# Mathematics 1S MATHS1002

• School: School of Mathematics and Statistics
• Credits: 20
• Level: Level 1 (SCQF level 7)
• Typically Offered: Semester 2
• Available to Visiting Students: Yes
• Available to Erasmus Students: Yes

#### Short Description

Mathematics 1S is intended to build on Mathematics 1R and to provide a further half-year's Mathematics course both for students who intend to specialize in Mathematics and for others.

#### Timetable

Four days weekly -10.00 am, 11.00 am or 4.00 pm; weekly tutorial; 5 laboratories.

#### Requirements of Entry

Pass in SCE Higher Mathematics or equivalent

#### Excluded Courses

Mathematics 1Y and 1T

#### Co-requisites

Mathematics 1R or 1X

#### Assessment

One examination (60%) (2 hours), (40%) assigned coursework.

Main Assessment In: April/May

#### Course Aims

Mathematics 1S is intended to build on Mathematics 1R and to provide a further half-year's Mathematics course both for students who intend to specialize in Mathematics and for others. It aims, in particular: a) to introduce the ideas and techniques used to study the behaviour of real functions. [These include the fundamental notions of function and limit, and the derived notions of continuity, differentiability, and integrability]. b) to extend students' knowledge and skills in algebra, geometry, and calculus; c) to explore logical matters relevant to Mathematics and to educate students in the notion of proof in Mathematics and in widely used techniques of proof.

#### Intended Learning Outcomes of Course

By the end of this course, students will be able to

■ articulate proofs of straightforward propositions, their contrapositives and converses

■ use proof by induction

■ make appropriate use of counterexamples

■ use the binomial theorem in various contexts, including those involving the trigonometric functions

■ perform the addition and subtraction of vectors and the multiplication of vectors by scalars

■ apply vectors to geometrical problems in 3 dimensions

■ calculate the scalar and vector products, including using the scalar and vector triple product

■ evaluate a wide range of integrals, using, when appropriate, change of variable, integration by parts, and partial fractions

■ solve first order O.D.E.s that are separable or linear and second order linear O.D.E.s with constant coefficients

■ apply suitable approximation techniques involving the Maclaurin series, Simpson's rule and the NewtonRaphson process

■ find the limit of a variety of functions.

#### Minimum Requirement for Award of Credits

[At least] 50% attendance at lectures and two-thirds participation in tutorials and 100% attendance for workshops.

Attendance at a minimum of 4 laboratories.

Completion of coursework.