Abstract: The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying ...

Abstract: There are some quasi-tridiagonal system of linear equations arising from numerical simulations, and some solving algorithms encounter great challenge on solving quasi-tridiagonal system of ...

The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. Find the equation of the line of symmetry and ...

Sparse methods are primarily valuable for systems in which the number of non-zero entries is substantially less than the overall size of the matrix. Such situations are common in physical systems, ...

The graphs of \(y = 2x + 1\) and \(y = 2x - 2\) are shown below. The graph of \(y = 2x + 1\) crosses the \(y\)-axis at (0, 1). The graph of \(y = 2x - 2\) crosses the ...

This section focuses on the key features and methods for working with linear graphs. It demonstrates how to sketch graphs from rules, derive rules from graphs, and calculate key features such as the ...

Master the Toolkit of AI and Machine Learning. Mathematics for Machine Learning and Data Science is a beginner-friendly Specialization where you’ll learn the fundamental mathematics toolkit of machine ...

The IBPS RRB Clerk Prelims 2025 serves as the first filter in selecting capable candidates for regional rural banks, emphasizing quick thinking and precision. With just 45 minutes to tackle two ...

Also available at the Bates Study Center and Gosnell 08-1200.

Trigonometric ratios are used to find the unknown side or angle of a right-angled triangle. There are three different trigonometric ratios, \(\sin(\theta), \cos(\theta)\), and \(\tan (\theta)\). Each ...