Courses / Module

INTRODUCTION TO CALCULUS (A)

Module code: MT105A
Credits: 7.5
Semester: 1
Department: MATHEMATICS AND STATISTICS
International:

	Overview
	Objectives: To introduce students to Differential Calculus in One Real Variable. Overview: Why study calculus? Sets and Functions. Review of Exponentials, Logarithms and Trigonometry. Inequalities, Limits: Idea of a limit, definition of a limit, continuity. Derivatives: Definition of a derivative, tangents, product rule, chain rule, quotient rule, higher derivatives, implicit differentiation, Newton's method for roots, exponential and logarithmic functions. Applications of derivatives: Maxima and minima, monotonic functions and the first derivative test. Concavity and points of inflection. Symmetry and curve sketching. Applied max-min problems and related rates.

Overview

Objectives: To introduce students to Differential Calculus in One Real Variable.

Overview: Why study calculus?
Sets and Functions. Review of Exponentials, Logarithms and Trigonometry. Inequalities, Limits: Idea of a limit, definition of a limit, continuity. Derivatives: Definition of a derivative, tangents, product rule, chain rule, quotient rule, higher derivatives, implicit differentiation, Newton's method for roots, exponential and logarithmic functions. Applications of derivatives: Maxima and minima, monotonic functions and the first derivative test. Concavity and points of inflection. Symmetry and curve sketching. Applied max-min problems and related rates.

	Learning Outcomes
	On successful completion of the module, students should be able to: Describe and manipulate functions. Evaluate limits of basic functions.. Obtain derivatives of basic functions and combinations of such functions. Solve max-min problems. Use Newton's method Sketch curves of the basic functions and combinations of such functions. Use the methods from the course to solve problems. State definitions and theorems covered in the course.

Learning Outcomes

Teaching & Learning methods

Assessment

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes Continuous assessment mark is carried forward to the Autumn. University scheduled written examination (Autumn): 120 minutes, On-campus

	Pre-Requisites
	Exposure to sets, functions, algebraic geometry of lines and circles, elementary algebra and trigonometry. Previous exposure to differential calculus is helpful, but not essential. Ordinary Level Leaving Certificate Mathematics is sufficient.

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Courses / Module

INTRODUCTION TO CALCULUS (A)

Semester 1

Semester 2