While in chapter 10 and 11 and 12 basics of ordinary differential equations, integrating factor, exact differential equation and linear differential equation of higher orders with constant coefficients and method to solve these equations and second order differential equations and various methods to solve them are discussed. While in chapter 8 infinite series and sequences are discussed.Ĭhapter 9 deals Fourier series which includes periodic function, even &odd function, Euler’s formulae, Fourier series for discontinuous functions, even and odd functions, Fourier Sine and cosine series. In chapter 7 differential and integral calculus which includes parametric representation of vector function, Gradient of a scalar field, divergence of a vector field, curl of a vector function, Green’ theorem, Gauss theorem and Stokes’s theorem are discussed. While in chapter 6 special functions which include Bessel’s equation, Legendre’s polynomial’s, Beta and Gamma functions along with properties including orthogonal properties are discussed. In chapter 5 we have discussed area, volume and Surfaces of Solids of Revolution of curves in Cartesian, polar and parametric coordinates, moment of inertia, improper and multiple integrals, Dirichlet’s Integral.
Asymptotes of the curve and curve tracing in Cartesian, polar and parametric coordinates are discussed. In chapter 4 Lagrange’s multipliers method to find extreme points of two and more variables, Convexity, Concavity, and Point of Inflection are discussed. While in chapter 3 partial derivatives of higher orders, homogeneous function including Euler’s theorem, Jacobian and its properties, Taylor’s series. In chapter 1 we have discussed matrix algebra which includes basic terminology of matrix, matrix inverse, rank of a matrix and solution of homogeneous and non-homogeneous simultaneous equations, characteristic roots and vectors, quadratic forms, applications of matrices.
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