Module Code - Title:

MA4602 - SCIENCE MATHEMATICS 2

Year Last Offered:

2025/6

Hours Per Week:

Lecture

3

Lab

0

Tutorial

1

Other

0

Private

6

Credits

6

Grading Type:

N

Prerequisite Modules:

MA4601

Rationale and Purpose of the Module:

To develop the fundamental concepts and basic tools of calculus. To introduce applications of calculus in science and technology. To develop and integrate the basic scientific mathematical skills.

Syllabus:

[Integration and applications:] indefinite integral as antiderivative; integration by substitution; definite integral as area; Fundamental Theorem of Calculus; integration by parts; calculation of areas; applications in science. Introductory treatment of SimpsonÆs Rule. [Functions of the Calculus:] domain and range; inverse trigonometric functions, hyperbolic functions, their graphs and derivatives. [Curve sketching:] symmetries; intercepts; restrictions on range; discontinuities; uses of first and second derivatives; turning points; behaviour for large and small x ; asymptotes. [Series:] sequences; arithmetic and geometric series; infinite series and convergence; ratio and comparison tests; power series; Maclaurin and Taylor series; addition, multiplication, differentiation and integration of power series; use as approximation of a function; limits, l'Hopital's rule.

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

On Successful conclusion of this module students should Have acquired a working knowledge of the important elementary functions of calculus. Be able to compute limits. Be able to compute and estimate definite integrals Be able to apply knowledge of integration to solve problems. Be able to sketch curves of varying complexity.

Affective (Attitudes and Values)

N/A

Psychomotor (Physical Skills)

N/A

How the Module will be Taught and what will be the Learning Experiences of the Students:

Lecture notes,tutorials with large input from the Mathematics Learning Centre.

Research Findings Incorporated in to the Syllabus (If Relevant):

Prime Texts:

Glynn James, et al (1992) Modern Engineering Mathematics , Prentice Hall

Stroud,K.A.,Booth,D. (2001) Engineering Mathematics , Palgrave

Other Relevant Texts:

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

alan.hegarty@ul.ie