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Prof Adam Ostoja-Ostaszewski

This course is compulsory on the BSc in Actuarial Science, BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available on the BSc in Economics, BSc in Management and MSc in Economics (2 Year Programme). This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Students should ideally have taken the course Mathematical Methods (MA100) or equivalent, entailing intermediate-level knowledge of calculus (proficiency in techniques of differentiation and integration)

This course develops ideas first presented in MA100. It 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, to a level of detail dependent on time constraints.

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Autumn Term.

Written answers to set problems will be expected on a weekly basis.

Useful background texts:

Adam Ostaszewski, Advanced Mathematical Methods, (Cambridge University Press 1999)

Ken Binmore and Joan Davies, Calculus, Concepts and Methods (Cambridge University Press 2002);

Robert C. Wrede and Murray R. Spiegel, Advanced Calculus (McGraw-Hill Education; 3rd edition 2010).

Exam (100%, duration: 1 hour and 30 minutes) in the January exam period.