# 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.

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

• Christoffel symbols

For more details, refer to the following book:

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

Single-variable Calculus

Multi-variable Calculus

Ordinary Differential Equations

Linear Algebra and its Applications