Mathematics B

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Show confidence in manipulating mathematical expressions, setting up and solving equations and constructing simple proofs
• Select and apply appropriate mathematical methods to solve abstract and real-world problems

Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Manage your own learning
• Apply problem solving techniques to familiar and unfamiliar problems

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Vector operations
• The mathematical methods of differential and integral calculus and of some simple solution methods for various types of differential equations

Differentiation

• understand the gradient of a curve at a point as the limit of the gradients of a sequence of chords
• use the derivative of xn, lnx, ex, sinx, cosx, tanx and constant multiples, sums/differences of these
• find gradient of a curve at a point
• find equation of tangent/normal to a curve at a point
• use the product and quotient rules
• use the chain rule to differentiate functions of the form f(g(x))
• understand that a derivative gives a rate of change
• find the second derivative of a function
• understand and be able to use the relationship dydxdxdy1=
• find the first derivative of a function which is defined parametrically
• find the first derivative of a function which is defined implicitly
• use logarithmic differentiation
• locate stationary points and distinguish between maxima and minima (by any method)

Integration

• understand integration as the reverse of differentiation; integrate xn (including

n =−1) ex sinx cosx sec2x together with sums/differences and constant multiples of these

• recognise integrands of the form kf ‘(x)/f(x) and kf(x)f ‘(x) and integrate
• integrate expressions requiring linear substitution e.g. sin(ax+b) and double angle formulae e.g. cos2x
• use integration to find a region bounded by a curve and two ordinates or by two curves
• recognise where an integrand may be regarded as a product and use integration by parts to integrate
• integrate rational functions using partial fractions
• integrate simple functions in parametric form
• use the mid-ordinate rule, the trapezium rule and Simpson’s rule to obtain approximate values for definite integrals
• apply integration to find volumes of revolution about the x-axis, centroids of uniform laminae, mean and rms values of functions

Differential Equations

• formulate a simple statement involving a rate of change as a differential equation
• find by integration a general form of a solution for a differential equation in which the variable are separable
• use initial condition(s) to find a particular integral

Vectors

• know difference between a scalar and a vector
• use vector notation to locate points in 3 dimensions
• add, subtract and multiply by a scalar
• use unit vectors, position vectors and displacement vectors
• find modulus of a vector
• calculate scalar product and use to find angle between two vectors and to show that vectors are parallel or perpendicular
• calculate vector product, interpret as area of a parallelogram and as a vector perpendicular to two others

Learning activities include

• Individual work on examples, supported by tutorial/workshop sessions/extra support sessions.
• Elements of the coursework module GENG0015 may support your learning in this module.

Teaching methods include

• Lectures, supported by example sheets.
• Tutorials/Workshops/support sessions.
• Printed notes will be available through Blackboard and/or through your module lecturer

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.