Advanced Calculus

• Credit value: 15 credits at Level 6
• Convenor: Maya Thompson
• Assessment: coursework (20%) and a two-hour examination (80%)

In this module you will learn advanced calculus techniques, focusing on calculus of several variables. We will cover material on calculus of more than one variable, including partial differentiation and multiple integrals, giving you a thorough grounding in these concepts.

The module is studied via distance learning. Each week, you will be guided through a series of learning steps. These include short instructional videos, online quizzes to test your understanding, livestreamed face-to-face examples classes, full course notes, and exercises to try at home.

Indicative syllabus

• Functions and differentiation: limits, formal definition of the derivative, partial differentiation, tangent planes, directional derivatives
• Integration: double integrals, splitting the integral, changing the order of integration, polar coordinates
• Optimisation problems: stationary points, Lagrange multipliers, the nature of stationary points
• Further concepts in partial differentiation: the chain rule, Taylor polynomial approximation of a function
• Ordinary differential equations: first order differential equations, exact differential equations and second order differential equations with constant coefficients

By the end of this module, you will:

• have knowledge and understanding of, and be able to use, mathematical methods and techniques
• have knowledge and understanding of a range of results in mathematics
• appreciate the need for proof in mathematics, and be able to follow and construct mathematical arguments
• understand the importance of assumptions and have an awareness of where they are used and the possible consequences of their violation
• appreciate the power of generalisation and abstraction in the development of mathematical theories.