Course Number & Title: MA001 Preparatory Mathematics-I
L-T-P-C: 3-2-0-10
Pre-Requisite: Nil
Matrices: Scalar Multiplication, Addition, Multiplication, Transpose operations on Matrices, Properties of Matrix Operations; Determinant of a matrix and its properties, Elementary Row Operations, Gauss-Jordan Elimination method, Rank of a Matrix, Linear System of Equations, Inverse of a Matrix. (All examples and problems on this topic may be restricted involving matrices upto 3x3 size). Ordinary differential equations: Order and degree; ODE of first order and first degree: Variable separable method, Reduction to variable separable form; Exact equations, Reduction to exact equations; Linear equations, Reducible to linear equations, orthogonal and oblique trajectories.
Second order homogeneous linear equations with constant coefficients.
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Course Number & Title: MA002 Preparatory Mathematics-II
L-T-P-C: 3-2-0-10
Pre-Requisite: Nil
Sequence of real numbers, limit of a sequence, limit theorems, monotone sequence, Cauchy sequences, subsequences, Bolzano-Weierstrass Theorem (without proof).
Series of Real Numbers, Convergence, Absolute convergence, Comparison test, Root test and Ratio test.
Functions: Limit of Functions, Limit Theorems; Continuous functions, Algebra of Continuous Functions, Continuous functions on intervals, Inverse Functions; Differentiable functions, Rolle’s theorem, Mean value theorem, L'Hospital Rule, Maxima and Minima.
Introduction to Riemann Integration.
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