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Few Topics are:

• Linear Algebra, Vectors, linear independence, subspaces, Matrix Algebra, Linear equations, inverses, linear transformations,eigenvalues/vectors.,Sequences and Series
• Limit and convergence , sequences and series.,Calculus,Limits,continuity, LU Decomposition,Solution of simultaneous equations, differentiable functions,differentiation of inverse functions
• integration, logarithms, exponentials,Taylor’s theorem,Abstract Algebra, groups, rings,fields ,vector spaces,Second-order Ordinary Differential Equations, Solution of equations,Inverse matrices,LinearAlgebra
• Linear Equations with constant coefficients;,Homogeneous and non-homogeneous cases,Complementary functions and particular integrals,Special cases with non-constant coefficients
• Partial Differentiation,Chain rule for partial differentiation, Gaussian Elimination,Cholesky's method, Taylor Series in Two variables,Second-order partial differential equations
• Matrices and Determinants,Definition of an m x n matrix,Matrix addition, subtraction, multiplication by a scalar,Matrix multiplication,Square matrices,,Determinants and properties
• Total derivatives,Theory of errors,Coordinate Systems, change of variables,Series and Limits,L'Hopital's Rule,Sequences and Series,Convergence,Power Series,Taylor and Maclaurin Series.,Functions of Two Variables,Maxima, minima and saddle points

Complex Topics are:

• First-order differential equations
• second-order linear differential equations
• determinants and matrices
• systems of linear differential equations
• Laplace transforms

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