数值分析

约 215 个字 预计阅读时间 1 分钟

课程信息

Lecture: 数值分析

• 课程概括: 了解计算器是怎么通过一系列的技巧和优化让离散的数据存储能够运算连续世界的问题的
• 授课：许威威
• 智云课堂: 🔗

评分细则

评分：Lecture Grade(100) = Lab(36) + inclass-quiz(4) + Reseacher Topics(15) + Homework(5) + Final Exam (40*)

Lab(36): 八个project

inclass-quiz(4): 两次（各两分），可用回答问题补分（一分/次）

Reseacher Topics(15): 组队完成，18个topic选一个，进行5~10min展示

课程架构

Basic Knowledge

• Chapter 1
  • Mean value theorem
  • Taylor expansion
  • Roundoff error

Solution of Equations

• Chapter 2
  • Solution of equations with one variable
• Chapter 6
  • Direct Matrix Solver
• Chapter 7
  • Iterative Matrix Solver
• Chapter 5
  • Initial value problem
  • Euler, Runge-kutta, multi-step

Convergence + Stability

Interpolation and approximation

• Chapter 3: interpolation

  • Lagrange polynomial
  • Piecewise polynomial

• Chapter 4

  • Numerical differentiation
  • Numerical integration

• Chapter 8: approximation

  • Orthogonal polynomials
  • Least squares
  • Chebyshev polynomial

Error