parts and Integration by substitution

Learning Outcomes

• N/A

• By the end of this module the student will have acquired the skills to be able to:
• select and use trigonometric identities and techniques as required in problems appropriate to the syllabus.
• confidently manipulate a range of Cartesian and vector equations in two and three dimensions.
• plot a graph using polar coordinates.
• understand and use complex numbers in a range of situations as appropriate to the syllabus.
• 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 both in the tackling of numerical problems and in the collecting, recording, interpreting and presenting of data.
• 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 seminars, tutorials and students' own time.
• Ability to recall, select and use knowledge and manipulative skills 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 tests and an end of module exam.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment

Students will be given self testing units on a weekly basis.