2019 Semester 1 - Unit Information for MATH1931: Calculus of one variable (SSP)
Classes
The Special Studies Program is formally attached to MATH1921 with one additional seminar and a special tutorial. In particular you attend:
- The same lectures as MATH1921;
- Seminar: Tuesday 4pm, New Law Room 022
- Tutorial: Thursday 10am, Carslaw Room 354 (replaces your MATH1921 tutorial).
The special topics in the seminar are independent of MATH1921. There will be three different topics presented by different lecturers.
The tutorial will be on the material in MATH1921
You will need all material for MATH1921. Check the MATH1921 Web page or the MATH1921 Unit Information Sheet on how to get these.
Special Topics
There will be three topics from various fields of mathematics and statistics presented by different lecturers:
- Weeks 2–5: Daniel Daners, Maps of the World
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The globe cannot be mapped onto a plane without distortion. We look at map projections of the world and study their properties like for instance area and angle distortions. We discuss suitability of some maps for navigation and other purposes.
- Weeks 6–9: Eduardo Altmann, Chaos in dynamical systems
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The goal of these four lectures is to learn how systems governed by known equations of motion, with no randomness, can still display an unpredictable temporal evolution. This seemingly contradictory phenomenon, known as deterministic chaos, was first discovered in Astronomy and Meteorology but is now known to appear in virtually all scientific disciplines. The complicated chaotic dynamics appears already in very simple (yet non-linear) equations, which we will study analytically and through simple computer simulations. Our excursion to understand chaos will lead us to some fundamental concepts in the mathematical theory of dynamical systems, such as attractors, bifurcations, invariant measure, Lyapunov exponents, and self-similarity.
- Weeks 10–13: Sharon Stephen, Introduction to fluid mechanics
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The applications of Newton's laws of motion to fluids leads to the mathematical models that govern the flow of air and water. The study of the mechanics of fluids is therefore basic to our knowledge of the world around us. The continuum hypothesis will be presented along with the topics of hydrostatics, Newtonian viscosity, conservation of mass, and Bernoulli's equation. Simple flows will be calculated.
Assessment
The final mark in MATH1931 is determined as follows:
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All assessments for MATH1921. For more detail look at the MATH1921 unit information sheet. This counts 80% of the total mark.
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Three equally weighted assignments, one on each special topics in the seminar. The three assignments count 10% towards the total mark. (bettermark applies if all assignments are handed in, otherwise no bettermark)
Assignment submission dates: 5 April (first topic), 10 May (second topic), 31 May (third topic)
All assignments have to be submitted through the LMS to be passed through the text matching software Turnitin (scanned handwritten assignments are fine, there is absolutely no need to spend time on typesetting!).
- One mark for every seminar participation, up to a total of 10. The total counts 10% towards the total mark. (no bettermark!)
Under exceptional circumstances you may be allowed to attend a MATH1921 tutorial. Contact the coordinator Daniel Daners for permission to do so.
Outcomes
The outcomes for MATH1931 include all outcomes for MATH1921 as well as the following: The student completing MATH1931 will
- gain an appreciation of a diverse range of mathematical problems and applications through participating in class discussions and the completion of assignments.
- be able to grasp new mathematical concepts beyond routine methods and calculations.