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Updated syllabus:
Chapter 1 (Complex numbers): Sections 1-7.
Chapter 2 (Analytic functions): Sections 1-4.
Chapter 3 (Elementary functions): Sections 1-3 & 5.
Chapter 4 (Complex integration): Sections 1-6.
Chapter 5 (Series representations of analytic functions): Sections 1-3 & 5-6.
Chapter 6 (Residue theory): Sections 1, 3, 7.
Chapter 7 (Conformal mapping): Sections 2, 3.
The lecture tomorrow (Monday 29.11) is cancelled! The final lecture will be on Tuesday instead.
Exercises for week 48:
Examination in MAT2300, Monday, December 14, 2009: Problem 1.
Eksamen i MAT2300, Mandag 15. desember 2008: Oppgave 1.
Eksamen i MAT2300, Mandag 18. desember 2006: Oppgave 1.
Eksamen i MAT2300, Tirsdag 2. desember 2006: Oppgave 2.
I completed Sections 6.7 (Rouche's theorem and open mapping property), 7.2 (Geometric considerations), and almost all of 7.3 (Möbius transformation). The remaining part of 7.3 is left for the lecture on Monday. Chapter 8 will be dropped from the curriculum. A part of the lecture on Monday will be devoted to re-capping the most "examination relevant" topics from the book.
Exercises for week 47:
Examination in MAT2300, December 14, 2009: Problems 2, 3
Eksamen i MAT2300, 15. desember 2008: Oppgaver 2 & 3
Eksamen i MAT2300, 16. desember 2005: Oppgave 3.
Eksamen i MAT2300, 1. desember 2004: Oppgave 5
I completed Sections 6.1 (Residue theorem), 6.3 (Improper integrals), and 6.7 (Argument principle but not yet Rouche's theorem).
Exercises for week 46:
Section 6.1: 1, 3, 4 ,6, 7
Section 6.3: 2, 5, 6, 11
Section 6.7: 1, 3, 6, 8, 10
Eksamen h2007: oppgave 1, oppgave 2
Eksamen h2005: oppgave 1
Solutions to mandatory assignment #2 has been posted [ CLICK HERE ].
I completed Sections 5.5 (Laurent series) and 5.6 (Zeros and singularities).
Exercises for week 45:
Section 5.5: 1, 4, 6,10
Section 5.6: 1, 2, 12, 19
The results for obligatory assignment #2 have been posted. For those of you that did not get the assignment approved, the deadline for submitting the second and final version is Thursday November 11, at 14:30.
I completed Sections 5.1 (Sequences and series), 5.2 (Taylor series), and partly 5.3 (Power series).
Exercises for week 44:
Section 5.1: 1, 2, 5, 6, 7, 11
Section 5.2: 3, 4, 5, 6, 10, 13, 14, 15, 16
Section 5.3: 2, 3, 5, 6, 13, 17
This week I completed Sections 4.4 (applications of deformation invariance theorem), 4.5 (Cauchy's integral formula), and 4.6 (bounds for analytic functions).
Exercises for week 43:
Section 4.4: 12, 13, 14, 15, 16, 17
Section 4.5: 2, 3, 4, 5, 6, 15
Section 4.6: 5, 6, 7, 13, 16, 17, 18
This week I covered Sections 4.2, 4.3, and parts of 4.4 (finished the proof of the deformation invariance theorem).
Exercises for week 42:
Section 4.2: 5, 6, 7, 11,13, 18
Section 4.3: 2, 5, 7, 11
Section 4.4: 1, 2, 3, 9
Mandatory assignment #2 has been posted [ CLICK HERE ].
Solutions to mandatory assignment #1 has been posted [ CLICK HERE ].
The lecture today was cancelled (too many with mid-term exams). This means that we will continue with contour integrals on Monday next week (Sections 4.2 and 4.3).
There will be lectures / exercises as usual next week.
This week I covered the remaining part of Section 3.3 (branch-cuts of the log function), Section 3.5 (complex powers and inverse trigonometric functions), and Section 4.1 (contours).
Exercises for week 40:
Section 3.3: 3, 5, 12, 15
Section 3.5: 1, 3, 9
Section 4.1: 1, 2, 5, 8
The results for obligatory assignment #1 will be posted Monday October 4. For those of you that did not get the assignment approved, the deadline for submitting the second and final version is Monday October 11, at 10:00.
Today I covered Section 3.2 (trigonometric and hyperbolic functions) and parts of Section 3.3 (Logarithmic function).
Exercises for week 39:
Section 3.2: 15, 17, 19, 20
Section 3.3: 1, 2
PS! The mandatory assignments will be corrected by Monday, October 4.
The exercises session on Thursdays will be moved back to "Auditorium 3". In addition, the format of these sessions will change a bit. They will now take the form of study sessions in which you can do exercises and ask individual questions to the instructor. Students experiencing difficulty in understanding the course material / exercises should particularly make an effort to attend such study sessions to have questions answered.
Some of the exercises will be solved on the blackboard. Send requests to the instructor (amandip.s.sangha[at]gmail.com) regarding which exercises you would like see solved in class.
FieldsmedaljevinnerCedric Villani gir torsdag 30. september fra 12.15 til 13.00 et populærvitenskapelig foredrag med tittel "Can one predict the fate of the Solar system?" i Sophus Lies auditorium.
Se for øvrig: Public lecture in Mathematics By Fields Medal Laureate Cedric Villani [ Poster ]
This week I covered Sections 3.1 (polynomials and rational functions) and 3.2 (exponential functions).
Exercises for week 38:
Section 3.1: 1, 2, 3, 7, 11, 13, 17
Section 3.2: 4, 6, 7
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Student representative: Afsoon Eshghipour (E-mail: afsoone"[at]"student.matnat.uio.no)
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The lecture on Tuesday next week will be replaced by exercises (Amandip Sangha is responsible).
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This week I covered Sections 2.1 (functions of a complex variable), 2.2 (limits and continuity), 2.3 (analyticity), and 2.4 (Cauchy-Riemann equations).
Exercises for week 37:
Section 2.1: 1, 2, 3, 5, 7, 8, 9.
Section 2.2: 1, 11.
Section 2.3: 4, 7, 9, 12.
Section 2.4: 1, 3, 7, 10, 12, 15.
Mandatory assignment #1 has been posted [ More ].
Regarding Exercises - Thursdays 12:15 -14:00. The room has been changed from Auditorium 3 to
Auditorium 5.
This week I covered Sections 1.5 (powers and roots), 1.6 (planar sets), and 1.7 (Riemann sphere and stereographic projection).
Exercises for week 36:
Section 1.5: 5, 7, 9, 10, 11, 18.
Section 1.6: 1, 2, 3, 4, 5, 6, 9,11,13,16,17,18.
Section 1.7: 1, 2, 5.
Here is a very tentative list of the required reading, which will be subject to change:
Chapter 1 (Complex numbers): Sections 1-7.
Chapter 2 (Analytic functions): Sections 1-4.
Chapter 3 (Elementary functions): Sections 1-3 & 5.
Chapter 4 (Complex integration): Sections 1-6.
Chapter 5 (Series representations of analytic functions): Sections 1-3 & 5-6.
Chapter 6 (Residue theory): Sections 1, 3, 7.
Chapter 7 (Conformal mapping): Sections 2, 3.
Chapter 8 (Transforms of applied mathematics): Sections 1, 2.
Today I covered Section 1.4 (complex exponential function, Euler's equation, polar coordinates revisited, De Moivre's formula).
Exercises from Section 1.4: 2, 3, 5, 7, 12,17.
Today I covered Section 1.3, including vector representation of complex numbers, polar form of complex numbers, argument of a complex number, the principal value of the argument, branch-cuts, and we re-visited multiplication of complex numbers in terms of polar coordinates, which provides a nice geometric interpretation of multiplication (similar interpretation for division).
Exercises from Section 1.3: 5, 7, 9, 22.