MA212 Calculus Double Integral and MA212 Calculus Questions. There are 5 sets of practice questions and solutions totalling over 100 pages of questions and answers. These are all unseen unique questions that have been extended from the course content and module pack as well as lectures, past exam papers and homework. We highly recommend these notes for students who want extra practice and for those looking to understand the methods behind solving these questions.
This course develops ideas first presented in MA100. It is divided into two halves: calculus and linear algebra. The calculus half explores how integrals may be calculated or transformed by a variety of manipulations, and how they may be applied to the solution of differential equations. This aim is achieved by studying the following topics: Limit calculations. Riemann integral. Multiple integration. Improper integrals. Manipulation of integrals. Laplace transforms. Riemann-Stieltjes integral (permitting application of the Laplace transform to discrete and continuous probability distributions), to a level of detail dependent on time constraints. The linear algebra half covers the following topics: Vector spaces and dimension. Linear transformations, kernel and image. Real inner products. Orthogonal matrices, and the transformations they represent. Complex matrices, diagonalisation, special types of matrix and their properties. Jordan normal form, with applications to the solutions of differential and difference equations. An application to population dynamics. Singular values, and the singular values decomposition. Direct sums, orthogonal projections, least square approximations, Fourier series. Right and left inverses and generalized inverses.