UO Mathematical Methods for Engineers 2

The aim of this course is to develop and extend mathematical concepts relevant to mechanical, civil and electrical engineering using both analytic and software approaches. the course includes Applied Linear Algebra
Vectors and matrices, linear dependence of vectors, linear systems of equations, row operations as matrix multiplications, row reduced echelon form (RREF), matrix inverse, determinants, eigenvalues and eigenvectors of a square matrix, degenerate eigenvalues, diagonalisation of a square matrix, application to coupled systems of ordinary differential equations with examples from mechanics and ecology. MATLAB exercises.
Ordinary Differential Equations (ODEs) and Techniques of Integration
Linear and separable differential equations of first order. Inverse trigonometric functions and their derivatives, hyperbolic functions. Techniques of integration: Integration by parts, integration using partial fractions, trigonometric integrals, trigonometric substitutions. Improper integrals. Applications of integration in mechanics: area, volume of regular bodies, centre of mass, moment of inertia, work. Linear differential equations of second order: reduction of order, homogenous and inhomogeneous equations, constant coefficient ODEs, applications in mechanics and electrical circuits. MATLAB exercises.