Mathematics 1S MATHS1002

  • Academic Session: 2018-19
  • 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.