Syllabus

Chapter 1 : Applications of Matrices and Determinants

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.

Chapter 2 : Complex Numbers

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.

Chapter 3 : Theory of Equations

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.

Chapter 4 : Inverse Trigonometric Functions

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.

Chapter 5 : Two Dimensional Analytical Geometry-II

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

Chapter 6 : Applications of Vector Algebra

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.

Chapter 7 : Applications of Differential Calculus

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.

Chapter 8 : Differentials and Partial Derivatives

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.

Chapter 9 : Applications of Integration

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.

Chapter 10 : Ordinary Differential Equations

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.

Chapter 11 : Probability Distributions

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

Chapter 12 : Discrete Mathematics

Introduction - Binary Operations - Mathematical Logic.

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