Unit name | Mathematics 1A20 |
---|---|

Unit code | MATH11004 |

Credit points | 20 |

Level of study | C/4 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Professor. Porter |

Open unit status | Open |

Pre-requisites |
'C' in A level in Mathematics, IB 6 Higher or equivalent |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

This unit is designed for students with A-level mathematics who want a 20 credit-point unit on mathematical techniques. Students who wish to study further mathematics can take the follow on units of 1AS or 1AM.

**Aims:**

To consolidate, develop and extend the skills in single variable calculus introduced at A level.

**Syllabus**

The numbers of lectures (shown in brackets) are a rough guide only. 1.General introduction, Review of algebra and trigonometry. (2) 2.Functions and graphs: important examples, inverse functions. (2) 3.Sequences and series; limits of functions; continuous functions (3) 4.Exponential function; natural logarithm; hyperbolic functions (2) 5.Complex numbers; Argand diagram, polar form, complex exponential, complex roots (4) 6.Differential calculus, differentiability, basic methods, higher derivatives, Leibniz formula; differentiation of inverse functions (3) 7.Taylor approximations; Taylor series; convergence of the series; ratio test for power series; applications of Taylor series: maxima and minima; l'Hospital's rule for limits (4) 8.Integration: integrals as antiderivatives and as area; standard techniques; infinite integrands; infinite ranges of integration. (4) 9.Differential equations: 1st-order separable and first order linear differential equations. (2) 10.2nd order linear differential equations with constant coefficients, homogenous including simple harmonic motion, inhomogeneous including resonance. (4) 11.Full-range Fourier series in [-pi, pi]. (4)

**Relation to Other Units**

This unit is a prerequisite for the TB2 units 1AM/1AS.

After taking this unit, students should have a thorough grasp of one-variable calculus and complex numbers, including simple differential equations and Fourier Series.

Transferable Skills:

Mathematical techniques for application in the physical sciences.

The unit is based on lectures and tutorials on how to apply the techniques of the calculus in solving problems.

The lecturer will distribute problem sheets based on the work done in lectures, and will set specific problems which you will be required to hand in to tutors for marking. From week 2 or 3 of the course, students will attend weekly tutorials in which homework questions and additional problems will be covered.

100% examination.

The following book is recommended, but it is not essential.

- Jordan, D.W. & Smith, P. Mathematical Techniques: An introduction for the engineering, physical, and mathematical sciences (4th edition), Oxford University Press, Oxford, 2008.