Computational and Applied Mathematics Course Overview
Dive into the world of computational and applied mathematics with Math 3310. Explore the principles and methods used by applied mathematicians to solve real-world problems through mathematical modeling, analysis, and numerical algorithms. Gain insights into the assessment scheme and course agenda, uncovering the differences between various math courses such as numerical analysis and mathematical modeling.
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Presentation Transcript
Math 3310: Computational & Applied Math. Course Outline Prof. Ronald Lui
Basic information Lecturer: Ronald Lui TA: Zhehao Xu (LSB222B); Qiguang Zhu (LSB222B) Email: lmlui@math.cuhk.edu.hk Office: LSB 207 Course website: https://www.math.cuhk.edu.hk/course/2425/math3310 Lecture time: Tu 4:30PM - 6:15PM (MMW 710); Th 1:30PM - 2:15PM (LSK LT4) Tutorial: Th 12:30PM - 1:15PM (LSK LT4)
Assessment Scheme 5 - 6 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 Applied Math: Solve real problems w/ Math Computational Math: Solve eqts +
What do applied mathematicians do? When an applied mathematician is given a real world problem, they will Analyze Physical phenomenon/Problem requirement & identify Rules (e.g. physical laws ) Convert the problems into mathematical formulation (Mathematical modeling) Math3290 Tackle the mathematical problem by solving equations: (Analytic (exact solution) or Numerical [approx.]) Math3310 Analysis of approximated solution & numerical algorithm
Agenda Motivation: how real world problems are converted into mathematical formulation; Analytic methods to solve eqt: ODE/PDE exact solution Analytic spectral (Fourier) method Numerical 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) <1 week 1 week 1 week 1 week 3.5 week 1.5 week 2.5 week 1.5 week
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 Math3XXX & Math 4XXX courses in pure mathematics; Try to help 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 applied mathematics techniques may not be covered!
