Course Code: 100102
Course Title: Engineering Mathematics–I
L-T-P-C: 3-1-0-4
Unit 1.0 – Linear Algebra-I (7 hrs)
- Elementary row operations, Gauss-Jordan method for finding matrix inverse
- Complex matrices: Hermitian, Skew-Hermitian, and Unitary matrices
- Vector space, subspaces, linear dependence and independence
- Linear span, basis, dimension, extension of basis of subspace
- Rank of a matrix, row and column space
- Solvability of system of linear equations
Unit 2.0 – Linear Algebra-II (7 hrs)
- Linear transformations, kernel and range
- Matrix representation of linear transformations
- Rank-Nullity Theorem
- Eigenvalues and eigenvectors, properties, and eigenbases
- Orthogonal and similarity transformations
- Matrix diagonalization, Cayley-Hamilton Theorem
Unit 3.0 – Calculus for Single Variable (7 hrs)
- Indeterminate forms and L’Hospital’s Rule
- Rolle’s Theorem, Mean Value Theorem
- Taylor and Maclaurin Series for single variable functions
- Riemann integration, Riemann sum, improper integrals
- Beta and Gamma functions and their properties
Unit 4.0 – Multivariable Calculus (Differentiation) (7 hrs)
- Functions of two or more variables: limit, continuity, and partial differentiation
- Total differentiation
- Taylor and Maclaurin series for functions of two variables
- Jacobian, maxima and minima
- Method of Lagrange multipliers
Unit 5.0 – Multivariable Calculus (Integration) (7 hrs)
- Double and triple integrals
- Change of order and variable in integration
- Conversion to polar, cylindrical, and spherical coordinates
- Applications: area and volume
Unit 6.0 – Vector Calculus (7 hrs)
- Scalar and vector fields
- Gradient, directional derivative, divergence, curl and their properties
- Line integrals, Green’s Theorem in a plane (without proof)
- Surface integrals, Stokes’ Theorem (without proof)
- Volume integral, Gauss-Divergence Theorem (without proof)
Text / Reference Books:
- Mathematics-I (Calculus & Linear Algebra)
– Reena Garg, Khanna Book Publishing Co.
ISBN-10: 9391505171 - Advanced Engineering Mathematics – Chandrika
Prasad & Reena Garg, Khanna Book Publishing Co., 2021
ISBN-10: 9386173522 / ISBN-13: 9789386173522 - Higher Engineering Mathematics – B.V. Ramana,
Tata McGraw Hill, 2010
ISBN-10: 007063419X / ISBN-13: 9780070634190 - Advanced Engineering Mathematics – S.R.K.
Iyengar, R.K. Jain, Narosa, 5th Edition
ISBN-10: 8184875606 / ISBN-13: 9788184875607 - Advanced Engineering Mathematics – Erwin Kreyszig, 9th Edition, John Wiley & Sons, 2006
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