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Abstract: UNIVERSITY OF WAIKATODepartment of Mathematics (FCMS)MATH31111A – Advanced CalculusPaper OutlineLecturerDr Yuri Litvinenko Room G3.04 Phone: 838 4466 x8363 Email: yuril

UNIVERSITY OF WAIKATO
Department of Mathematics (FCMS)
MATH31111A – Advanced Calculus
Paper Outline
Lecturer
Dr Yuri Litvinenko Room G3.04 Phone: 838 4466 x8363 Email: yuril
http://www.math.waikato.ac.nz/~yuril/
Office Hours
Wednesday and Thursday 2.00 – 3.00 pm
Lecture Times
Tuesday 11.00 am  11.50 am G3.33
Wednesday 11.00 am  11.50 am G3.33
Thursday 11.00 am  11.50 am G3.33
Friday 3.10 pm  4.00 pm G3.33 (Tutorial)
Prescribed Texts (available for purchase from Bennetts Bookshop)
Schaum's Outline of Advanced Calculus, R. Wrede and M. Spiegel.
Schaum's Outline of Complex Variables, M. Spiegel, S. Lipschutz, J. Schiller, and D. Spellman.
Syllabus for the Real Analysis section (Text: Advanced Calculus)
• Vector calculus (Chapter 7)
• Line and surface integrals (Chapter 9), integral theorems of Gauss and Stokes (Chapter 10)
• Fourier series (Chapter 13)
• Improper integrals (Chapter 12), Gamma and Beta functions (Chapter 15)
Syllabus for the Complex Analysis section (Text: Complex Variables)
• Complex functions, differentiation, CauchyRiemann equations (Chapters 13)
• Complex integration (Chapters 45)
• Taylor's and Laurent's series (Chapter 6)
• The residue theorem, evaluation of integrals (Chapter 7)
Recommended Textbooks (available in the University library)
Mathematical Methods in the Physical Sciences, M.L. Boas.
Foundations of Applied Mathematics, M.D. Greenberg.
Div, Grad, Curl, and All That, H.M. Schey.
Introductory Complex Analysis, R.A. Silverman.
Advanced Calculus, D.V Widder.
Assessment
The internal assessment will consist of WEEKLY assignments worth a total of 40% and TWO onehour
tests, one for Real Analysis and one for Complex Analysis, each worth 30% of the final mark.
Assignments must be handed in via the slot under the G3.19 Mathematics Reception counter. All work
handed in must be your own. No late assignments will be accepted.
Provisional TEST dates (held in usual lecture times)
Test 1 Thursday, 7 April 11am G3.33
Test 2 Thursday, 26 May 11am G3.33
Overall assessment
The internal assessment : final examination ratio will be 1/2 : 1/2 or 0 : 1, whichever works in your favour.
Other information
All notices about this paper, as well as printouts of your internal assessment marks, will be posted on the
MATH311 noticeboard. For information on the University policies and regulations regarding plagiarism and
complaints procedures please visit
http://www.math.waikato.ac.nz/studentinfo.html
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