EP30.FSF1105 — Numerical Analysis
Course description
This course provides an in‑depth introduction to the theory and application of numerical methods for solving mathematical problems encountered in scientific computing. Students study error analysis, numerical solutions of equations and systems, interpolation, numerical differentiation and integration, and numerical solutions of differential equations. Emphasis is placed on algorithmic understanding, accuracy, stability, and computational implementation.
Knowledge Objectives: Provide learners with fundamental knowledge of numerical methods for function approximation (including interpolation, uniform approximation, and least-squares approximation); methods for solving various types of equations (algebraic and transcendental equations, linear systems, Cauchy problems and boundary-value problems for ordinary differential equations, and partial differential equations); as well as numerical techniques for approximating derivatives and integrals.
Skills Objectives: Learners must master the theoretical foundations and be able to apply them creatively to solve common practical problems. They should develop algorithmic thinking and computational skills, including problem analysis, algorithm design, construction of detailed computational schemes, programming, and performing numerical experiments on a computer. Throughout the course, learners are required to complete several computational assignments involving numerical experimentation.
Course requirements
Requirements for taking final /terminal exams
Students are allowed to take the final exam/terminal exams (50%) if their attendance score (10%) reaches 5 points or more (on the scale of 10).
Requirements for attending classes
Students are responsible for attending all classes. In case of absence from school due to force majeure reasons, sufficient and reasonable proofs must be provided. For each absence, 1 point will be deducted 1 point. Students who miss any classes more than 3 times, with or without reason, will be considered as failing to complete the course and have to re-register.
Students will be awarded points for constructive comments these points are added to attendance points and group assignments.
Groups who do not submit the group work will receive a score of 0 (zero). Late submissions will be deducted for each day of late submission.
Requirements for in-class behaviour
The course is conducted on the principle of respecting learners and lecturers. Any behaviour that affects the teaching and learning process is strictly prohibited.
Students must come to class on time. Students who are late more than 10 minutes after class starts will not be allowed to attend the class. Do not make noise and affect others during the learning process.
Laptops and tablets are only used for the purpose of taking notes and calculating for lectures and exercises, absolutely forbidden to use for other purposes.
Detailed content
The course content is organized into five chapters:
Chapter 1: Mathematical Preliminaries and Error Analysis
Chapter 2: Solutions of Equations in One Variable
Chapter 3: Interpolation and Polynomial Approximation
Chapter 4: Numerical Differentiation and Integration
Chapter 5: Initial-Value Problems for ODEs
Lecturers
- Le Thi Anh
- Phung Minh Duc
- Bui Quoc Hoan
- Nguyen Duc Nam
- Doan Trong Tuyen
- Tong Thanh Trung
Teaching plan
Week 1
Week 1
Week 2
Learning resources
- Numerical Analysis — Richard L. Burden and J. Douglas Faires, Ninth Edition, 2011
- Introduction to Numerical Analysis — J. Stoer, Bulirsch, Springer, 1999
- Numerical methods: design — Greenbaum, T.P. Chartier, analysis and computer implementation of algorithms, 2012