MAS250 Mathematics II (Materials)

Semester 1, 2021/22 10 Credits
Lecturer: Dr Nils Mole Timetable Reading List
Aims Outcomes Teaching Methods Assessment Full Syllabus

This module is part of a series of second-level modules designed for the particular group of engineers shown in brackets in the module title. Each module consolidates previous mathematical knowledge and develops new mathematical techniques relevant to the particular engineering discipline.

Prerequisites: MAS153 (Mathematics (Materials))
No other modules have this module as a prerequisite.

Outline syllabus

    Office hours

    1-2 pm on Tuesdays, but you are welcome to email questions to me at any time.


    Aims

    • To consolidate previous mathematical knowledge.
    • To continue introducing students to basic mathematical techniques used in the area of Engineering Materials.

    Learning outcomes

    • Partially differentiate functions of two variables and be able to apply the chain rule.
    • Be able to apply simple statistical methods (including linear regression using least squares, and t and χ2 tests) to datasets.
    • Understand and manipulate gradient, divergence, curl and Laplacian.
    • Expand a function defined over a finite domain in a Fourier series.
    • Solve simple partial differential equations e.g. Laplace's equation, wave equation and heat conduction equation.

    Teaching methods

    Lectures, tutorials, independent study


    36 lectures, 12 tutorials

    Assessment

    One two-hour written examination for 80% of assessment.
    Four marked homeworks for 20% of assessment.

    Full syllabus

    Partial Differentiation
    Chain Rule for functions of two variables. Small increments. Concept of a partial differential equation.
    Statistical Methods
    Moments, correlations. Linear regression. Tests (Student t, chi-squared).
    Basic Vector Calculus
    Scalar and vector fields. Gradient, divergence, curl, Laplacian.
    Fourier Series
    Periodic functions. Trigonometric series. Fourier coefficients. Examples. Even and odd functions. Cosine and sine series.
    Partial Differential Equations
    Laplace’s equation. Wave equation. Heat conduction equation. Separation of variables. Boundary conditions. Examples.

    Reading list

    Type Author(s) Title Library Blackwells Amazon
    B Kreyszig Advanced Engineering Mathematics
    B O'Neill Advanced Engineering Mathematics
    B Stroud Engineering Mathematics 510.2462 (S) Blackwells Amazon

    (A = essential, B = recommended, C = background.)

    Most books on reading lists should also be available from the Blackwells shop at Jessop West.