Mathematical Methods for Engineering Applications

Catalog description

According to Galileo, the book of Nature is written in the language of mathematics. Physics is often regarded as the poetry of mathematics. A firm grasp of mathematical techniques is essential to understand the physical nature of matter. Good familiarity with mathematics also helps a student to comprehend and develop scientific ideas. Most fundamental problems in physical sciences may be impossible to solve because of the complexity of Nature. However, a well-formulated simple mathematical problem may indeed be solvable and give a preliminary understanding of the underlying physical phenomena. It is, thus, essential for graduate students to be exposed to standard topics in mathematics and understand how mathematical tools are applied to physical sciences and engineering problems. This course focuses on applications of mathematical methods. No rigorous mathematical derivations are included. The course covers five major topics listed below. 1. Complex Analysis 2. Integral Transforms (Fourier and Laplace) 3. Linear Algebra (Transformations and Tensors) 4. Sturm-Liouville Theory of Linear Differential Equations 5. Partial Differential equations These topics find applications in understanding the Quantum mechanical, electronic, optical, mechanical properties of materials, solving electromagnetic, sound elastic wave propagations in different media, diffusion and its kinetics and Machine Learning.