Mathematics – IA (BS-M101)
5 units: Calculus (Integration), Calculus (Differentiation), Matrices, Vector Spaces, Vector Spaces (Continued) · L-T-P 3L+1T/week.
Detailed syllabus
Unit 1: Calculus (Integration) (8 hours)
Calculus (Integration): Evolutes and involutes; Evaluation of definite and improper integrals; Beta and Gamma functions and their properties; Applications of definite integrals to evaluate surface areas and volumes of revolutions.
Unit 2: Calculus (Differentiation) (6 hours)
Calculus (Differentiation): Rolle’s Theorem, Mean value theorems, Taylor’s and Maclaurin’s theorems with remainders; Indeterminate forms and L'Hospital's rule; Maxima and minima.
Unit 3: Matrices (7 hours)
Matrices: Matrices, Vectors: addition and scalar multiplication, matrix multiplication; Linear systems of equations, linear Independence, rank of a matrix, determinants, Cramer’s Rule, inverse of a matrix, Gauss elimination and Gauss-Jordan elimination.
Unit 4: Vector Spaces (9 hours)
Vector Spaces: Vector Space, linear dependence of vectors, Basis, Dimension; Linear transformations (maps), Range and Kernel of a linear map, Rank and Nullity, Inverse of a linear transformation, Rank- Nullity theorem, composition of linear maps, Matrix associated with a linear map.
Unit 5: Vector Spaces (Continued) (10 hours)
Vector Spaces (Continued): Eigenvalues, Eigenvectors, Symmetric, Skew-symmetric, and Orthogonal Matrices, Eigenbases. Diagonalization; Inner product spaces, Gram-Schmidt orthogonalization.
Source: official document
