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XuetangX

Numerical Analysis

Xihua University via XuetangX

Overview

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In today’s information age, numerical analysis has become an indispensable tool in a wide range of fields. As an important branch of mathematics, Numerical Analysis aims to solve practical problems in science, engineering, economics, and other areas. This course provides an in-depth introduction to the fundamental principles and methods of numerical analysis. Through clear and engaging explanations combined with practical examples, complex concepts and methods are made easier to understand. By studying this course, students will not only master classical mathematical methods and algorithms, but also improve their logical thinking and problem-solving skills. Whether you are engaged in scientific research, engineering applications, economic management, or other fields, this course will provide valuable knowledge and practical support.



Syllabus

  • Introduction
    • 0.1 Understanding Computational Methods
    • 0.3 Errors and Significant Digits
  • Chapter 1 Interpolation
    • 1.1 Interpolation
    • 1.2 Newton Form of Polynomial Interpolation
  • Chapter 2 Least-Squares Fitting
    • Chapter 3 Solving Nonlinear Equations
      • Chapter 4 Direct Methods for Solving Linear Systems of Equations
        • 4.3 Direct Factorization Methods
      • Chapter 5 Iterative Methods for Solving Linear Systems of Equations
        • Chapter 6 Numerical Integration and Numerical Differentiation
          • 6.1 Newton–Cotes Numerical Integration
        • Chapter 7 Numerical Solutions of Ordinary Differential Equations
          • 7.1 Euler’s Method
        • Final Exam

          Taught by

          Hou Zhibo and Dou Hongxia

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