219753 – Numerical analysis
Classroom: SCB 4303, 4305
Class meeting: Tue Fri at 11.00 am - 12.30 pm
Semester: 2/2565
Instructor: Nattapol Ploymaklam
Office: MB 2225
Email: nattapol.p@cmu.ac.th
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Midterm
Exam Date: Thursday, January 26, 2023 at 12:00 to 15:00 PM
Location: TBA
1 Mathematical
Preliminaries
1.0
Introduction
1.1 Basic
Concepts and Taylor's Theorem
1.2 Orders of
Convergence and Additional Basic Concepts
1.3 Difference
Equations
2 Computer
Arithmetic
2.0
Introduction
2.1
Floating-Point Numbers and Roundoff Errors
2.2 Absolute
and Relative Errors: Loss of Significance
2.3 Stable and
Unstable Computations: Conditioning
3 Solution of Nonlinear
Equations
3.0
Introduction
3.1 Bisection
(Interval Halving) Method
3.2 Newton's
Method
3.3 Secant
Method
3.4 Fixed
Points and Functional Iteration
3.5 Computing
Roots of Polynomials
4 Solving
Systems of Linear Equations
4.0
Introduction
4.1 Matrix
Algebra
4.2 LU and Cholesky Factorizations
4.3 Pivoting
and Constructing an Algorithm
4.4 Norms and
the Analysis of Errors
4.5 Neumann
Series and Iterative Refinement
4.6 Solution of
Equations by Iterative Methods
5 Selected
Topics in Numerical Linear Algebra
5.0 Review of
Basic Concepts
5.1 Matrix
Eigenvalue Problem: Power Method
5.2 Schur's and Gershgorin's Theorems
5.3 Orthogonal
Factorizations and Least-Squares Problems
5.4
Singular-Value Decomposition and Pseudoinverses
5.5 QR-Algorithm
of Francis for the Eigenvalue Problem
Final
Exam Date: Thursday
March 23, 2023 at 15:30 PM to 18:30 PM
Location: TBA
6 Approximating
Functions
6.0
Introduction
6.1 Polynomial
Interpolation
6.2 Divided
Differences
6.3 Hermite Interpolation
6.4 Spline
Interpolation
6.5 B-Splines:
Basic Theory
6.6 B-Splines:
Applications
6.7 Taylor
Series
6.8 Best
Approximation: Least-Squares Theory
6.9 Best
Approximation: Chebyshev Theory
7 Numerical
Differentiation and Integration
7.1 Numerical
Differentiation and Richardson Extrapolation
7.2 Numerical
Integration Based on Interpolation
7.3 Gaussian
Quadrature
7.4 Romberg
Integration
8 Numerical
Solution of Ordinary Differential Equations
8.0
Introduction
8.1 The
Existence and Uniqueness of Solutions
8.2
Taylor-Series Method
8.3 Runge-Kutta Methods
8.4 Multistep
Methods
8.5 Local and
Global Errors: Stability
8.6 Systems and
Higher-Order Ordinary Differential Equations
8.7
Boundary-Value Problems
8.8
Boundary-Value Problems: Shooting Methods
8.9
Boundary-Value Problems: Finite-Differences
9 Numerical
Solution of Partial Differential Equations
9.0
Introduction
9.1 Parabolic
Equations: Explicit Methods
9.2 Parabolic
Equations: Implicit Methods
9.3 Problems Without Time Dependence: Finite-Differences