Courses :: Module, MATHEMATICS I

	Overview
	Indicative Syllabus • Introduction, motivation and scope of course. • Number systems • Complex numbers • Complex conjugate • Exponential and polar form • Inequalities • Sequences and series • Arithmetic and geometric series • Finite and infinite sums • Convergence • Limits and continuity • Maclaurin and Taylor series • Differential calculus • Tangents to curves • L'Hopital's rule • Sum, product, quotient and chain rules for derivatives • Critical points, maxima, minima and points of inflexion • Integral calculus • Integrals as areas and limits of sums • Definite and indefinite integrals, integration techniques • Applications of Integration • Calculation of lengths, areas and volumes • Mean and RMS values • Introduction to numerical integration • Differential equations • First order differential equations • Introduction to second order differential equations

Overview

Indicative Syllabus • Introduction, motivation and scope of course. • Number systems • Complex numbers • Complex conjugate • Exponential and polar form • Inequalities • Sequences and series • Arithmetic and geometric series • Finite and infinite sums • Convergence • Limits and continuity • Maclaurin and Taylor series • Differential calculus • Tangents to curves • L'Hopital's rule • Sum, product, quotient and chain rules for derivatives • Critical points, maxima, minima and points of inflexion • Integral calculus • Integrals as areas and limits of sums • Definite and indefinite integrals, integration techniques • Applications of Integration • Calculation of lengths, areas and volumes • Mean and RMS values • Introduction to numerical integration • Differential equations • First order differential equations • Introduction to second order differential equations

	Learning Outcomes
	On successful completion of the module, students should be able to: add, subtract and multiply complex numbers and Convert complex numbers between Cartesian and polar forms; differentiate all commonly occurring functions including polynomials, exponential functions, trigonometric functions, hyperbolic functions and combinations thereof; distinguish between the two main meanings of a derivative, namely the derivative as a tangent and the derivative as a rate of change; integrate certain standard functions, constructed from polynomials, exponential functions, trigonometric functions, hyperbolic functions and combinations thereof; distinguish between the two main meanings of integration, namely the integral as the inverse of the derivative and the integral as the area under a curve; apply Taylor series to numerically approximate functions and Apply Simpson's rule to numerically evaluate integrals; solve simple first and second order ordinary differential equations; apply and select the appropriate mathematical techniques to solve a variety of associated engineering problems.

Learning Outcomes

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes The continuous assessment mark is carried forward to the Autumn examinations as there is no facility available for repeating the continuous assessment components of the course. University scheduled written examination (Autumn): 120 minutes Is Supplemental Continuous Assessment registration permitted? No Is Supplemental Continuous Assessment capped? No

Autumn Supplementals/Resits

	Timetable
	This timetable is not currently available, please contact the International Engineering College Department.

Timetable

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Courses / Module

MATHEMATICS I