Explore the fundamentals of numerical solutions for differential equations in this 22-minute lecture from the University of Oxford's 3rd Year Mathematics Undergraduate Course. Delve into the various problems involving differential equations that arise in scientific and engineering applications, guided by Professor Endre Suli. Learn about the evolution of crack-fields, computational grids, and complex differential equations. Discover the mathematics behind numerical algorithms, including the basic idea and Euler's method. Gain insights into cosmological simulations of the Universe's evolution. After the lecture, attend tutorials to further discuss the material and work through problem sheets with a tutor. Access additional course materials online and explore related lectures on differential equations from other years of study.