## Lecture Notes on Numerical Methods

Taught by Tiejun Li

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Sketch**

### Chapter 1 Solving linear system

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Lect1 Introduction**

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Lect2 Direct methods for solving linear system**

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Lect3 Iterative methods for solving linear system**

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Lect4 Eigenvalue problem for linear system**

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Lect5 Singular value decomposition and applications (PCA)**

### Chapter 2 Numerical optimization

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Lect6 Linear programming**

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Lect7 Nonlinear programming**

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Lect8 Integer programming and other topics**

### Chapter 3 Solving nonlinear system

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Lect9 Solving nonlinear system**

### Chapter 4 Approximation of functions

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Lect10 Polynomial interpolation**

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Lect11 Fast Fourier Transform (FFT)**

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Lect12 Wavelets and applications**

### Chapter 5 Numerical integration

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Lect13 Numerical integration: basics**

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Lect14 Numerical integration: adaptive and Gaussian quadrature**

### Chapter 6 Monte Carlo methods

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Lect15 Generation of RVs**

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Lect16 Monte Carlo integration**

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Lect17 Metropolis algorithm and SSA**

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Lect18 Simulated annealing and Genetic algorithm**

### Chapter 7 Numerical ODEs

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Lect19 One-step method for numerical ODEs**

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Lect20 Multi-step method and stability condition**

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Lect21 Stability regions and stiff ODEs**

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Lect22 Symplectic algorithm**