Handbook

MATH1251 builds on the calculus and linear algebra in MATH1151.  Matlab is used throughout.  In linear algebra, abstract vector spaces and linear transforms are introduced so that the study of vectors and matrices in MATH1151 can be applied to a wide range of applications. The concepts such as spans, linear independence, basis, dimension, kernel, image are studied in both abstract and concrete examples, with links made to data fitting and differential equations.  Eigenvalues and eigenvectors are studied along with their applications to Markov chains and systems of differential equations. In calculus, further techniques of integration and the theory and applications of first and second order ordinary differential equations are studied, including existence and uniqueness results and numerical methods. Double integrals, including change of variables are introduced. Convergence results for sequences and series are developed along with Taylor polynomials in both one and two variables and their applications.  Optimisation techniques, including classification of critical points and Lagrange multipliers are studied.