## 15 Points

Division of Health Engineering Computing & Science
School of Computing and Mathematical Sciences
Department of Mathematics and Statistics

### Staff

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#### Librarian(s)

: alistair.lamb@waikato.ac.nz

You can contact staff by:

• Calling +64 7 838 4466 select option 1, then enter the extension.
• Extensions starting with 4, 5, 9 or 3 can also be direct dialled:
• For extensions starting with 4: dial +64 7 838 extension.
• For extensions starting with 5: dial +64 7 858 extension.
• For extensions starting with 9: dial +64 7 837 extension.
• For extensions starting with 3: dial +64 7 2620 + the last 3 digits of the extension e.g. 3123 = +64 7 262 0123.
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### What this paper is about

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Real Analysis and Complex Analysis form the essential building blocks of the mathematics governing the physical world around us.

Although we adopt a formal approach to the subject, we are also motivated by a range of practical examples occurring in nature.

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### How this paper will be taught

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The paper will be taught via face-to-face lectures and tutorials.

There will be (roughly) 3 lectures and 1 tutorial per week, over 12 weeks.

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### Learning Outcomes

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Students who successfully complete the course should be able to:

• Construct proofs of mathematical results with an appropriate rigour using techniques such as induction and contradiction
• Demonstrate understanding of mathematical results in real analysis including those on limits, convergence, sequences, series, power series, functions, differentiability
• Find Taylor polynomials and make use of error formulae
• Determine the integrability of a function and be able to find values of integrals
• Differentiate analytic functions, use the Cauchy-Riemann equations, find Taylor and Laurent series
• Evaluate integrals using Cauchy's theorem, Cauchy's integral theorem and the residue theorem
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### Assessments

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#### How you will be assessed

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More or less weekly assignments.

Two tests, at dates to be determined, the first test occurring in Week 6 and the second test in week 12.

A final examination which counts for 50% of the final mark.

Please note that, as part of any assessment, students may be asked to complete an oral examination (viva voce) at a later date.

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The internal assessment/exam ratio (as stated in the University Calendar) is 50:50. There is no final exam. The final exam makes up 50% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 50:50 or 0:0, whichever is more favourable for the student. The final exam makes up either 50% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. Assignments
10
2. Test 1
20
3. Test 2
20
4. Exam
50
 Assessment Total: 100
Failing to complete a compulsory assessment component of a paper will result in an IC grade
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