# MTH:165 List Of Solved Problems,Mid term,End term,Notes

## List Of Solved Problems(MTH 165)

Unit I Linear Algebra : Review of matrices, Elementary operations of matrices, Rank of a matrix, Linear dependence and independence of vectors, Solution of Linear system of equations, Inverse of matrices, Eigen values and Eigen vectors, Properties of Eigen values, Cayley-Hamilton theorem Unit II Differentiatial and integral calculus : General rules of differentiation, Derivatives of standard functions, Derivatives of Parametric forms, Derivatives of implicit functions, Logarithmic differentiation,, properties of indefinite integral, Methods of integration-By Parts, Methods of integration-By Partial fractions, Properties of definite integral Unit III Fourier series : Introduction and Euler's formulae, Conditions for a Fourier Expansion and Functions having points of discontinuity, Change of interval, Even and odd functions, Half Range series, Perseval's Formula, Complex form of Fourier Series Unit IV Multivariate functions : Functions of two variables, Limits and Continuity, Partial derivatives, Total derivative and differentiability, Chain rule, Euler's theorem for Homogeneous functions, Maxima and Minima, Lagrange method of multiplier Unit V Multiple Integrals : Double integrals, change of order of integration, Triple integrals, change of variables, Application of double integrals to calculate area and volume, Application of triple integrals to calculate volume. Unit VI Linear Programming Problems : Formulation of the problem, Graphical Method, General LPP, Canonical and standard form of LPP, Simplex method, Duality concept

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