MAS250 Mathematics II (Materials)

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

Semester 1, 2019/20 10 Credits
Lecturer: Dr Nils Mole uses MOLE Timetable Reading List
Aims Outcomes Teaching Methods Assessment Full Syllabus

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


Outline syllabus




    Aims

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

    Learning outcomes

    • Solve first-order ordinary differential equations (variables separable, homogeneous, linear).
    • Solve second-order inhomogeneous ordinary differential equations with constant coefficients using trial functions for the particular integral.
    • Partially differentiate functions of two variables and be able to apply the chain rule.
    • 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 75% of assessment.
    Five marked homeworks for 25% of assessment.

    Full syllabus

    Ordinary Differential Equations
    First-order equations: variables separable, homogeneous and linear. Linear second-order equations with constant coefficients: complementary function and particular integral.

    Partial Differentiation
    Definition, second-order derivatives. Chain Rule for functions of two variables. Concept of a partial differential equation.
    Statistical Methods
    Moments, correlations. Linear regression.
    Basic Vector Calculus
    Scalar and vector fields. Gradient, divergence, curl, Laplacian.
    Fourier Series
    Motivation. Periodic functions. Trigonometric series. Fourier coefficients. Examples. Even and odd functions. Cosine and sine series.
    Partial Differential Equations
    Motivation with examples. 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.