Introduction – Inverse of a Non-Singular Square Matrix – Elementary Transformations of a Matrix – Applications of Matrices: Solving System of Linear Equations – Applications of Matrices: Consistency of system of linear equations by rank method.

Introduction – Complex Numbers – Basic Algebraic Properties of Complex Numbers -Conjugate of a Complex Number – Modulus of a Complex Number – Geometry and Locus of Complex Numbers – Polar and Euler form of a Complex Number – de Moivre’s Theorem and its Applications.

Introduction – Basics of Polynomial Equations – Vieta’s Formulae and Formation of Polynomial Equations – Nature of Roots and Nature of Coefficients of Polynomial Equations – Applications of Polynomial Equation in Geometry – Roots of Higher Degree Polynomial Equations – Polynomials with Additional Information – Polynomial Equations with no additional information – Descartes Rule.

Introduction – Some Fundamental Concepts – Sine Function and Inverse Sine Function -The Cosine Function and Inverse Cosine Function – The Tangent Function and the Inverse Tangent Function – The Cosecant Function and the Inverse Cosecant Function -The Secant Function and Inverse Secant Function – The Cotangent Function and the Inverse Cotangent Function – Principal Value of Inverse Trigonometric Functions -Properties of Inverse Trigonometric Functions.

Introduction – Circle – Conics – Conic Sections – Parametric form of Conics – Tangents and Normals to Conics – Real life Applications of Conics.

Introduction – Geometric Introduction to Vectors – Scalar Product and Vector Product -Scalar triple product – Vector triple product – Jacobi’s Identity and Lagrange’s Identity -Application of Vectors to 3-Dimensional Geometry – Different forms of Equation of a plane – Image of a point in a plane – Meeting point of a line and a plane.

Introduction – Meaning of Derivatives – Mean Value Theorem – Series Expansions -Indeterminate Forms – Applications of First Derivative – Applications of Second Derivative – Applications in Optimization – Symmetry and Asymptotes – Sketching of Curves.

Introduction – Linear Approximation and Differentials – Functions of Several Variables – Limit and Continuity of Functions of Two Variables – Partial Derivatives – Linear Approximation and Differential of a Function of Several Variables.

Introduction – Definite Integral as the Limit of a Sum – Fundamental Theorems of Integral Calculus and their Applications – Bernoulli’s Formula – Improper Integrals -Reduction Formulae – Gamma Integral – Evaluation of Bounded Plane Area by Integration – Volume of a Solid obtained by Revolving Area about an Axis.

Introduction – Differential Equation, Order, and Degree – Classification of Differential Equations – Formation of Differential Equations – Solution of Ordinary Differential Equations – Solution of First Order and First Degree Differential Equations – First Order Linear Differential Equations – Applications of First Order Ordinary Differential Equations.

Introduction – Random Variable – Types of Random Variable – Continuous Distributions -Mathematical Expectation – Theoretical Distributions: Some Special Discrete Distributions.

Introduction – Binary Operations – Mathematical Logic.