# 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.

Ordinary Differential Equations