Page 31 of 241 5 Symmetric and Skew Symmetric Matrices 2 6 Determinants, Minors, Cofactors, Inverse of a matrix 3 II Linear Algebra and Vector Calculus 12 18 7 Linear Independence: Characteristic equations, 1 8 Eigen values, Eigen Vector 2 9 Solving system of linear equations: Gauss Elimination Method, Gauss Jordan method, Gauss Siedel Methods 3 10 Vectors: Definition Magnitude of a vector, Types of Vectors, Vector addition 2 11 Dot products and Cross products 2 12 Vectors in 2- and 3-space 2 III Differentiation 11 17 13 Limits; Definition (concept only), Derivative of a Point, Derivative at Function 2 14 Differentiation:
Definition, Differentiation from first principle, Differentiation of important function 2 15 Product rule, Quotient rule 3 16 Derivative of function of a function 2 17 Logarithmic differentiation 2 IV Integration 11 17 18 Integration: Integral as Anti-derivative, Indefinite integral & constant of integration 2 19 Fundamental theorems, Elementary Standard results 2 20 Integral of different functions, Integration by Substitution 3 21 Definite Integrals, Properties of definite integrals 2 22 Evaluation of Definite Integrals by Substitution 2 V Open Ended Module – Application Level 12 1 Discuss topics from the following: • Differential Equation. • Concept of First Order ODE’s.
• Concept of Second Order ODE’s. • Application of Logarithm. • Combinatorics. • Trigonometric concept. • Applications of Matrices in various field of computer like image processing, cryptography etc. • Real-world examples for using eigen values and eigen vectors. • Vectors assist in GPS technology to provide accurate 10