Sample problem
How can we tell the age of paintings? Some pigments contain a mineral which has two unstable isotopes occurring naturally. These isotopes decay at different rates, and one of them is a biproduct of the other’s decay process. By knowing their original relative proportions in the pigment and applying a bit of calculus, it is possible to give quite accurate estimates of age, and hence to detect forgeries.
Brook Taylor, 1685-1731, contributed greatly to 18th century mathematics — much more so than the single result that bears his name would suggest. He was a champion of Newton’s approach to calculus and produced many important works developing that area of mathematics. He invented the “calculus of finite differences” and “integration by parts”, as well as discovering “Taylor’s series”.Sample problem The interaction of two species, one a predator and the other its prey, can be studied using linked first order differential equtions. By varying the initial conditions (essentially the numbers of each species) different scenarios can be considered, the critical one being the circumstances under which the prey becomes extinct. We will solve the equations in class and also graph the changing populations using computer software. |
MATH104 Supplementary Calculus 2First Semester, Second Semester, 9 points Paper detailsBeginning with a brief review, the paper extends some of the topics covered in MATH 160, and introduces others that are new. It includes a section on useful functions, methods of solving differential equations (and examples of their many uses), and further integration techniques and applications. Knitting the whole section together are power series.Potential studentsMATH 104 is taken only by students who need the calculus component (but not the algebra) of MATH 170. This situation may arise when a student has transferred from another university, or is majoring in another subject (possibly computer science, for example) which requires a knowledge of calculus but not the same level of algebra.Main topics
PrerequisitesMATH 160 or Math102 or high achievement (mostly Excellences and Merits) in NCEA Level 3 Mathematics with CalculusRequired textMATH 170 Calculus Outline Notes(Available from the Print Shop.) Useful referencesSeveral standard texts are suitable for reference. For example:Calculus with Analytic Geometry by Howard Anton (Wiley) Calculus and Analytic Geometry by George Thomas and Ross Finney (Addison Wesley) Calculus by James Stewart (Brooks/Cole) * the latest edition is by no means essential. Lecturer1st semester: Dr Bram Evans (Room 217), Dr Jonathan Brown (Room 310a)2nd semester: Dr Bram Evans (Room 217) LecturesApproximately 25 lectures, Tues and Thurs at 12 noonTutorialsAttendance at tutorials is voluntary. An open system operates: tutorial classes run for up to 10 hours per week (depending on demand), and students may attend as many as they need to and are able to.Office HoursMonday and Thursday 10am-11:50am, Room 229 (Dr Brown)Internal AssessmentFive computer Skills Tests make up 20% of your final mark. The other 80% comes from a mix of your final exam mark and the internal assessment mark which is based solely on the ten marked weekly assignments.You can check your marks by clicking on the Resources link at the top of this page. Terms RequirementYou have to fulfil the terms requirement in order to be allowed to sit the final exam. In this paper, to pass “terms” you need to gain at least 6/10 in each of the first four Skills Tests.Exam formatThe 90-minute final exam is answered in spaces provided on the question booklet. All questions should be attempted and the number of marks available for each question is indicated on the paper. There are usually about 15 questions.Past exams are printed in the Outline Notes for the course. Final markThe final mark F is calculated from:F = max { E, (4E + A)/5 } + T where E (exam mark) is out of 80, A (internal assessment) is out of 80, T (test mark) is out of 20.The “max” corresponds to plussage: if your internal assessment mark is greater than your exam mark then it is combined in the proportion shown. If it is less then it is ignored and the exam mark itself is used. So your internal assessment counts at 1/5 weighting if that helps you. PlagiarismStudents should make sure that all submitted work is their own. “Plagiarism is a form of dishonest practice. Plagiarism is defined as copying or paraphrasing another’s work and presenting it as one’s own” (University of Otago Calendar). In practice this means that plagiarism includes any attempt in any piece of submitted work (e.g. an assignment or test) to present as one’s own work the work of another (whether of another student or a published authority). Any student found to be responsible for plagiarism in any piece of work submitted for assessment shall be subject to the University’s dishonest practice regulations which may result in various penalties, including forfeiture of marks for the piece of work submitted, a zero grade for the paper, or in extreme cases exclusion from the University. The University of Otago reserves the right to use plagiarism detection tools.
While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.
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