Calculus class notes for gate

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Calculus class notes for gate

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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
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