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## Course Content

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GENERAL INFORMATION

LINEAR ALGEBRA

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Rank of Matrix
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Linear Equations
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Determinant
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Vector Spaces
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Change of Basis
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Orthogonality
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Symmetric Matrices
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Similar Matrices
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CALCULUS

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Dirichlet Theorem
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Centre of Mass
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Moment of Inertia
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Surface Area
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Continuity
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Differentiability
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Monotonicity
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Critical Points
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Maxima and Minima
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Rolle Theorem
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Taylors Theorem
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ORDINARY DIFFERENTIAL EQUATION

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DYNAMICS AND STATICS

Gradient
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Problems on Gradient
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Divergence and Curl
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Greens Theorem
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Stokes Theorem
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ALGEBRA

Defining Groups
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Modulo Arithmetic
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Cayley Table
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Unit Group
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Group of Matrices
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Subgroup
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Problems on Groups
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Cyclic Groups
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Permutation Group
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REAL ANALYSIS

Set Theory
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Countability of Sets
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Real Numbers
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Open Sets
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Closed Sets
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Limit Points
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Monotonic Sequence
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Limit Points
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Subsequence
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Cauchy Sequence
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Alternating Series
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Power Series
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NUMERICAL ANALYSIS AND COMPUTER PROGRAMMING

Bisection Method
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Regula Falsi Method
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Interpolation
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MECHANICS AND FLUID DYNAMICS

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Coupled Oscillation
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Angular Momentum
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