MA3160 - Class information:
  • Class meets Monday, Wednesday, Friday; 1:30 pm - 3:00 pm; Room: JTB 310, Office hours: by appointment

  • Information such as, most important results to know after each section, homework assignments, practice exams, solutions to the exams, and different important announcements about the class activities will be POSTED HERE.

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    1. Important results of the first Chapter:
      • Basic properties of complex numbers, sum, product, ratio, algebraic and exponential form
      • Conjugate and absolute value with their properties
      • Geometrical interpretation of the sum, difference, and conjugate
      • Principal argument and little argument
      • Roots of unity
    2. Important result of the second Chapter, Sections 12 - 18:
      • Computation of finite limits
      • Definition of continuity
      • Rules for limits at infinity and infinite limits

    Homework due on Wednesday July 6, 2011:
    • Section 2: 1(a),2,11; Section 3: 1; Section 4: 1(a),3,4,5,6;
    • Section 5: 1(b)(d), 7, 9, 10, 13, 14; Section 8: 1,2,6,10;
    • Section 10: 6,7,8; Section 12: 1,2,3,4; Section 14: 1,3,7,8;
    • Section 18: 3,5,10,11;

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    1. Important results of the second Chapter, Sections 19-23:
      • Definition of the complex derivative
      • The derivative if the sum, difference, product, and quotient of two differentiable complex functions
      • Fluid flow iknterpretation for the complex differential
      • Cauchy-Riemann conditions for differentiability

    Homework due on Wednesday July, 13:
    • Section 20: 1,2,8
    • Section 23: 1,3,5

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    1. Important results of the second Chapter, Sections 24-27:
      • Definition of analytic functions
      • Operations with and properties of analytic functions
      • Harmonic functions. The real and imaginary parts of an analytic function are harmonic
      • Determination of the harmonic conjugate for a given harmonic function
    2. Important results for Chapter 3, Sections 29-36:
      • The exponential function is entire. Opertions with the exponential function
      • The logarithm is a multivalued function
      • Principal value of logarithm and its properties. Different branch cuts of the logarithm
      • Power function with complex exponents. Definition and properties
      • Trigonometric functions. Definition and properties
      • Hyperbolic functions. Definition and properties
    3. Important results in Chapter 4:
      • The mathematical definition of the complex integral and its properties
      • The physical interpretation of the complex integral
      • Contour parametrization and the computation of integrals with the fundamental theorem of calculus
      • Cauchy's theorem and its consequences
      • Cauchy's integral theorem and its corollaries
      • Liouville's theorem and the maximum modulus principle

    Homework due on Wednesday July, 20:
    • Section 25: 1,2,4
    • Section 26: 1(c),3,8,9
    • Section 29: 1,2,3,6,10,11,12,13
    • Section 31: 1,3,5,8,9,11
    • Section 32: 1,2
    • Section 33: 1,2,3,8,9
    • Section 34: 11,15
    • Section 35: 16
    • Section 42: 1,2,3
    • Section 43: 1,2
    • Section 45: 1,2,3

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    Midterm exam (Midterm) due on Wednesday July 27

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    FINAL EXAM (PRESENTATIONS) TO BE HELD IN OUR CLASSROOM FROM 12:30PM - 2:30PM

    Hints for your presentations:
    • In the begining offer the audiance the motivation behind your presentation. Why do you think it is important
    • Also in the first part of your presentation try to offer a short outline of the whole presentation so that your colleagues will have a general idea about what to expect
    • Clearly prepared slides. A good slide should not contain much information, just what is neccesary for you to convey your message. The main part of a presentation is oral. Oraly explain a lot your arguments!!!
    • Fix among your team members a few (2 or 3) important ideas the audience should understand and build your presentation arround them.

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