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.