Explore quantum algorithms for dynamics simulation in this comprehensive lecture focusing on Hamiltonian simulation and general differential equations. Delve into cutting-edge research presented by Di Fang from Duke University as part of IPAM's Mathematical and Computational Challenges in Quantum Computing Tutorials. Gain insights into the first part of a two-part series that addresses the complexities of quantum dynamics and their computational applications. Discover how these advanced algorithms are shaping the future of quantum computing and their potential impact on solving complex mathematical and physical problems.