Mathematics has evolved over the period of time. In the modern era, it is not restricted to pure theory, infact its models and simulations have found their uses in various industries for problem solving. Applied mathematics focuses on the application of mathematical concepts across diverse disciplines of science, engineering, business, computer science, etc. The significant concepts of applied mathematics such as differential equations, approximation theory, probability, etc. have been discussed in detail within this text. It unravels the recent studies in this field. It will serve as a reference to a broad spectrum of readers and will also help those who are researching in this field.