First-year engineering mathematics shared by most AICTE and VTU-pattern programmes: Laplace transforms, Fourier series, eigenvalues and eigenvectors, partial differentiation, and vector calculus (gradient, divergence and curl).
5 reference pages
The Laplace transform definition, a table of standard transforms, the first shifting theorem, and solving a linear ODE with initial conditions.
The Fourier series formulas for a periodic function, and a fully worked derivation of the Fourier series for f(x) = x on (-π, π).
The characteristic equation for finding eigenvalues and eigenvectors, with a fully worked 2x2 example verified two ways: by substitution and by the trace/determinant check.
How to take partial derivatives of a multivariable function, with a worked example that also verifies equality of mixed second partial derivatives by direct computation.
The gradient, divergence, and curl operators explained, with worked examples computing each directly from a scalar and a vector field.