Contents

Final exam will cover the following sections. A "aid-sheet" (two 11x8.5 papers, but three sided) for formulas and a calculator will be allowed for the final exam. You also need to bring your York photo ID.

**Chapter 1. Optimization Methods**

- Section 1 Search Methods in 1D (Golden and Fibonacci)
- Section 2 The Simplex Method in 2D
- Section 3 The Steepest Descent Method and The Newton's Method in R^n

**Chapter 2. The Preconditioned Conjugate Gradient Methods**

- Section 1 The Gradient Method and The Conjugate Direction Method
- Section 2 The Conjugate Gradient Method (CG)
- Section 3 The Preconditioned Conjugate Gradient Method (PCG)
- Section 4 The Nonlinear CG Methods

**Chapter 3. Numerical Methods for Initial Value Problems of ODEs**

- Section 1 The Euler's and High-order Taylor's Methods
- Section 2 The Runge-Kutta Methods
- Section 3 The Multi-step Methods
- Section 4 Adaptive Step Technique
- Section 5 Stability
- Section 6 Systems of ODEs and High-Oredr Equations

**Chapter 4. Numerical Methods for BV Problems of ODEs**

- Section 1 The Nonlinear Shooting Methods
- Section 2 The Finite Difference Methods for Linear Problems
- Section 3 Error Analysis

**Chapter 5. Approximation Theory**

- Section 1 Orthogonal Polynomials and Least Squares Approximation
- Section 2 Chebyshev Polynomials and the Economization
- *Section 3* Pade approximation
- Section 4 Fourier Approximation and Fast Fourier Transforms (FFT)