The recent development of quantum algorithms has significantly pushed forward the frontier of using quantum computers for performing a wide range of scientific computing problems. This includes solving numerical linear algebra tasks for very large matrices, such as solving linear systems, eigenvalue decomposition, singular value decomposition, matrix function evaluation etc, as well as solving certain high dimensional linear and nonlinear differential equations, such as heat equations and wave equations. This workshop aims to bring together leading experts across different disciplines, including experts in solving related tasks using classical computers that can potentially inspire the development of new quantum algorithms; discuss recent progress made in the development of quantum algorithms for linear algebra and differential equations and the advances in classical algorithms; foster the discussion and pave the path towards identifying and overcoming challenging problems in science and engineering and for various industrial and technological applications.