Engineering Mathematics

Learning Outcomes

Integration • Line integrals and conservative vector fields. • Green’s Theorem in the Plane • Surface and triple Integrals • Stokes’s theorem • Divergence Theorem of Gauss • Boundary and initial conditions. Ordinary Differential Equations • Constant coefficient linear ODEs. Euler equations. • Homogeneous linear ODE with constant coefficients • Nonhomogeneous ODEs Matrix algebra: • rank; eigenvalues and eigenvectors; Symmetric, Skew-Symmetric, and Orthogonal Matrices; Eigenbases. Diagonalization. Quadratic Forms Further Calculus: • Chain rule for partial derivatives; higher partial derivatives; total differentials and small errors • Partial Differential Equations. • Separation of variables • Use of Fourier Series • Two-Dimensional Wave Equations • Rectangular Membrane. Double Fourier Series • Heat Equation and the Laplacian • Solution by Fourier Series. • Steady Two-Dimensional Heat Problems. • Laplace’s Equation in Cylindrical and Spherical Coordinates. Numerical Mathematics • Discrete numerics, sampling, DFT • Numerical approximation, numerical integration, numerical differentiation • Use of MATLAB in numerical caculaitons: curve fitting, numerical simulation of solutions to equations Systems • Systems of ODEs as Models in Engineering Applications • Basic Theory of Systems of ODEs. • Matrix Solutions to coupled second order ODEs • Nonhomogeneous Linear Systems of ODEs • The method of reduction of order. • The method of variation of parameters. • Sturm-Liouville Theory. Examples of Sturm-Liouville problems. • Eigenfunction expansions.

Taught using a blended approach, incorporating “flipped mode” teaching and traditional problem classes. • Comprehensive explanatory video lectures on each topic • Case study recordings • Weekly discussion tutorials and seminars • Case study based problem sheets • Weekly intensive problem classes – problem sheets worked on • Self-study notes for each topic. • Self-testing on each block • Mini-test at end of each block • Past examination papers and solutions. • Computing Labs on data analysis and numerical Computation