老学长代写代考留学生Numerical Analysis assignment take home

这门课程要求，学生对于matlab的掌握程度非常熟练，

HW占比40%, 大project占比30%，有的学期是Project 15%, Midterm 15%

知识范围

• §1. Finite difference and finite volume approximations;
• §2. Boundary value problems;
• §3. Elliptic equations;
• §5. Initial value problems;
• §6. Zero-stability and convergence;
• §7. Absolute stability;
• §8. Stiff ODEs;
• §9. Method of lines代写;
• §10. Hyperbolic systems代写;

Interpolation for functions of one variable

The idea of interpolation is to estimate values of a function (of one or more variables) between given points (nodes, or locations), not necessarily equally spaced. The data might come from a known function that is very dicult or slow to evaluate except at certain points, or experimentally. A fundamental property of interpolation is that the interpolating curve (n = 1) or hypersurface (n 2), called the interpolant, goes through the given data points exactly. Hence interpolation is necessarily dierent from a process such as least squares regression.

Recall that a Taylor polynomial approximates a function using its value and values of a certain number of derivatives all at one point, while on the other hand a Lagrange polynomial approximates a function using its values at many dierent points. In between there are interpolating polynomials that approximate a function by matching its values and some derivative values at several points. These a called osculating polynomials. If we seek to match up only function values and the rst derivative values at given nodes we obtain Hermite polynomials.