Calculus class notes for gate

# Calculus class notes for gate

Calculus: Functions of single variable; Limit, continuity and differentiability; Mean value
theorems, local maxima and minima, Taylor and Maclaurin series; Evaluation of definite
and indefinite integrals, application of definite integral to obtain area and volume; Partial
derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities, Directional
derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher
order linear equations with constant coefficients; Euler-Cauchy equations; Laplace
transform and its application in solving linear ODEs; initial and boundary value problems.
Partial Differential Equation (PDE): Fourier series; separation of variables; solutions of one dimensional diffusion equation; first and second order one-dimensional wave equation
and two-dimensional Laplace equation.

1. Differentiation
2. Integration
3. Partial Differentiation
4. multiple Integrals
5. Vector  Differentiation
6. Vector integration
7. Fourier series 