We will cover sections from Chapters 1–6. See the outline below.
1.1 The algebra of complex numbers 1.2 Point representation of complex numbers 1.3 Vectors and polar forms 1.4 The complex exponential 1.5 Powers and roots 1.6 Planar sets 1.7 The Riemann sphere 2.1 Functions of a complex variable 2.2 Limits and continuity 2.3 Analyticity 2.4 The Cauchy-Riemann equations 2.5 Harmonic functions
3.1 Polynomials and rational functions 3.2 Exponential, trigonometric and hyperbolic functions 3.3 The logarithm 3.5 Complex powers and inverse trigonometric functions 4.1 Contours 4.2 Contour integrals 4.3 Independence of path 4.4 Cauchy's integral theorem 4.5 Cauchy's integral formula 4.6 Bounds for analytic functions
5.1 Sequences and series 5.2 Taylor series 5.3 Power series 5.4 Convergence 5.5 Laurent series 5.6 Zeros and singularities 5.7 The point at infinity 6.1 The residue theorem 6.2 Trigonometric integrals 6.3 Improper integrals 6.7 Argument principle 7.3 Moebius transformations 7.4 Moebius transformations, ctd.
There will be weekly homework assignments, usually due on Mondays. Late homework will not be accepted. A selection of problems will be graded. I will drop the lowest homework score.
Graded homework will be available for pickup at the Math Learning Centre
There will be two midterm exams, on Friday October 6, and Friday, November 10. There are no make-up midterms. If you miss a midterm for a valid medical reason, the weighting for the final will be adjusted. Other than this, no re-negotiating of the weights of the different components of the overall grade will be considered.
There will be a final exam during the December exam period.
The following applies to all exams in Math 300: No calculators, notes, books, electronic devices or aids of any kind.
Your grade will be computed as follows:
|Homework (lowest score dropped):||10%|
Check back here for homework assignments and solutions, notes and links as the term progresses.
|Wed Sept 6||1.1||Introduction, arithmetic operations||1.1: 6(a), 8, 10, 20(a,b,c) 30 due: Mon Sept 11|
|Fri Sept 8||1.2||Geometry of complex numbers modulus, conjugate, basic inequalitites||1.2: 7(def), 16, 17 due: Mon Sept 18|
|Mon Sept 11||1.3, 1.4||basic inequalitites, set descriptions, complex exponentials||1.3: 5(d), 7(e), 11, 13, 23; 1.4: 3(c), 12(b), 20(b) due: Mon Sept 18|
|Wed Sept 13||1.5||complex exponentials ctd, polar form, arg and Arg||1.5: 5(ae), 11, 16 due: Mon Sept 18|
|Fri Sept 15||geometry of multiplication, roots of unity|
|Mon Sept 18||1.6, (1.7)||roots of a complex number, classification of sets. (If time, Riemann sphere. I won't test you on this.)||1.6: 2-8(a)(b), due: Mon Sept 25|
|Wed Sept 20||2.1||Complex Functions||2.1: 3(abcd), 5(abcde), 6(abc), 10(a), 11(a) due: Mon Sept 25|
Here is a Julia set demo