Interesting.
I didn't know calculus 4 was a thing. I though it all ended in calculus III.
See this guy's list
https://www.quora.com/What-is-Calculus-4
In my university, for mechanical engineering and electronic engineering...
Calculus 1: basic, single variable calculus. Includes:
- Limits and continuity
- Derivatives and differentiation
- Taylor polynomials for approximation
- Indefinite integrals
- Definite integrals
- Geometrical applications of integrals (centroids, volumes of revolution, etc)
- 1st order differential equations, linear and nonlinear
- N-th order differential equations, linear and some nonlinear cases
- Systems of differential equations
- Improper integrals
- Series and convergence
- Special functions (Gamma, Zeta, etc)
- Multivariable functions
- Multivariable limit and continuity
- Multivariable differentiation, gradient and hessian matrix
- Parametric curves in space
- Vector fields, divergence, rotor and laplacian operators
- Potential functions
- Double, triple and surface integrals
- Stokes', Green's, Gauss' and Helmholtz's theorem
- Complex valued functions
- Holomorphic functions and Cauchy-Riemann equations
- Integration and Cauchy's integral formula
- Conformal mappings
- Complex Taylor and Laurent series
- Zeros, poles and residues
- Improper integral calculations
- Laplace transform
- Tensor calculus
- Convolution product
- Fourier series and transform
- Partial differential equations
