Instructor(s): Michael Montgomery

Course on canvas.dartmouth.edu ⇗

Syllabus

Course Summary
Date Details Due
Mon Mar 30, 2026 Assignment Lecture: 1.1 The Complex Plane [Supp. Problems 1.1: 12, 14, 15, 18, 23, 27]
Wed Apr 1, 2026 Assignment Lecture: 1.2,1.3 The Complex Plane [Supp. Problems 1.2: 6, 10, 13; 1.3: 4, 5, 10]
Fri Apr 3, 2026 Assignment Lecture: 1.4, 1.5 Complex exponentials and powers, Suggested problems: [Sect. 1.4: 3, 6, 13, 17]; [Sect. 1.5: 3, 5, 9, 12]
Mon Apr 6, 2026 Assignment Homework 1; [Section1.1: 4, 8, 10, 21 and 30] [Section1.2: 7adeh, 16, 17] [Section1.3: 7deg, 8, 11, 13, 16]
Assignment Lecture: 1.6 Domains; Suggested problems [1.6: 1, 9, 14, 15, 20]
Wed Apr 8, 2026 Assignment Lecture: 2.1, 2.2 Functions of complex variables and continuity, Suggested problems [2.1: 1, 11, 13] [2.2: 3, 9, 11]
Fri Apr 10, 2026 Assignment Lecture: 2.3, 2.4 Analyticity and the Cauchy Riemann Equation: Suggested Problems [2.3: 11, 13, 14] [2.4: 1, 2, 6]
Mon Apr 13, 2026 Assignment Lecture: 2.4 cont'd 2.5, Cauchy Riemann Equations and Harmonic Functions, Suggested Problems [2.4: 11, 15] [2.5: 3, 5, 7, 14]
Assignment Homework 2 [1.4: 4, 11, 20] [1.5: 5aef, 12] [1.6: 2, 6, 12, 13, 20]
Wed Apr 15, 2026 Assignment Lecture: 2.5 cont'd, 3.1 Fluid Flow, Polynomials, and Rational Functions [3.1: 3, 7, 11, 13, 14, 17]
Fri Apr 17, 2026 Assignment Lecture: 3.2, 3.3 Exponential, Trigonometric, and Logarithmic Functions, Suggested Problems [3.2: 6, 7, 9, 10, 15, 21] [3.3: 3, 4, 9, 15]
Mon Apr 20, 2026 Assignment Lecture: 3.5: Complex powers, inverse trig: Suggested problems [3.5: 3, 5, 6, 15]
Assignment Homework 3 [2.1: 6, 12] [2.2: 6, 21] [2.3: 4, 12] [2.4: 8, 10, 12]
Wed Apr 22, 2026 Assignment Lecture 3.5 cont'd 1.7: Inverse Trig and the Riemann Sphere
Fri Apr 24, 2026 Assignment Midterm 1
Assignment Lecture 4.1: Contours
Mon Apr 27, 2026 Assignment Homework 4
Assignment Lecture 4.2, 4.3 Suggested problems [4.1: 1, 3, 5, 7, 9] [4.2: 1, 3, 9, 12, 14]
Wed Apr 29, 2026 Assignment Lecture: 4.3, 4.4 Suggested Problems [4.3: 1, 5, 7, 11] [4.4: 9, 11, 15]
Fri May 1, 2026 Assignment Lecture 4.5 Cauchy's Integral Formula Suggested Problems [4.5: 3, 7, 9, 13]
Mon May 4, 2026 Assignment Homework 5
Assignment Lecture 4.6, 4.7 Bounds for Analytic and Harmonic functions: Suggested Problems [4.6: 3, 5, 11, 13] [4.7: 3, 7]
Wed May 6, 2026 Assignment Lecture 4.7 cont'd and 5.1 Harmonic functions and series Suggested problems [5.1: 1a, 2bd, 5, 8]
Fri May 8, 2026 Assignment Lecture: 5.1-5.3 Taylor Series and Power Series Suggested Problems [5.2: 3, 5, 11] [5.3: 3, 5, 7, 13, 18]
Mon May 11, 2026 Assignment Homework 6
Assignment Lecture 5.2, 5.3, 5.5 Taylor Series, Power series, and Laurent Series: Suggested Problems [5.5: 1, 3, 5, 9, 13]
Wed May 13, 2026 Assignment Lecture: 5.5 Laurent Series Cont'd.
Fri May 15, 2026 Assignment Lecture 5.5-5.7 Laurent Series, Poles, Singularities, and zeros Suggested Problems: [5.6: 1, 3, 5, 9, 15, 17] [5.7: 1, 6, 7]
Mon May 18, 2026 Assignment Midterm 2 Part 1
Assignment Midterm 2
Tue May 19, 2026 Assignment Midterm 2 Part 2 during the xhour
Wed May 20, 2026 Assignment Homework 7
Assignment Lecture: 5.7-5.8 Poles at infinity and Analytic continuation: Suggested Problems [5.8: 1, 13]
Fri May 22, 2026 Assignment Lecture 6.1-6.3 Residue Theory and integration Techniques: Suggested Problems [6.1: 1eh, 3bef] [6.2: 1, 5, 9] [6.3: 1, 3, 9]
Wed May 27, 2026 Assignment Homework 8
Assignment Lecture: 6.3 Cont'd
Fri May 29, 2026 Assignment Lecture: 6.7, 6.4 Rouche's Theorem and more Residue integration techniques Suggested Problems [6.7: 5, 9, 13] [6.4: 3, 5, 10]
Mon Jun 1, 2026 Assignment Lecture: 6.4-6.5 Residue Integration Suggested Problems [6.4: 1, 3, 10, 12] [6.5: 1, 4, 10]
Wed Jun 3, 2026 Assignment Review
Assignment Homework 9
Sun Jun 7, 2026 Assignment Final
Wed Jun 10, 2026 Assignment Final Course Grade