Unit I: Algebra, vectors, and geometry
solution of equations
linear algebra: Determinants, matrices
vector Algebra and solid Geometry
Unit II: calculus
differential Calculus and its applications
partial differentiation and its applications
integral calculus and its applications
multiple Integrals and Beta, Gamma functions
vector calculus and its applications
Unit III: series
infinite series
Fourier series
Unit IV: differential equations
differential equations of first order
applications of differential equations of first order
linear differential equations
applications of linear differential equations
differential equations of other types
series solution of differential equations and special functions
partial differential equations
applications of partial differential equations
Unit V: complex analysis
complex Numbers and functions
calculus of complex functions
Unit VI: transforms
Laplace transforms
Fourier transforms
z-transforms
Unit VII: numerical techniques
empirical laws and curve-fitting
statistical methods
probability and distributions
sampling and inference
Numerical solution of equations
finite difference and interpolation
Numerical differentiation and integration
difference equations
Numerical solution of ordinary differential equations
Numerical solution of partial differential equations
Unit VIII: special topics
Calculus of variations.