# 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.

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# Lecture Notes For MATH301

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# Downloads For MATH301

# Updates For MATH 301

### Jan. 4: Laurent series, residues

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

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

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

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### Jan. 15: infinite sums.

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### Jan. 18: Multiple-valued functions.

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### Jan. 20: Multiple-valued Functions

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### Jan. 22: Computing integrals using branch cuts.

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

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

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

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### Feb 1: Conformal mappings.

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### Feb. 3: Examples of conformal mappings. Laplace equation

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

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### Feb. 8: Family Day

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### Feb. 10: Mobius transform. Properties.

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

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

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

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

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

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

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### March 7: Conformal mapping and fluid equations.

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### March 9: Flow past obstacles.

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### March 14: Fourier Transforms. Lecture Note 11.

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### March 16: Fourier Transform. Lecture Note 11.

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### March 18: Fourier Transform. Lecture Note 11.

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

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### March 23: Laplace Transform. Lecture Note 12.

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

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

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

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### April 8: Nyquist criterion. Lecure note 14.

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# Announcements For MATH 301

### Midterm test date: Feb. 26, in class.

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### Coverage of Midterm test: up to Lecture Note 7.

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### No office hours on March 21, March 23.

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

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