A STEP class

The curve C has polar coordinates satisfying the differential equation

d2r/dθ2 + 4r = 5sin(3θ)

for π/5≤θ≤3π/5. When θ=π/2, we have r=1 and dr/dθ=−2. Show that C forms a closed loop whose area is

π/5+25(sin(π/5)-sin(2π/5))/48.

a curve described in polar coordinates

This STEP preparation course, a joint effort between Sheffield's School of Mathematics and Statistics and the FMSP, will provide a systematic introduction to the advanced problem solving skills required for STEP examinations.

Classes will be delivered by staff with prior experience in delivering STEP preparation. Some sessions will introduce the additional syllabus material required for the STEP examinations. The course will have fifteen sessions (twelve pure mathematics and three applied). The pure mathematics sessions are on a Tuesday; the applied sessions will be scheduled by January 2017. Also to be scheduled by January for the late Spring are mock examinations in the style of STEP 1, 2 and 3.

This course is free to all students holding university offers who can demonstrate the necessary commitment. Participating students are expected to solve problems in class on whiteboards or on paper. To book places on this course or for further enquiries contact James Cranch at somas-outreach@sheffield.ac.uk.

Timetable

Subject Date and time Venue
Proof Tuesday 24th January 2017 (1600–1800) Hicks E36
Division by zero Tuesday 31st January 2017 (1600–1800) Hicks E36
Coordinate geometry Tuesday 7th February 2017 (1600–1800) Hicks E36
Trigonometry Tuesday 14th February 2017 (1600–1800) Hicks E36
Half term in Sheffield: no class
Inequalities Tuesday 28th February 2017 (1600–1800) Hicks E36
Calculus Tuesday 7th March 2017 (1600–1800) Hicks E36
Vectors Tuesday 14th March 2017 (1600–1800) Hicks E36
Numbers, sequences, series
(with Dr Evgeny Shinder)
Tuesday 21st March 2017 (1600–1800) Hicks E36
Applied mathematics
(with Prof Alan Zinober)
Monday 27th March 2017 (1600–1800) Hicks G7
(STEP 3) Hyperbolic functions Tuesday 28th March 2017 (1600–1800) Hicks E36
Easter holidays: no classes
Applied and probability 1
(with Prof Alan Zinober)
Monday 24th April 2017 (1600–1800) Hicks G7
(STEP 3) Complex numbers
(with Dr Fionntan Roukema)
Tuesday 25th April 2017 (1600–1800) Hicks E36
(STEP 3) Proof, series, trigonometry Tuesday 2nd May 2017 (1600–1800) Hicks E36
Applied and probability 2
(with Prof Alan Zinober)
Wednesday 3rd May 2017 (1600–1800) Hicks G7
(STEP 3) Differential equations Tuesday 9th May 2017 (1600–1800) Hicks E36
Mock exam (STEP 1) Tuesday 23rd May 2017 (1330-1630) Hicks LT 11
Mock exam (STEP 2) Wednesday 24th May 2017 (1330-1630) Hicks LT 11
Mock exam (STEP 3) Thursday 25th May 2017 (1330-1630) Hicks LT 11