MAS250 Mathematics II (Materials)

Note: This is an old module occurrence.

You may wish to visit the module list for information on current teaching.

Semester 1, 2018/19 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


    Office hours

    1-2pm on Wednesdays, but you are welcome 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

    • 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.

    Timetable

    Mon 09:00 - 09:50 lecture   Hicks Lecture Theatre 3
    Mon 10:00 - 10:50 tutorial (group MT) Hicks Lecture Theatre 3
    Wed 09:00 - 09:50 lecture   Hicks Lecture Theatre 3
    Thu 16:00 - 16:50 lecture   Hicks Lecture Theatre C