B.Tech Preparatory in Mathematics

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.

References:
1. G. Schay, Introduction to Linear Algebra, Narosa, 1998.
2. S. L. Ross, Differential Equations, 3rd Edition, 2007
3. David Poole, Linear Algebra: A Modern Introduction, 4th Edition, Cengage Learning India Pvt. Ltd., 2014.
4. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley, 2015.

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.

References:
1. G. B. Thomas Jr. and R. L. Finney, Calculus and Analytic Geometry, 9th Edition/ Any Edition, Pearson, 2010.
2. K. A. Ross, Elementary Analysis: The Theory of Calculus, Springer, First Indian Reprint, 2004.
3. R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis, 4th Edition, Wiley, 2014.

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