MATH1571: SINGLE MATHEMATICS B

• A level Mathematics at Grade A or better, orequivalent.

• Single Mathematics A (MATH1561).

• Mathematics for Engineers and Scientists (MATH1551)may not be taken with or after thismodule.

• This module has been designed to supply mathematics relevant to students of the physical sciences.

• Vectors: including scalar and vector products, derivativeswith respect to scalars, two-dimensional polar coordinates.
• Ordinary differential equations: including first order,second order linear equations, complementary functions and particularintegrals, simultaneous linear equations, applications.
• Fourier analysis: including periodic functions, odd and even functions, complex form.
• Functions of several variables: including elementaryvector algebra (bases, components, scalar and vector products, lines andplanes), partial differentiation, composite functions, change ofvariables, chain rule, Taylor expansions. Introductory complex analysis and vector calculus
• Multiple integration: including double and tripleintegrals.
• Introduction to probability: including sample space,events, conditional probability, Bayes' theorem, independent events, random variables, probability distributions, expectation andvariance.

Subject-specific Knowledge:

• By the end of the module students will: be able to solve arange of predictable or less predictable problems inMathematics.
• have an awareness of the basic concepts of theoreticalmathematics in these areas.
• have a broad knowledge and basic understanding of thesesubjects demonstrated through one or more of the following topicareas: Vectors.
• Ordinary differential equations.
• Fourier analysis.
• Partial differentiation, multiple integrals.
• Vector calculus.
• Probability.

Subject-specific Skills:

Key Skills:

• Lectures demonstrate what is required to be learned and theapplication of the theory to practical examples.
• Initial diagnostic testing fills in gaps related to the widevariety of syllabuses available at Mathematics A-level.
• Tutorials provide the practice and support in applying themethods to relevant situations as well as active engagement and feedbackto the learning process.
• Weekly coursework provides an opportunity for studentsto consolidate the learning of material as the module progresses (thereare no higher level modules in the department of Mathematical Scienceswhich build on this module). It serves as a guide in the correctdevelopment of students' knowledge and skills, as well as an aid indeveloping their awareness of standards required.
• The end-of-year written examination provides a substantialcomplementary assessment of the achievement of the student.

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