## A beginner's course to applied mathematics

Lecturer: Tiejun Li

**
Outline**

**
Lect1 Introduction**

**
Lect2 Lagrange and Newton interpolation**, **
Homework 1**

**
Lect3 Spline interpolation**, **
Homework 2**

**
Lect4 Least squares fitting**, **
Homework 3**

**
Lect5 Numerical integration**, **
Homework 4**

**
Lect6 Gaussian quadrature**, **
Homework 5**

**
Computer project 1**

**
Lect7 Adaptive quadrature**, **
Homework 6**

**
Lect8 Solving linear system I**, **
Homework 7**

**
Lect9 Solving linear system II**, **
Homework 8**

**
Lect10 Multigrid method**, **
Homework 9**

**
Computer project 2**

**
Lect11 Eigenvalue problem**, **
Homework 10**

**
Lect12 Two-point BVP**, **
Homework 11**

**
Lect13 Newton's Method**, **
Homework 12**

**
Lect14 FFT**, **
Homework 13**

**
Computer project 3**

**
Lect15 Monte Carlo method: basics**, **
Homework 14**

**
Lect16 Metropolis algorithm**, **
Homework 15**

**
Lect17 Simulated annealing and QMC**

**
Computer project 4**

**
Lect18 Laplace asymptotics**, **
Homework 17**

**
Lect19 Stationary phase approximation**, **
Homework 18**

**
Lect20 Method of steepest descent**, **
Homework 19**

**
Lect21 Asymptotics for sums**, **
Homework 20**