219753 – Numerical analysis
Classroom: SCB 4301
Class meeting: Mon Thu at 9.30 am - 11.00 pm
Semester: 2/2568
Instructor: Nattapol
Ploymaklam
Office: MB 2225
Email: nploymaklam “at” gmail
“dot” com
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Midterm Exam Date: Saturday,
January 24, 2026
at 15:30 PM to 18:30 PM
Location: TBA
Final Exam Date: Sunday, March 22, 2026 at 12:00 PM 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
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