Calculus and Linear Algebra 2 (MTHS130)

Learning outcomes

Upon completion of this unit, students will be able to:

1. identify and apply appropriate techniques of integration, such as integration by parts, substitution, and partial fractions, to a range of functions of one variable;
2. identify and apply appropriate tests for convergence of a range of infinite series, and relate this concept to the power series expansion and approximation of smooth functions;
3. relate the concept of implicit parametrisation to the loci of a range of plane curves as represented in either cartesian or polar coordinates, and apply this with integration to compute arc-length;
4. identify and apply appropriate techniques to solve elementary differential equations of first or second order, placed in the context of specific mathematical models from physical and biological science; and
5. compute determinants, eigenvalues and eigenvectors of matrices in terms of real, or more generally, complex numbers where necessary, and appreciate their significance in mathematical modelling.