Module FOUD0638: Maths Application Advanced

Department: Foundation Year (Durham)

FOUD0638: Maths Application Advanced

Prerequisites

• Core Foundation Maths for Scientists

Corequisites

• None

Excluded Combination of Modules

• Mathematical Thinking, Maths Applications for Economics and Computing. Foundation of Statistics.

Aims

• To extend knowledge of Cartesian coordinates in two and three dimensions to include equations of circles, lines and planes.
• To introduce and develop a knowledge of matrices and applications.
• To develop a knowledge of vectors and their applications in two and three dimensions to include equations of lines and planes.
• To introduce various types of functions and relations
• To improve confidence in algebraic and trigonometric manipulation.
• To introduce and develop understanding of trigonometric identities and their uses.
• To extend understanding of a range of standard techniques for differentiation and integration.
• To introduce and develop a knowledge of first and second order differential equations and their applications.
• To introduce and develop knowledge of complex numbers and concept of polar coordinates.
• To develop students' abilities to apply mathematics to problems based on physical situations.
• To provide the opportunity for students to engage in logical reasoning, algorithmic thinking and applications.
• To introduce basic knowledge of statistics.

Content

• Set, functions and types, domain, range and inverse functions.
• Trigonometrical functions of angles and graphs.
• Matrices (n x m): addition, subtraction, multiplication, determinant, transpose, inverse. Applications to simultaneous equations.
• Cartesian equations of straight lines, perpendicular lines and equation of circles and tangent to radius.
• Complex numbers: +, -, x, /, complex conjugate, polar form, Argand diagrams, De Moivre's theorem.
• Vectors in two dimensions including: use of column and unit vectors, addition, subtraction and multiplication by scalar. Scalar (dot) and vector (cross) product and their applications.
• Differentiation of functions defined parametrically and implicitly.
• Applications of first order differential equations.
• Second order differential equations.
• Partial differentiation
• Newton’s Laws and mathematical modeling to solve problems based on physical situations.
• Spanning trees (Prim's and Kruska's algorithm and travelling salesperson problem).
• Critical Path Analysis.
• Mean, Median and Mode, Standard Deviation and Normal Distribution

Learning Outcomes

• By the end of the module the student will be able to
• Solve a range of predictable problems in Discrete Mathematics. (SSK1)
• Give standard Cartesian equations for circles and lines (SSK2)
• Understand vectors and rules of application in two and three dimensions. (SSK3)
• State the rules for addition, subtraction and multiplication of matrices and for finding inverses. (SSK4)
• Understand set, and define various types of functions and relations including trigonometry functions (SSK5)
• Understand parametric and implicit functions and first order differential equations and second order differential equations (SSk6)
• Solve a range of physical problems in Mechanics including circular motion. (SSK7)
• Solve simple statistics problem (SSK8)

• By the end of this module the student will have acquired the skills to be able to:
• apply discreet mathematics to a variety of problems. (SSS1)
• confidently manipulate a range of Cartesian and vector equations in two and three dimensions. (SSS2)
• use matrices in a number of mathematical situations. (SSS3)
• confidently manipulate various functions and solving equations. (SSS4)
• select and use trigonometric identities and techniques as required in problems appropriate to the syllabus. (SSS5)
• understand and use complex numbers in a range of situations as appropriate to the syllabus. (SSS6)
• recall, select and use knowledge of appropriate integration and differentiation techniques as needed in a variety of contexts.(SSS7)
• understand and use first and second order differential equations in a range of situations as appropriate to the syllabus. (SSS8)
• do partial differentiation (SSS9)
• apply mathematics to a variety of problems based on physical situations. (SSS10)
• confidently manipulate a range of algebraic and trigonometric expressions as required in problems appropriate to the syllabus. (SSS11)

• By the end of the module students will be able to
• apply number in the tackling of numerical problems (KS1)
• effectively use algebra in mathematical modelling (KS2)
• demonstrate problem solving skills (KS3)

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.
• In class tests, developing or consolidating the previous weeks’ work will be set which will contribute towards final the module mark. These tests also perform a formative role enabling students to reflect on their own performance, identify areas of weakness, and practice some of the skills and techniques which will be required in the final exam.
• Ability to recall, select and use knowledge and manipulative skills will be tested by: tasks set by the tutor on a weekly basis, mid-module invigilated tests and an end of module exam.
• In addition to obtaining an overall weighted mark of 50% or above, students must obtain a mark of 50% or above for the following element/s - Test 1, Test 2 and Final Exam.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Students will be given self-testing units on a weekly basis in the form of worksheets with answers and/or DUO quizzes. Portfolio tasks with a rapid marking turnaround fulfill a formative as well as summative role (See Section 14). Students have access to two or more mock papers and answers to help prepare for the class tests and the exam. The module has variety form of assessment; portfolio tasks with a rapid marking turn around fulfill a formative as well as summative role.

■ 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