Module FOUD0301: MATHS APPLICATIONS (COMBINED)

Department: Foundation Year (Durham)

FOUD0301: MATHS APPLICATIONS (COMBINED)

Prerequisites

• Core Foundation Maths 1 or Core Foundation Maths (combined) or equivalent.

Corequisites

• None.

Excluded Combination of Modules

• Maths Applications 1 and 2

Aims

• 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

• By the end of the module the student will be able to
• Define the 6 trigonometrical functions (SSK1)
• State the standard forms for general solutions of second order differential equations (SSK2)
• Give standard Cartesian equations for circles and lines (SSK3)

• 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.
• 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.
• 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.
• Test 1 will assess: ssk 1, SSK3, SS1, SS2, SSS6, KS1, KS2, KS3. Test 2 will assess SSK1, SSS4, SSS6, KS1, KS2, KS3.
• Portfolio will assess SSK 1-3, SSS 1-6, KS 1-3
• Exam will assess SSK 1-3, SSS 1-6, KS 1-3

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.

■ 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