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 nonlinear) equations; higher
order linear equations with constant coefficients; EulerCauchy 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 onedimensional wave equation
and twodimensional Laplace equation.
Limits and continuity
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 nonlinear) equations; higher
order linear equations with constant coefficients; EulerCauchy 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 onedimensional wave equation
and twodimensional Laplace equation.
Limits and continuity
 Differentiation
 Integration
 Partial Differentiation
 multiple Integrals
 Vector Differentiation
 Vector integration
 Fourier series
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