Module overview
This module offers an introduction to the differential and integral calculus that underpins engineering mathematics.
Aims and Objectives
Learning Outcomes
Transferable and Generic Skills
Having successfully completed this module you will be able to:
- Apply problem solving techniques to familiar and unfamiliar problems
- Manage your own learning
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
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
Syllabus
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 and Teaching
Teaching and learning methods
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
Type | Hours |
---|---|
Preparation for scheduled sessions | 35 |
Tutorial | 36 |
Lecture | 36 |
Follow-up work | 35 |
Revision | 6 |
Completion of assessment task | 2 |
Total study time | 150 |
Assessment
Assessment strategy
External repeat students will have marks carried forward from the previous year for tests (5%), and therefore exam will contribute 95% of total assessment.
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Final Assessment | 100% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Set Task | 100% |
Repeat Information
Repeat type: Internal & External