1M2 (MATH19662)

 

Unit specification

Aims

To provide a second-semester course in calculus and algebra to students with A-level mathematics or equivalent in school of MACE.

Brief description

5 Lectures :- Second-order Ordinary Differential Equations. Linear Equations with constant coefficients; homogeneous and non-homogeneous cases; complementary functions and particular integrals, Special cases with non-constant coefficients.

3 Lectures :- Partial Differentiation. Introduction. Chain rule for partial differentiation. Total derivatives. Theory of errors. Coordinate Systems (Cartesian, Cylindrical, Spherical), change of variables.

3 Lectures :- Series and Limits. Definition of Limits. L'Hopital's Rule. Sequences and Series; convergence; Power Series, Taylor and Maclaurin Series.

2 Lectures :- Functions of Two Variables. Maxima, minima and saddle points. Taylor Series in Two variables.

3 Lectures :- Second-order partial differential equations (wave, heat/diffusion, Laplace/Poisson. Solution by separation of variables.

5 Lectures :- Matrices and Determinants: Definition of an m x n matrix. Matrix addition, subtraction, multiplication by a scalar, matrix multiplication; square matrices, determinants and properties; Solution of equations; inverse matrices.

3 Lectures :- LinearAlgebra: LU Decomposition; solution of simultaneous equations; Gaussian Elimination; Cholesky's method.

Intended learning outcomes

Knowledge and understanding: Be familiar with second order ordinary differential equations, partial differentiation, series and limits, partial differential equations and matrices.

Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.

Transferable skills and personal qualities: Have a set of tools and methods that can be applied in the courses given in the host school or in subsequent years.

Textbooks

link2lists

KA Stroud, Engineering Mathematics, Palgrave

E Kreyszig, Advanced Engineering Mathematics, Wiley

Learning and teaching processes

Two lectures in weeks 1-11. One smallish-group tutorial in weeks 2-12. Revision Classes in week 12.

Lectures : 22

Tutorials : 11

Revision Classes: 2

Hours of private study : 65

Assessment

Coursework 1 (week 5); Weighting within unit 10%

Coursework 2 (week 10); Weighting within unit 10%

2 hour end of semester 2 examination; Weighting within unit 80%

to the top

Arrangements

This is a first-year, second semester calculus course for students in the school of Mechanical, Aerospace and Civil Engineering. There are two lectures per week.

The lectures for course 1M2 (MATH19662) for 2012-13 are as follows

• Wednesday 9 am : Renold/C16
• Friday 9 am : Renold/C16
• Lectures given by Prof N Gray

Tutorials start in week 2. Each student is assigned to a group which meets once per week. Students should prepare their answers to the various questions in connection with the timetable.