**Engineering Mathematics**

**Engineering Mathematics**

**Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry.**

**In engineering mathematics, one may deal with the following topics:**

**Fourier series and approximation by trigonometric polynomials****Orthogonal and generalized Fourier series****Fourier integrals****Fourier cosine and sine transforms****Fourier transform****Basic concepts in partial differential equations (PDEs)****Wave equation and its solution by separating of variables****D'Alembert's solution for wave equations****The heat equation and its solution by Fourier series****Single-variable complex functions****Limits, continuity, and derivatives of complex functions****Cauchy-Riemann equation and Laplace's equation****Line integral in the complex plane****Cauchy's integral theorem****Cauchy's integral formula****Conformal mapping**

For more details, refer to the following book:

Kreyszig, E. (2009). Advanced Engineering Mathematics, 10th Edition.

**Advanced Engineering Mathematics**

**A course on advanced engineering mathematics may include other optional topics such as**

**A review of essential concepts in****linear algebra****like the notions of vector spaces, basis and dimension of a vector space, inner product, and orthogonal basis****Einstein's summation convention****Dual bases****Second-order tensor as a linear mapping****Representation of cross product and rotation by a second-order tensor****Tensor product****Representation of a tensor with respect to a basis****Special operations on second-order tensors****The inner product of second-order tensors****Decomposition of second-order tensors****Vector- and tensor-valued functions and their differential calculus****Tangent vectors and metric coefficients****Gradient, covariant and contravariant derivatives****Deformation gradient****Christoffel symbols**

For more details, refer to the following book:

Itskov, M. (2019). Tensor algebra and tensor analysis (with applications to continuum mechanics). Springer.