production

Course Overview

This course follows Engineering Mathematics 1 in introducing all the mathematical objects and techniques needed by engineers.  It  has three parts:

• Matrices: definitions, operations, inverse and determinant; application to systems of linear equations.
• Ordinary differential equations: 1st order (linear and separable), 2nd order with constant coefficients, forced oscillations and resonance.
• Functions of two variables: partial derivatives and extrema, the chain rule, the heat equation and the wave equation.

Course Details

Study Type Level Undergraduate 2 First Sub Session 15 credits (7.5 ECTS credits) Aberdeen No Dr Richard Hepworth

Qualification Prerequisites

• Either Programme Level 1 or Programme Level 2

None.

No

Course Description

1. Matrices: Basic definitions and notation. Algebra of matrices: multiplication by scalar, addition and subtraction of matrices, multiplication. Zero matrix, identity matrix, transpose, symmetric & anti-symmetric matrices. The meaaning of matrix inversion. Inverse of 2x2 matrix. Determinants, with some work on row & column operations together with general expansion formula. Systems of linear equations. Geometrical interpretation. Discussion of various possibilities: unique solutions, no solution, infinitely many solutions. Gaussian reduction. Solution of systems of linear equations by formal Gaussian reduction with partial pivoting down to upper triangular form followed by backsubstitution.
2. Ordinary Differential Equations: First Order: Separations of variables and integrating factors. Second Order: Theory and applications of linear equatinos with constatn coefficients. Revision of differentiation and integration: differentiation as linear approximation; examples of differential equaations; linearity. First and second order linear differential equations with constant coefficients: initial value conditions; solutions of homogenous equations andinvestigation of the form of the solution; solution of non-homogeneous equations using complementary function and particular integral; forced oscillations and resonance.
3. Partial Differentiation: Introduction to partial differentiation; the heat equation and wave equation as examples of two-variable (space and time) problems; partial differentiation as linear approximation; representation of a function of two variables by a surface; estimation of small errors; the chain rule; 2nd order approximation for a function of two variables; maxima, minima and saddle-points; application of the chain rule to solve the wave equation

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

• 1 Seminar during University weeks 8 - 18
• 1 Tutorial during University weeks 9 - 18

Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

2x coursework (30% each)

Timed online test (40%)

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

Compatibility Mode

We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.