L 3 C 3
Teachers Continuous Evaluation: as per university examination norms. End Term Theory Examination: as per university examination norms.
Course outcomes
- Ability of students to understand, apply and analyze the basic concepts of linear algebra and matrix theory. [K1,K2,K3,K4]
- Ability of students to solve system of linear equations, determine eigenvalue, eigen vectors and apply them to real world problems. [K1, K2, K3]
- Ability of students to solve ordinary differential equations to solve engineering problems. [K1,K2, K3]
- Ability of students to solve some important partial differential equations like wave, heat and laplace equation. [K1, K2, K3, K4]
Unit I (8 lectures)
Linear Algebra I: Vector space, subspaces, linear dependence and independence of vectors, bases, and dimension, matrices, Rank and nullity of a matrix, rank -nullity theorem (without proof), Projection matrix, symmetric, skew-symmetric matrix, Orthogonal and unitary matrix, Idempotent matrix, Partition matrix
Unit II (8 lectures)
Linear Algebra II: Solution of systems of linear equations, Gaussian elimination, Eigenvalues and Eigenvectors with applications, Algebraic and geometric multiplicity, Determinant and its properties, Projections, LU decomposition, Singular value decomposition, Quadratic forms
Unit III (8 lectures)
Ordinary Differential Equations: First order linear and nonlinear differential equations: : Separable ODEs, exact ODEs and integrating factor, Bernoulli equations. Homogeneous linear ODEs of second (and higher) order with constant coefficients, Euler-Cauchy equations, Wronskian, Solution of non homogeneous linear ODEs: : method of undetermined coefficients, Method of variation of parameters
Unit IV (8 lectures)
Partial Differential Equations: Basic concepts of PDEs, heat, wave, and Laplace equation and their solution by method of separating variables, D’Alembert’s solution of wave equation.
Textbooks
- Kreyszig, E. (2025). Advanced engineering mathematics (11th Indian adaptation ed.). Wiley India
- Friedberg, S. H., Insel, A. J., & Spence, L. E. (2022). Linear algebra (5th ed.). Pearson.
References
- Stroud, K. A., & Booth, D. J. (2020). Engineering mathematics (8th ed.). Macmillan International Higher Education.
- Zill, D. G. (2022). Advanced engineering mathematics (7th ed.). Jones & Bartlett Learning.