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.

Single-variable Calculus

Multi-variable Calculus

Ordinary Differential Equations

Linear Algebra and its Applications