Syllabus for Several Variable Calculus for Data Science

Learning outcomes

On completion of the course, the student should be able to:

• give an account of the concepts of limit, continuity, partial derivative, gradient and differentiability for functions of severable variables,
• parametrise curves and surfaces,
• compute partial derivatives of elementary functions,
• use partial derivatives to compute local and global extreme values - with and without constrains,
• outline the definition of the multiple integral, compute multiple integrals and use multiple integrals to compute volumes, centres of gravity, etc.,
• compute line integrals of vector fields in the plane,
• exemplify and interpret important concepts in specific cases,
• account for how the concepts in the previous paragraph are theoretically connected:
• express problems from relevant areas of applications in a mathematical form suitable for further analysis,
• use the theory, methods and techniques of the course to solve mathematical problems.

Content

Polar, cylindrical and spherical coordinates. Parameterisations of curves and surfaces.

Level curves and level surfaces. Arc length. Scalar and vector valued functions of several variables. Partial derivatives, differentiability, gradient, direction derivative, differential. Derivatives of higher order. The chain rule. Taylor's formula. Optimisation: local and global problems, problems with equality constraints. Multiple integrals, change of variables especially polar coordinates, improper integrals, applications of multiple integrals: volume, centres of mass, etc. Line integrals of vector fields. Green's theorem in the plane.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

This course cannot be included in the same degree as 1MA016, 1MA017, 1MA183 or 1MA324.