It is nearly impossible to argue why numerics is not important as it exists everywhere in the field of science and engineering, predictive analysis, decision making, risk mitigation etc. Nowadays, digital twin creation is leading the industrial and business world as a form of revolutionary technology to optimize a certain product, process or service. The objective of a digital twin/technological innovation is to make better and more informed decisions. Usually one applies simulations on the digital model itself to identify the parameter settings, predict performance under various operating conditions, identify the processes that could improve a product/system and perform a predictive analysis. Numerical methods/approximations are the core behind technological innovations, optimization, and finding solutions of physics driven complex systems of equations. In this course, we introduce the fundamental concepts behind numerical mathematics and analysis. We focus towards developing an understanding on numerical methods for solving complex systems of equations/ODEs/PDEs, building algorithms and implementing them in Python, and doing a sensitivity/error analysis. We develop a basic know-how on how a problem is stated, what it’s connection is to reality, how to anticipate errors and do a predictive analysis for different kind of problems. Every topic is accompanied by Python files to illustrate the concepts.