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    Develops the differential and integral calculus of functions of a complex variable, and its applications.

    This paper provides an introduction to the mathematics and analysis of complex numbers, which are a central topic of pure and applied mathematics.

    About this paper

    Paper title Complex Analysis
    Subject Mathematics
    EFTS 0.15
    Points 18 points
    Teaching period Semester 2 (On campus)
    Domestic Tuition Fees ( NZD ) $981.75
    International Tuition Fees Tuition Fees for international students are elsewhere on this website.
    MATH 201
    Schedule C
    Arts and Music, Science
    This paper is particularly relevant to Mathematics and Physics majors.

    For more information, contact MATH and COMO200-300 Level Advisor Jörg Hennig at

    Teaching staff

    Dr. Robert A. Van Gorder

    Paper Structure

    Main topics:

    • Complex numbers (modulus, argument, etc; inequalities, powers, roots, geometry and topology of the complex plane)
    • Analytic functions (Cauchy-Riemann equations, harmonic functions, polynomials, power series, exponential, trigonometric and logarithmic functions)
    • Complex integration (curves, rectifiability, curve integrals, domains, starlikeness, homotopy, simple-connectedness, Cauchy's theorem via Goursat's lemma, Cauchy's integral formulae, Cauchy's inequalities, Liouville's theorem, mean value theorem (for harmonic functions), fundamental theorem of algebra, maximum modulus principle, Morera's theorem, isolated singularities, Weierstrass's theorem, residue theorem, real integrals, Rouche's theorem, Schwarz's lemma)
    Teaching Arrangements

    Three lectures per week.

    One Tutorial per week.


    Lecture notes are available from Uniprint in the Library.

    Graduate Attributes Emphasised
    Critical thinking.
    View more information about Otago's graduate attributes.
    Learning Outcomes

    Students who successfully complete this paper will demonstrate in-depth knowledge of basic concepts of complex analysis and mathematical proof.


    Semester 2

    Teaching method
    This paper is taught On Campus
    Learning management system


    Stream Days Times Weeks
    A1 Monday 14:00-14:50 29-35, 37-42
    Wednesday 14:00-14:50 29-35, 37-42
    Friday 14:00-14:50 29-35, 37-42


    Stream Days Times Weeks
    A1 Thursday 14:00-14:50 29-35, 37-42
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