Syllabus for Applied Mathematics II (Fall, 2019)
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<br>Textbook
<br>Mathematical Methods in the Physical Sciences (3rd edition)
<br>by Mary Boas
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<br>Important Dates
<br>Midterm (Nov 7, 2019)
<br>Simulation Report (Dec 26, 2019)
<br>Final (Jan 6, 2020)
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<br>Main topics
<br>Calculus of Variations (3 lectures) 
<br>Tensor Analysis (4 lectures) 
<br>Special functions (8 lectures)
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<br>Partial Differential Equations (4 lectures)
<br>Complex Analysis (5 lectures)
<br>Probability and Statistics (4 lectures)
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<br>Week 1
<br>Sep 9 (Mon) intro to applied math
<br>Sep 12 (Thu) brachistochrone problem (Chap 9)
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<br>Week 2
<br>Sep 16 (Mon) Euler-Lagrange equation (Chap 9)
<br>Sep 19 (Thu) variations with constraints (Chap 9)
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<br>Week 3
<br>Sep 23 (Mon) Cartesian tensors (Chap 10)
<br>Sep 26 (Thu) pseudo-tensors and dual tensors (Chap 10)
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<br>Week 4
<br>Sep 30 (Mon) curvilinear coordinates (Chap 10)
<br>Oct 3 (Thu) curved Spacetime (Chap 10)
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<br>Week 5
<br>Oct 7 (Mon) Gamma, beta and error functions (Chap 11)
<br>Oct 10 (Thu) National Day
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<br>Week 6
<br>Oct 14 (Mon) asymptotic series and elliptic functions (Chap 11)
<br>Oct 17 (Thu) separation of variables for PDE (Chap 12)
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<br>Week 7
<br>Oct 21 (Mon) Legendre functions (Chap 12)
<br>Oct 24 (Thu) orthogonality for Legendre functions (Chap 12)
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<br>Week 8
<br>Oct 28 (Mon) Bessel functions (Chap 12)
<br>Oct 31 (Thu) orthogonality for Bessel functions (Chap 12)
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<br>Week 9
<br>Nov 4 (Mon) Hermite and Laguerre functions (Chap 12)
<br>Nov 7 (Thu) Midterm (Chap 9-12)
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<br>Week 10
<br>Nov 11 (Mon) midterm discussion
<br>Nov 14 (Thu) writing a scientific report 1
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<br>Week 11
<br>Nov 18 (Mon) wave equations (Chap 13)
<br>Nov 21 (Thu) diffusion equations (Chap 13)
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<br>Week 12
<br>Nov 25 (Mon) Schrodinger equation (Chap 13)
<br>Nov 28 (Thu) Poisson equation (Chap 13)
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<br>Week 13
<br>Dec 2 (Mon) analytic functions (Chap 14)
<br>Dec 5 (Thu) Laurent series (Chap 14)
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<br>Week 14
<br>Dec 9 (Mon) residue theorem (Chap 14)
<br>Dec 12 (Thu) writing a scientific report 2
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<br>Week 15
<br>Dec 16 (Mon) Laplace transform and its inverse (Chap 14)
<br>Dec 19 (Thu) Kramers-Kronig relations (Chap 14)
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<br>Week 16
<br>Dec 23 (Mon) random variables (Chap 15)
<br>Dec 26 (Thu) Gaussian distribution (Chap 15)
<br>Dec 26 (Thu) deadline for simulation report
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<br>Week 17
<br>Dec 30 (Mon) Poisson distribution (Chap 15)
<br>Jan 2 (Thu) central limit theorem (Chap 15)
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<br>Week 18
<br>Jan 6 (Mon) Final (Chap 13-15)
<br>Jan 9 (Thu) final discussions
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