Module Content

The module covers

  • Limits and continuity (8 lectures),
  • The derivative of a function (8 lectures),
  • The anti-derivative of a function (8 lectures),
  • and explains how these topics can be applied to problems such as

  • existence of two global positions with equal air pressure,
  • rates of change problems,
  • population dynamics.

Module Coordinates

  • Lecturer: Prof Graham Ellis
  • Lectures: Mon 1pm in IT250 and Tue 10am in the Anderson Theater.
  • Tutorials: Workshops begin on Monday 17th September. Details can be found here.
  • Recomended text: The MA180 calculus lectures are based on the textbook: "Calculus, early transcendentals " by James Stewart (Sixth Edition). Only so much of an explanation can be achieved in lectures, and this book can be used to reinforce (or maybe even clarify!) explanations given in lectures. It also contains many problems (some with fully worked solutions) on which you can practice. Even if you drop maths in second year, this will be a handy book for your scientific bookshelf. And if you continue with maths in second year then you'll be able to use the book again then.
  • Problem sheet: available here.
  • Module Website: Information and module documents will be posted to this site, which is linked from the Blackboard Calculus MA180/MA185/MA190(Semester I) pages. Blackboard will also be used for announcements and for posting grades.

Module Assessment

MA180 and MA190 students:

  • The end of semester exam is worth 60% of the total Semester I assessment. It will consist of three questions corresponding to the above three topics. A model exam paper is available here.
  • The continuous assessment is worth 40% of the total Semester I assessment. It will consist of six online problem sheets which will be made available here. Submission deadlines are strict. There are about 10 questions per problem sheet and to score 100% on the Semester I CA component you need to submit 50 or more correct answers.
A similar arrangement holds for MA180/MA190 in Semester 2 and in order to pass the module students must score a pass on the the year's continuous assessment and also score a pass on the weighted average of the year's continuous assessment and two end of semester exams.

MA185 students:

  • The end of semester exam is worth 100% of the total score returned for the MA185 module. It will consist of three questions corresponding to the above three topics. A model exam paper is available here.
  • The associated continuous assessment contributes towards 50% of the score returned for the MA187 Mathematical Skills module. The continuous assessment in Semester 2 contributes towards the remaining 50% of the MA187 assessment. The Semester I continuous assessment will consist of six online problem sheets which will be made available here. Submission deadlines are strict. There are about 10 questions per problem sheet and to score 100% on the Semester I CA component you need to submit 50 or more correct answers.

Supplementary Material and News

CLICKER OPINION POLLING may be used in some lectures.

WHAT IS MATHEMATICS?

I'm not too sure of the answer. But whatever it is it is possibly something a bit larger than what was taught in your school mathematics classes. If you are interested in the question then you should browse this article by Fields Medallist William Thurston. He won the Fields Medal for his work in geometry. You could also take a look at the lovely little book A Mathematician's Apology by G.H. Hardy which is available online here.

WHAT ARE THE EMPLOYMENT PROSPECTS FOR A MATHS GRADUATE?

Have a look at this link to answer this question.

STUDENT FEEDBACK

I'll place student feedback here.

Lecture Notes

Lecture Notes
Lecture Summaries
1
We considered a stone being dropped from the top of the Eiffel Tower. We assumed that the distance at time t is 4.9t2 (something physicists tell us should be true). We used the formula y= 4.9t2 to begin a discussion of functions. A function assigns one output to each input. We then asked the question: what is the speed of the stone at time t=2 seconds? To answer this we used the notion a limit

For a more detailed summary of what calculus is all about, read the section "A Preview of Calculus" in Stewart, pages 2-9,
2
We recalled that a function f:D--->C consists of a domain D, a codomain D and a rule for assigning precisely one element of the codomain to each element of the domain. When the domain and codomain are not explicitly specified then we just take D to be the largest subset of the reals for which the "function rule" makes sense, and we just take C to be the set of all real numbers. We recalled that functions can be represented by graphs and we studied some examples. During the examples we met concepts such as "horizonal asymptote", "vertical asymptote", "x-intercept", "y-intercept", "range of a function".

For more on the basics of functions read Stewart, Section 1.1.
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