Syllabus:

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.
Complex Numbers     
Introduction to Complex Numbers – 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.
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 to Geometrical Problems – Roots of Higher Degree Polynomial Equations – Polynomials with Additional Information – Polynomial Equations with no additional information – Descartes Rule.
Inverse Trigonometric Functions
Introduction – Some Fundamental Concepts – Sine Function and Inverse Sine 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.
Two Dimensional Analytical Geometry-II
Introduction – Circle – Conics – Conic Sections – Parametric form of Conics – Tangents and Normals to Conics – Real life Applications of Conics.
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 – Different forms of Equation of a Straight line – Different forms of Equation of a plane – Image of a point in a plane – Meeting point of a line and a plane
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 
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 
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
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
Probability Distributions
Introduction – Random Variable – Types of Random Variable – Continuous Distributions – Mathematical Expectation – Theoretical Distributions – Some Special Discrete Distributions 
Discrete Mathematics 
Introduction – Binary Operations – Mathematical Logic

Course Outcomes