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A First Course on Operations Research and Information Theory by Sanat Kumar Mazumder, published by New Central Book
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Core Core Syllabus & Topic Details:-
While individual university curriculums (such as MAKAUT or other technical universities) vary slightly, a standard Volume I (Engineering Mathematics-I) syllabus comprehensively includes the following mathematical branches and modules:
1. Matrix Theory & Linear Algebra
- Matrices and Determinants: Basic properties, rank of a matrix, and inverse of a matrix via elementary transformations.
- System of Linear Equations: Consistency of linear systems and solution methods (Gaussian elimination, Gauss-Jordan).
- Eigenvalues & Eigenvectors: Characteristic equations, Cayley-Hamilton Theorem and its applications, and diagonalization of matrices.
2. Differential Calculus (Single & Multivariable)
- Successive Differentiation: Higher-order derivatives and Leibniz’s Theorem.
- Mean Value Theorems: Rolle’s Theorem, Lagrange’s Mean Value Theorem, and Cauchy’s Mean Value Theorem.
- Series Expansion: Taylor’s and Maclaurin’s series expansions for single variables.
- Partial Differentiation: Functions of several variables, total derivative, and Euler’s theorem on homogeneous functions.
- Applications: Maxima and minima of functions of single and multiple variables (including Lagrange’s multipliers method), jacobians, curvature, asymptotes, and curve tracing.
3. Integral Calculus
- Definite Integrals: Fundamental properties, reduction formulae, and evaluation of integrals.
- Improper Integrals: Beta and Gamma functions and their mathematical properties.
- Multiple Integrals: Double and triple integrals, changing the order of integration, and computing areas and volumes.
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