Units | Topics |
Applications of Matrices and Determinants | Introduction, Inverse of a Non-Singular Square Matrix, Adjoint of a square Matrix, Properties of inverses of matrices, Row-Echelon form and others. |
Complex Numbers | Introduction to Complex Numbers, Powers of imaginary unit, Rectangular form, Properties of complex numbers, Geometrical representation of conjugate of a complex number, Properties of Complex Conjugates, others. |
Theory of Equations | Introduction, Basics of Polynomial Equations, Different types of Polynomial Equations, Quadratic Equations, Vieta’s Formulae and Formation of Polynomial Equations and more. |
Inverse Trigonometric Functions | Introduction, Some Fundamental Concepts, Domain and Range of trigonometric functions, Graphs of functions, Amplitude and Period of a graph, Inverse functions and more. |
Two Dimensional Analytical Geometry-II | Introduction, Circle, Equation of a circle in standard form, Conics, The general equation of a Conic, Parabola, Hyperbola, Geometric description of conic section, and more. |
Applications of Vector Algebra | Introduction, Geometric Introduction to Vectors, Scalar Product and Vector Product, Geometrical interpretation, Application of dot and cross products in Geometry, Vector triple product and more. |
Applications of Differential Calculus | Early Developments, Meaning of Derivatives, Derivative as rate of change, Equations of Tangent and Normal, A Limit Process and more |
Differentials and Partial Derivatives | Introduction, Linear Approximation and Differentials, Errors: Absolute Error, Relative Error, and Percentage Error, Differentials, |
Applications of integration | Introduction, Fundamental Theorems of Integral Calculus and their Applications, Improper Integrals, Reduction Formulae, Gamma Integral, Evaluation of Bounded Plane Area by Integration |
Ordinary Differential Equations | Introduction, Differential Equation, Order, and Degree, Formation of Differential Equations, Solution of First Order and First Degree Differential Equations, Applications of First Order Ordinary Differential Equations. |
Probability Distributions | Random Variable , Types of Random Variable, Discrete random variables, Cumulative Distribution Function or Distribution Function, Continuous Distributions, Distribution function from Probability density function |
Discrete Mathematics | Binary Operations, Definitions, Some binary operations on Boolean Matrices, Modular Arithmetic, Compound Statements, Logical Connectives, and Truth Tables, Duality. |
