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.

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.