Module FOUN0361: CORE FOUNDATION MATHS FOR SCIENTISTS

Department: Foundation Year

FOUN0361: CORE FOUNDATION MATHS FOR SCIENTISTS

Prerequisites

• None.

Corequisites

• None.

Excluded Combination of Modules

• Core Foundation Maths for Business and Economics.

Aims

• To improve confidence in algebraic manipulation through the study of mathematical techniques and development of investigative skills.
• To introduce and develop a knowledge of logarithms and their uses.
• To introduce and develop a knowledge of trigonometry.
• To introduce and develop understanding of a range of standard techniques for differentiation and integration.
• To include trigonometric and logarithmic functions.

Content

• Quadratic equations, factorisation, graphs, quadratic formula.
• Trigonometry, sine, cosine, tangent.
• Sequences and Series , Arithmetic, geometric, use of sigma notation.
• Indices and Logarithms: laws, solution of equations.
• Reduction of a given relation to linear form, graphical determination of constants.
• Rate of change, increasing/decreasing functions, maxima and minima.
• Differentiation of: algebraic polynomials ,composite functions (chain rule), sum, product or quotient of two functions, trigonometric and exponential functions.
• Evaluation of integrals by using standard forms or partial fractions.
• Second derivatives of standard functions.
• Binomial expansion of (a+b)(to the power n) for positive integer n.
• Factor theorem.
• Percentage use
• Linear equations, Substitution and transposition of formulae
• Pythagoras' theorem
• Standard Index form
• Area and Volume, Symmetry
• Applications in scientific calculations

Learning Outcomes

• By the end of this module the student will have acquired the knowledge to be able to:
• confidently manipulate a range of algebraic expressions as needed in a variety of contexts.
• use logarithms to solve problems and to predict relationships from graphs.
• differentiate and integrate a number of different types of functions.

• By the end of this module the student will have acquired the skills to be able to:
• recall, select and use knowledge of appropriate integration and differentiation techniques as needed in a variety of contexts.
• confidently manipulate a range of algebraic expressions and use a range of techniques 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.
• Invigilated test covers learning outcomes:SSK1. SSK2, SSK3, SSS1, SSS2, KS1, KS2, KS3, (ie everything)
• Class tests cover all above
• Coursework covers all above.

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 and seminars.
• Much of the learning, understanding and consolidation will take place through the use of structured exercise during seminar and tutorial sessions and students own time.
• Manipulative skills and ability to recall, select and apply mathematics including calculus will be assessed by an end of module test and a portfolio of tasks including some short invigilated tests and solutions to questions set on a weekly basis.
• Logarithms and prediction of relationships from graphs will be consolidated and assessed within a coursework task.

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