Mathematics I

Module aims

This module introduces mathematics as a logical and structured discipline, focussing on providing the mathematical knowledge and skills required for their First Year Civil Engineering programme.  
 
It provides a basis for the more advanced mathematical techniques which are required in subsequent years of the programme, with an emphasis on application of mathematics to the solution of engineering problems. 

Learning outcomes

· Characterise functions and apply differential calculus to the solution of optimisation, related rates and approximation problems.  
 
· Manipulate complex numbers in algebraic, polar and exponential forms. Use MacLaurin and Taylor series to establish approximations to functions.  
 
· Integrate functions using a variety of techniques and apply them to the determination of areas, volumes and average values of functions.  
 
· Find the inverse of matrices by the Gauss-Jordan method and the solution of linear algebraic equations by Gaussian elimination and LU factorisation.  
 
· Solve certain first and second order ordinary differential equations. 

Module syllabus

Functions of One Variable: Definitions, Limits, Continuity, Differentiation, Curve Sketching & Applications Complex Numbers Series: 
 
Definitions, Taylor, Maclaurin & Binomial Series Integration: Techniques, Definite Integral, Improper Integral & Applications Parametric Functions, Polar Coordinates & Hyperbolic Functions Functions of More Than One Variable:  
 
Derivatives, Directional Derivative, Gradient & Applications Matrices & Vectors:  
 
Basic Operations, Geometric Interpretation, Rank, Systems of Linear Equations, Gaussian Elimination Determinants, Cramer’s Rule, Inverse of a Matrix & Gauss-Jordan Elimination Eigenvalues and Eigenvectors, Diagonalisation and Powers of Matrices Vector Algebra: Scalar & Vector Products, Equations of Lines & Planes First order ODEs: Formation, Linear ODEs and Integration Factors, Exact ODEs & Applications Second Order ODEs: Double and Complex Roots, Undetermined Coefficients 

Assessments

Assessment Information is provided separately in Blackboard Learn.

Reading list

Module leaders

Dr David Taborda