• Term taught 
  •             Michaelmas term 2017-2018
  • Lecturer
  •             Dr. Victoria Lebed
                E-mail: lebed (at) maths.tcd.ie
                Office: 1.5, School of Mathematics
                Any questions or remarks or calls for help are welcome!
  • Schedule
  •             Monday 12:00 (MacNeil Theatre, Hamilton Building)
                Tuesday 12:00 (MacNeil Theatre, Hamilton Building)
                Friday 9:00 (MacNeil Theatre, Hamilton Building)
  • Tutorials and homework
  •              Every Friday your homework assignment appears here and on the tcd.blackboard page of the module. It is to be handed in at the end of the tutorial of the following week. During the tutorial you can discuss with the tutors the homework and/or the problems from a supplementary problem sheet.
                 Homework problems: HW1 (due: week 2), HW2 (due: week 3), HW3 (due: week 4).
                 Final exam problems will be very close to your homework assignments, so spending some time on your homework and trying to solve problems independently of your classmates is a key to success at the exam!
  • Plan
  •             1. Introduction. The notion of a function. Slides
                2. Domain and range of a function. Digression on intervals, rays, and operations on them. Slides
                3. Building new functions from old ones: arithmetic operations and composition. Slides
                4. Functions with symmetries. Parametric families of functions. Slides
                5. Classical functions: polynomial, rational, algebraic, trigonometric. Slides
                6. Inverse functions: definition, examples, uniqueness, x-y symmetry. Slides
                7. Inverse functions: graphs, existence, inverse trigonometric functions. Cf. slides from Lecture 6.
  • Grading
  •              Homework  20% +  final exam 80%.
                 There will be a single exam and a single mark for the module MA1S11, which means that half of the exam paper will be about calculus and the other half about linear algebra/discrete mathematics (the part taught by Prof. McLoughlin).

  • Suggested reading
  • You can borrow a copy from the Hamilton Library, or buy one from second-year students (for this you might have a look at the TCD noticeboard). If you are going to buy a new one, avoid the editions subtitled "Single Variable". They contain only the first 8 or 9 chapters, and you will need further chapters of the more complete editions for the second semester (MA1S12).

  • Topics covered
  •     Functions
        Limits and Derivatives
        Integration
        Trigonometrical, Logarithmic, and Exponential Functions
        Applications

  • If you need help
  •             Ask me directly after class, e-mail me your questions or make an appointment, talk to your tutors, attend the School of Mathematics help room (the New Seminar Room in the School of Mathematics, 1-2pm Monday to Friday). Remember that the whole system is there to help you get the best out of the classes!