Math 3310 Computational Applied Math Course Outline Prof

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Math 3310: Computational & Applied Math. Course Outline Prof. Ronald Lui

Math 3310: Computational & Applied Math. Course Outline Prof. Ronald Lui

Basic information Lecturer: Ronald Lui TA: Ho LAW (LSB 222 B); Xihao HE (LSB

Basic information Lecturer: Ronald Lui TA: Ho LAW (LSB 222 B); Xihao HE (LSB 222 C) Email: lmlui@math. cuhk. edu. hk Office: LSB 207 Course website: https: //www. math. cuhk. edu. hk/course/1920/math 331 0 Lecture time: Mon 2: 30 PM – 4: 00 PM, LSB LT 3; Wed 2: 30 PM - 3: 15 PM, LSB LT 4 Tutorial: Wed 3: 30 PM - 4: 15 PM, LSB LT 4

Assessment Scheme � 6 – 7 Bi-weekly Homework (with simple programming problems) 15% �Midterm

Assessment Scheme � 6 – 7 Bi-weekly Homework (with simple programming problems) 15% �Midterm examination 35% �Final examination 50%

What is our goal? �Get a basic understanding about computational mathematics and applied mathematics

What is our goal? �Get a basic understanding about computational mathematics and applied mathematics Applied Math: Computational Math: Solve real problems + Solve eqts… w/ Math

What do applied mathematicians do? When an applied mathematician is given a real world

What do applied mathematicians do? When an applied mathematician is given a real world problem, they will… Analyze Physical phenomenon/Problem requireme & identify Rules (e. g. physical laws…) Math 3290 Convert the problems into mathematical formulatio (Mathematical modeling) Tackle the mathematical problem by solving equat (Analytic (exact solution) or Numerical [approx. ]) Math 3310 Analysis of approximated solution & numerical algorithm

Agenda <1 week � Motivation: how real world problems are converted into mathematical formulation;

Agenda <1 week � Motivation: how real world problems are converted into mathematical formulation; � Analytic methods to solve eqt: ◦ ODE/PDE exact solution ◦ Analytic spectral (Fourier) method � Numerical 1 week 3. 5 week 1. 5 week 2. 5 week 1. 5 week approaches: ◦ Numerical spectral method; ◦ Iterative method for large linear system (Jacobi, Gauss. Seidel, SOR, (preconditioned) conjugate gradient method) ◦ Multigrid method � Eigenvalue problems � Conformal method (solving eqt on complicated domains)

Differences between courses? � Math 3230: Numerical Analysis ◦ Covers conventional numerical methods, such

Differences between courses? � Math 3230: Numerical Analysis ◦ Covers conventional numerical methods, such as interpolation, numerical differentiation/integration; ◦ Usually involves solving a big linear/non-linear systems BUT won’t through efficient methods to compute it; � Math 3240: Numerical Methods for differential equations ◦ Convert differential equations into linear systems; ◦ Won’t go though efficient methods to compute it. � Math 3290: Mathematical modeling ◦ Formulate problems mathematically; ◦ Usually involves solving a big linear/non-linear systems BUT won’t through efficient methods to compute it; � Math 3310: Computational and Applied Mathematics ◦ Covers up-to-date & practical & efficient methods to solve the equations arisen from the mathematical formulation of real-world problems ◦ ALL methods are being used by applied mathematicians everyday in their research.

Good news: �Comparatively easier than other Math 3 XXX & Math 4 XXX courses;

Good news: �Comparatively easier than other Math 3 XXX & Math 4 XXX courses; �Try to give minimal amount of workload while helping you to get most important things about computational and applied mathematics;

Bad news: �May not be able to cover everything in applied mathematics; �Less important

Bad news: �May not be able to cover everything in applied mathematics; �Less important applied mathematics techniques may not be covered!