Maths SLM

  Syllabus (PDF 964 KB)

Semester I	Title	Video Lecture
Unit 1	Matrices	Some Types of Matrices,  Rank of Matrix, Finiyely generated Space, Dimention of Space, Rank of Matrix, Solution of Non Homogeneous Linear Equation, Elementary Operations of Matrixes, Adjoint and inverse of a Matrix, Singular & Nonsingular Matrices, Nature of general solution of a system of non linear homogeneous equations, Negative Integral Power Of Matrix, Relation, Equivalence Relations and Partition, Congruence Modulo n, Metric Spaces
Unit 2	Trigonometry	Trigonometric and Hyperbolic Functions
Unit 3	Differential Calculus	Types Of Discontinuities And Intermediate Value Theorem, Geometrical and mathematical Definition of Tangent, Indeterminate Form, Function of single variable, Fuzzy Set Theory

Semester II	Title	Video Lecture
Unit 1	Integral Calculus	Integral Calculus l, Integral Calculus ll, Beta Gamma Functions l, Beta and Gamma Functions ll ,Integral Calculus, Beta Gamma Function, Integral Calculus
Unit 2	Vector Analysis	Characteristic Roots and Vectors, The Plane

 

Semester III	Title	Video Lecture
Unit 1	Group Theory	Group Theory Part 1,  Group Theory Part 2, Cyclic Group, Homomorphism, Cyclic groups – Definition & Example , Coset Decomposition, Properties of Cyclic Group, Classification of Subgroups of Cyclic Groups, Isomorphism and Cayley`s Theorem, Lagrange`s Theorem and its Consequences,   Permutation Group, Properties of a Normal Group, Normalizer and Centralizer, Properties of Isomorphisms, Classification of Subgroups of Cyclic Groups, Abelian Group, Finite and Infinite, Order of a finite Group, Homomorphism Of Groups, Subgroup Defination and Theorem
Unit 2	Analytical Geometry	Predicates, Minimum Spanning Tree

 

Semester IV	Title	Video Lecture
Unit 1	Ordinary Differential Equations	Reducible homogeneous differential equations, Linear Differential Equation Of First Order But Not Of First Degree, Nature of general solution of a system of non linear homogeneous equations, Solution of Non Homogeneous Linear Equation, Frobenous Method
Unit 2	Ring Theory	Algebra, linear Transformation, linear operator, Isomorphism with example

 

 

Semester V	Title	Video Lecture
Unit 1	Real Analysis	Sequence of Measurable Functions, Functions of Bounded Variation
Unit 2	Functions of several variables and Partial Differential Equations
Unit 2	Numerical Analysis and Operations Research	Linear Programming Problem – Big-M Method, Maximal Flow Problem

 

Semester VI	Title	Video Lecture
Unit 1	Complex Analysis
Unit 2	Mechanics