In the majority of problems arising in applied mathematics, integrals and differential equations occur which cannot be evaluated or solved exactly and/or...

In the majority of problems arising in applied mathematics, integrals and differential equations occur which cannot be evaluated or solved exactly and/or expressed in terms of known functions. The aim of this course is to develop analytical techniques which enable insight into the structure and properties of solutions of differential equations and the values of integrals to be obtained and thereby provide analytical support to direct numerical evaluation.

This module consists of two parts: first an introduction to programming for the mathematical sciences (4 weeks) and then an introduction to multivariable...

This module consists of two parts: first an introduction to programming for the mathematical sciences (4 weeks) and then an introduction to multivariable calculus (5 weeks). Programming is becoming an increasingly important tool for mathematicians both in industry and in research. In view of this, some elements of basic scientific computation should be part of any modern undergraduate curriculum in Mathematics. Multivariable calculus on the other hand is of fundamental importance in a variety of fields of pure and applied mathematics such as electromagnetism, fluid mechanics, differential geometry and integration theory. The aim of the first part is to introduce the students to the ideas of computer programming and its uses in scientific computing for science and its applications. The programming language Python will be considered in the course, but the underlying principles are general. Students should learn how to write accurate programs for the computational solution of mathematical problems. The aim of the second part is to introduce the students to the ideas of the calculus of several variables, and to develop their understanding of functions of several variables, their derivatives and integrals.

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