Mathematics and Applications 2

This course continues on from MATH1013. It emphasises an understanding of the fundamental results from calculus and linear algebra which both can be applied across a range of fields including the physical and biological sciences, engineering and information technologies, economics and commerce, and can also serve as a base for future mathematics courses. Many applications and connections with other fields will be discussed although not developed in detail. Topics to be covered include: Calculus - Integration and techniques of integration, including multiple and iterated integrals. Sequences and series. Functions of several variables - visualisation, continuity, partial derivatives, and directional derivatives. Lagrange multipliers. Linear Algebra - theory and application of Euclidean vector spaces. Vector spaces: linear independence, bases and dimension; eigenvalues and eigenvectors; orthogonality and least squares.