- Title: Mathematics 1M2
- Unit code: MATH19662
- Credit rating: 10
- Level: 1
- Pre-requisite units: 1M1 (MATH19661)
- Co-requisite units: None
- School responsible: Mathematics
- Member of staff responsible: Dr CDC Steele, Prof N Gray
- 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
- 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%
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.