Maths Vol - 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
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 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
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
Maths Volume-2
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
