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### 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 osciallations 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) None. No Dr Jean-Baptiste Gramain

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### 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

### Further Information & Notes

The course is compulsory for all 2nd year Engineering students.

It is only available to Engineering students.

### Contact Teaching Time

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

### Summative Assessments

1st Attempt: One written examination of three hours duration (80%) and in-course assessment (20%).

Resit: One written examination of three-hours duration (100%). Mark awarded is the higher of (a) the resit examination paper (80%) and earlier continuous assessment (20%) OR (b) the resit examination paper alone (100%)

### Formative Assessment

A class test in the form of an online series of multiple choice questions will be provided. After which they will be given marks and the correct answers and the correct reasoning

### Feedback

The students will be given feedback in the tutorials concerning their ability to solve mathematics problems.

The class tests will also allow specific and generic feedback to be communicated automatically.

Whole-class feedback will be provided via MyAberdeen, where we will also put a mock exam to give the students the chance to self-assess their own performance.

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