Mathematical Methods for Engineers 2

In this course, students will develop and extend mathematical concepts relevant to mechanical, civil and electrical engineering using both analytic and software approaches. Module 1: Linear Algebra (Applied) Vectors and matrices, linear dependence of vectors, linear systems of equations, row operation 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. Module 2: ODE's 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 o.d.e's, applications in mechanics and electrical circuits. MATLAB exercises.