Courses :: Module, INTEGRATION

	Overview
	Module Objective: To complete the student�s grasp of the techniques and skills of one-variable calculus. It proceeds largely in the same non-rigorous spirit as the Leaving Certificate course, with the emphasis on problem-solving techniques. Some time will be spent as needed on prerequisites, including Differentiation, the Fundamental Theorem of Calculus, the Mean Value theorem, Riemann Sums, the notion of continuity and continuous functions. Certain limits will also be emphasised, in particular those involving trigonometric functions. Some applications of integration: volume by parallel cross-sections, volume by the shell method. Elementary transcendental functions. Logs, exponentials, trigonometric functions and their inverses. Techniques of Integration: Parts, partial fractions, powers and products of sines and cosines. Numerical integration. Improper integrals.

Overview

Module Objective:
To complete the student�s grasp of the techniques and skills of one-variable calculus. It proceeds largely in the same non-rigorous spirit as the Leaving Certificate course, with the emphasis on problem-solving techniques.

Some time will be spent as needed on prerequisites, including Differentiation, the Fundamental Theorem of Calculus, the Mean Value theorem, Riemann Sums, the notion of continuity and continuous functions. Certain limits will also be emphasised, in particular those involving trigonometric functions. Some applications of integration: volume by parallel cross-sections, volume by the shell method. Elementary transcendental functions. Logs, exponentials, trigonometric functions and their inverses. Techniques of Integration: Parts, partial fractions, powers and products of sines and cosines. Numerical integration. Improper integrals.

	Learning Outcomes
	On successful completion of the module, students should be able to: State and use some of the classical theorems of calculus in one variable. Integrate the basic functions and combinations of such functions using standard techniques. Use integrals to find areas and volumes. Evaluate integrals using numerical techniques. Use the methods from the course to solve problems. State definitions and theorems covered in the course.

Learning Outcomes

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes University scheduled written examination (Autumn): 120 minutes, On-campus

Autumn Supplementals/Resits

	Pre-Requisites
	+H2 in HLC

Pre-Requisites

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INTEGRATION

Semester 1

Semester 2