Course Catalogue

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This course introduces the basic theory of functions of a single variable. Topics include function, limit and continuity; differential calculus of one variable functions; integral calculus of one variable functions and differential equations with constant coefficients.

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 will be used when calculating the resit grade.

This course aims to provide a mathematical foundation for functions of a single variable encountered throughout engineering, including both theory and extensive practice.

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

■ find the limits of functions; analyse the continuity of a function, classify discontinuous points and describe the general properties of a continuous function in closed interval;

■ calculate first and higher-order derivatives, find the derivative of an implicit function, and apply derivatives to solve extreme value problems;

■ explain the concept of a differential, and derive a linear approximation of a function;

■ explain the concept of indeterminate form, and evaluate limits using l'Hôpital's rule;

■ describe the concepts of primitive function and indefinite integral, and apply basic integration formulas;

■ describe the concept of definite integral, prove the fundamental theorem of Calculus, use the substitution rule and integration by parts; describe the geometrical and physical applications of definite integrals;

■ describe the basic concepts of differential equations and solve separable differential equations, first-order and second-order linear differential equations, and selected nonhomogeneous linear differential equations; apply linear differential equations with constant coefficients to solve related problems in engineering.

Students must submit at least 75% by weight of the components (including examinations) 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.