Teaching Responsibility

LJMU Schools involved in Delivery:

LJMU Partner Taught

Learning Methods

Lecture

Module Offerings

3102CIT-SEP-PAR

Aims

This module aims to provide students with the mathematical knowledge, understanding and skills which are required to use mathematics as an analytical tool in engineering and technology subjects.

Learning Outcomes

1.
Understand the concept of limits and know the methods of finding limits.
2.
Understand the concept of derivatives and know the methods of finding derivatives.
3.
Represent functions in a graphical form.
4.
Understand the concept of integrals and know the methods of finding integrals
5.
Know how to solve a range of differential equations.

Module Content

Outline Syllabus:1. Functions, Limits and Continuity • Functions and elementary functions; • Limit of a sequence, limits of a function and limit laws; • Infinitesimal and infinity, infinitesimal order comparison; • Two important limit results (the squeeze theorem, the "e" limit); • Continuity; properties of continuous functions on closed intervals. 2. Single Variable Differential Calculus • Concepts of derivatives and derivative laws (including derivatives of high orders, inverse function derivation, composite function derivation, implicit function derivation and function derivation determined by parameter equations); • Concepts of differentials, differential laws and applications to the approximate calculation; • Related rates of change; • The mean value theorem (Fermat-RoUe-Lagrange-Cauchy); • Indeterminate forms and L'Hospital's rule; • Taylor's theorem; • Applications of derivatives to monotonicity, local and global extrema; • Applications of derivatives to concavity, inflection point, and curvature; • Function graphing. 3. Single Variable Integral Calculus • Definitions and properties of antiderivatives and indefinite integrals; • Integration by substitution and integration by parts; • Rational functions integration; • The fundamental theorem of calculus; • Improper integrals; • Numerical integration (the trapezoidal rule and Simpson's rule); • Applications of the definite integral (in geometry and physics). 4. Ordinary Differential Equations • Basic concepts of ordinary differential equations; • Separable differential equations; • Homogeneous equations; • First -order linear differential equations; • Exact differential equations; • Reducible high-order differential equations; • High-order linear differential equations; • Nonhomogeneous second-order differential equations with constant coefficients; • Introduction to Euler's method and the power series method.
Additional Information:The modules introduces students functions, limits and continuity, single variable differential and integral Calculus Ordinary, and differential equations. Classroom Performance is based on assessment activity in the classroom Reports are 2500 maximum word count. Examinations are 2 hour duration.

Assessments

Exam
Report