Course Catalogue

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This course extends the basic operation skills of calculus to infinite series, differential calculus for multivariable functions, integral calculus for multivariable functions, and integration of multi-vector valued functions.

Course will be delivered continuously in the traditional manner at UESTC.

Mandatory Entry Requirements

None

Recommended Entry Requirements

None

None

None

Assessment

Examinations 75 % - 25% closed-book mid-term exam, 50% closed-book final exam.

Coursework 25% - attendance, homework and quizzes 

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.

Due to the nature of the coursework and sequencing of courses, it is not possible to reassess the coursework.

The initial grade on coursework project will be used when calculating the resit grade.

The aim of this course is to ensure that students are competent in higher mathematics encountered throughout engineering, particularly functions of more than one variable, including both theory and extensive practice.

By the end of this course students will be able to:

■ apply calculus to parametric functions and vector-valued functions; understand the inner and cross products of vectors, and apply them to lines and planes in space; introduce polar coordinates and related equations;

■ calculate partial derivatives, total differential and high-order partial derivatives of multivariable functions; find the derivative of implicit functions;

■ explain the concepts of directional derivative and gradient and calculate them in two and three dimensions; apply partial derivatives to find the tangent plane and normal line of a surface; locate extreme values of a multivariable function, both unconstrained and under given conditions, and apply the Lagrange multiplier method;

■ describe the meaning of double integrals (Cartesian coordinates and Polar coordinates) and evaluate them; similarly for triple integral (Cartesian coordinates, Cylindrical coordinates and Spherical coordinates);

■ explain the definition of line integrals for scalar-valued functions and vector fields, be aware that the results of a line integral depends on the path in general; determine that a line integral is independent of path in conservative fields;

■ apply Green's theorem to integrals in the plane; express given surfaces in an appropriate form and evaluate surface integrals over surfaces; apply the theorems of Green, Gauss and Stokes to line, surface and volume integrals and explain their significance in engineering;

■ state what is meant by a sequence and series, find limits of sequence; apply criteria for convergence of series with terms of the same sign or alternating sign; distinguish between absolute convergence and conditional convergence; establish conditions for convergence of power series, other functional series and Taylor series; derive Maclaurin expansions of elementary transcendental functions such as sin(x) and cos(x); apply direct and indirect expansion methods of some simple functions to applications of power series in approximate calculations.

Students must attend the degree examination and submit at least 75% by weight of the other components of the course's summative assessment.

Students should attend at least 75% of the timetabled classes of the course.

Note that these are minimum requirements: good students will achieve far higher participation/submission rates. Any student who misses an assessment or a significant number of classes because of illness or other good cause should report this by completing a MyCampus absence report.