MATH301-201 :       Applied Analysis and Complex Variables   (2nd term 2015/2016)

Lecture   I: Monday 11am--12:00pm, LSK 460.

Lecture   II: Wednesday 11am--12:00pm, LSK 460.

Lecture   III: Monday 11am--12:00pm, LSK 460.

Office Hours: Every Monday, Wednesday, Friday, 5:20pm-6pm, LSK 303B.

Lecture Notes For MATH301

Lecture Notes Lecture Notes 1

Lecture Notes Lecture Notes 2

Lecture Notes Lecture Notes 3

Lecture Notes Lecture Notes 4

Lecture Notes Lecture Notes 5

Lecture Notes Lecture Notes 6

Lecture Notes Lecture Notes 7

Lecture Notes Lecture Notes 8

Lecture Notes Lecture Notes 9

Lecture Notes Lecture Notes 9.5: Schwartz-Christoffel Formula

Lecture Notes Lecture Notes 10

Lecture Notes Lecture Notes 11

Lecture Notes Lecture Notes 12

Lecture Notes Lecture Notes 13

Lecture Notes Lecture Notes 14

Downloads For MATH301

Download 1: Syllabus

Download 2: Practice Problems I (no need to hand in)

Download 3: Assignment 1 (due date: Jan. 20, 2016)

Download 4: Practice Problems II (no need to hand in)

Download 5: Solutions to Assignment 1

Download 6: Assignment 2 (due date: Feb. 3, 2016)

Download 7: Assignment 3 (due date: Feb. 22, 2016)

Download 8: Practice Problems III (no need to hand in)

Download 9: Solutions to Assignment 2

Download 10: Solutions to Assignment 3

Download 11: Review Questions Solutions

Download 12: Old Problems I

Download 13: Old Problems II

Download 14: Old Problems III

Download 15: Old Problems IV

Download 16: Midterm Test

Download 17: Solutions to Midterm Test

Download 18: Assignment 4 (due date: March 9, 2016)

Download 19: Assignment 5 (due date: March 18, 2016)

Download 20: Solutions to Assignment 4

Download 21: Solutions to Assignment 5

Download 22: Assignment 6 (due date: April 1, 2016) Remark to Assignment 6

Download 23: Solutions to Assignment 6

Download 24: Assignment 7 (due date: April 13, 2016)

Download 25: A complete list of formulas (and theorems)

Download 26: Solutions to Assignment 7

Updates For MATH 301

Jan. 4: Laurent series, residues

Jan. 6: Cauchy residue theorems, computations of complex integrals.

Jan. 11: Computations of real integrals. Case 1 and Case 2. Jordan's Lemma.

Jan. 13: Computations of real integrals with other contours. Infinite Sums. Multiple-valued functions.

Jan. 15: infinite sums.

Jan. 18: Multiple-valued functions.

Jan. 20: Multiple-valued Functions

Jan. 22: Computing integrals using branch cuts.

Jan. 25: Computing real integrals using branch cuts. Finished Lecture Note 3.

Jan. 27: Computing integrals with residues at infinity. Lecture Note 4.

Jan. 29: Last integral in Lecture Note 4. Conformal mapping.

Feb 1: Conformal mappings.

Feb. 3: Examples of conformal mappings. Laplace equation

Feb. 5: Using conformal mapping to solve Laplace equation.

Feb. 8: Family Day

Feb. 10: Mobius transform. Properties.

Feb. 12: Examples of Mobius transform. Lecture Note 7.

Feb. 22: Solving Laplace Equations. Lecture Note 8.

Feb. 24: Solving Laplace Equation. Mobius transform from circle to circle. Lecture Note 9.

Feb. 29: Solving Laplace Equation. Continue on Mobius transform from circle to circle. Symmetric Points. Lecture Note 9.

March 2: Mobius transforms from cicle/lines to circle/lines. Lecture Note 9.

March 4: Schwarz-Christoffel mapping from upper half space to a triangle. Lecture Note 9.5.

March 7: Conformal mapping and fluid equations.

March 9: Flow past obstacles.

March 14: Fourier Transforms. Lecture Note 11.

March 16: Fourier Transform. Lecture Note 11.

March 18: Fourier Transform. Lecture Note 11.

March 21: End of Fourier Transform. Start on Lecture 12 on Laplace Transform.

March 23: Laplace Transform. Lecture Note 12.

March 30: Laplace Transform. Applications to ODEs and PDEs. Lecture Note 12.

April 1: Laplace transform and applications. Lecture Note 13.

April 5: Periodic functions and Laplace transform. Lecture Note 13.

April 8: Nyquist criterion. Lecure note 14.

Announcements For MATH 301

Midterm test date: Feb. 26, in class.

Coverage of Midterm test: up to Lecture Note 7.

No office hours on March 21, March 23.

Final Exam: April 15, 2016, 07:00PM, BUCH B213

I will be in my office from 10am to 4pm next week (April 11-15). Please feel free to knock on my door.

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