Scientific Computing Homework

This repository contains homework assignments for the Scientific Computing course taught by Professor Pan Jianyu.

Course Information

• Instructor: Professor Pan Jianyu (潘建瑜)
• Textbook: Course Lecture Notes (Brief Introduction to Scientific Computing)

Course Topics

1. Introduction to Scientific Computing

• Linear Algebra Fundamentals
• Errors in Numerical Computation
• Assignments: 1.1, 1.2, 1.4, 1.6, 1.8

2. Numerical Methods for Nonlinear Equations

• Bisection Method / Fixed-Point Iteration / Steffensen's Method
• Newton's Method / Secant Method / Parabolic Method
• Assignments: 2.1, 2.2, 2.3, 2.5
• Optional: 2.4, 2.6, 2.7, 2.8
• Programming Assignment: hwm202501.pdf

3. Direct Methods for Linear Systems

• Gaussian Elimination / Matrix Factorization Methods
• Perturbation Analysis / Solution Refinement
• Assignments: 3.1, 3.3, 3.4, 3.5, 3.7, 3.8, 3.10
• Optional: 3.2, 3.6, 3.9, 3.11, 3.12
• Programming Assignment: hwm202502.pdf

4. Iterative Methods for Linear Systems

• Stationary Iterative Methods
• Convergence Analysis / Classical Iterative Methods
• Steepest Descent Method & Conjugate Gradient Method
• Assignments: 4.1, 4.2, 4.5, 4.6, 4.7, 4.9, 4.10
• Programming Assignment: hwm202503.pdf

5. Linear Least Squares Problems

6. Function Interpolation

7. Numerical Integration and Differentiation

Repository Structure

Scientific_Computing_homework/
├── README.md
├── hw1/                # Nonlinear Equations
├── hw2/                # Direct Methods for Linear Systems
└── hw3/                # Iterative Methods for Linear Systems

Key References

• Numerical Analysis (5th Edition) - Li Qingyang et al., Tsinghua University Press, 2008
• Numerical Analysis and Algorithms (3rd Edition) - Yu Wenjian, Tsinghua University Press, 2020
• Numerical Analysis (3rd Edition) - T. Sauer, Pearson, 2018
• Matrix Computations (4th Edition) - Golub & van Loan, 2013

Acknowledgments

Thanks to Professor Pan Jianyu for an excellent course in Scientific Computing.

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Last Updated: November 2025