| Applications of Matrices and Determinants |
| 1.1 Introduction |
| Zero Matrix |
| Ex 1.1.1 (i) Find the Adjoint of 2 x 2 Matrix |
| Ex 1.1.1 (ii) Find the Adjoint of 3 X 3 Matrix |
| Ex 1.1.1 (iii) Adjoint of 3 X 3 Matrix |
| Ex 1.1.2 (i) Find the Inverse of 2 x 2 Matrix |
| Ex 1.1.2 (ii) Find the inverse of 3 X 3 Matrix |
| Ex 1.1.2 (iii) Find the inverse of 3 X 3 Matrix |
| Ex 1.1.3 |
| Ex 1.1.4 |
| Ex 1.1.5 |
| Ex 1.1.6 |
| Ex 1.1.7 Reversal Law for Inverses |
| Ex 1.1.8 How to Find a Matrix from its Adjoint |
| Ex 1.1.9 Find the inverse of 3 X 3 Matrix Using Adjoint |
| Ex 1.1.10 |
| Ex 1.1.11 Matrices & Determinants |
| Ex 1.1.12 |
| Ex 1.1.13 |
| Ex 1.1.14 |
| Ex 1.1.14 |
| Unit Matrix |
| 1.2 Inverse of a Non-Singular Square Matrix |
| 1.3 Elementary Transformations of a Matrix |
| 1.4 Applications of Matrices: Solving System of Linear Equations |
| 1.5 Applications of Matrices: Consistency of system of linear equations by rank method |
| 2 Complex Numbers |
| 2.1 Introduction to Complex Numbers |
| 2.2 Complex Numbers |
| 2.3 Basic Algebraic Properties of Complex Numbers |
| 2.4 Conjugate of a Complex Number |
| 2.5 Modulus of a Complex Number |
| 2.6 Geometry and Locus of Complex Numbers |
| 2.7 Polar and Euler form of a Complex Number |
| 2.8 de Moivre's Theorem and its Applications |
| 3 Theory of Equations |
| 3.1 Introduction |
| 3.2 Basics of Polynomial Equations |
| 3.3 Vieta’s Formulae and Formation of Polynomial Equations |
| 3.4 Nature of Roots and Nature of Coefficients of Polynomial Equations |
| 3.5 Applications to Geometrical Problems |
| 3.6 Roots of Higher Degree Polynomial Equations |
| 3.7 Polynomials with Additional Information |
| 3.8 Polynomial Equations with no additional information |
| 3.9 Descartes Rule |
| 4 Inverse Trigonometric Functions |
| 4.1 Introduction |
| 4.2 Some Fundamental Concepts |
| 4.3 Sine Function and Inverse Sine Function |
| 4.4 The Cosine Function and Inverse Cosine Function |
| 4.5 The Tangent Function and the Inverse Tangent Function |
| 4.6 The Cosecant Function and the Inverse Cosecant Function |
| 4.7 The Secant Function and Inverse Secant Function |
| 4.8 The Cotangent Function and the Inverse Cotangent Function |
| 4.9 Principal Value of Inverse Trigonometric Functions |
| 4.10 Properties of Inverse Trigonometric Functions |
| 5 Two Dimensional Analytical Geometry-II |
| 5.1 Introduction |
| 5.2 Circle |
| 5.3 Conics |
| 5.4 Conic Sections |
| 5.5 Parametric form of Conics |
| 5.6 Tangents and Normals to Conics |
| 5.7 Real life Applications of Conics |
| 6 Applications of Vector Algebra |
| 6.1 Introduction |
| 6.2 Geometric Introduction to Vectors |
| 6.3 Scalar Product and Vector Product |
| 6.4 Scalar triple product |
| 6.5 Vector triple product |
| 6.6 Jacobi’s Identity and Lagrange’s Identity |
| 6.7 Different forms of Equation of a Straight line |
| 6.8 Different forms of Equation of a plane |
| 6.9 Image of a point in a plane |
| 6.10 Meeting point of a line and a plane |
| 7 Applications of Differential Calculus |
| 7.1 Introduction |
| 7.2 Meaning of Derivatives |
| 7.3 Mean Value Theorem |
| 7.4 Series Expansions |
| 7.5 Indeterminate Forms |
| 7.6 Applications of First Derivative |
| 7.7 Applications of Second Derivative |
| 7.8 Applications in Optimization |
| 7.9 Symmetry and Asymptotes |
| 7.10 Sketching of Curves |
| 8 Differentials and Partial Derivatives |
| 8.1 Introduction |
| 8.2 Linear Approximation and Differentials |
| 8.3 Functions of Several Variables |
| 8.4 Limit and Continuity of Functions of Two Variables |
| 8.5 Partial Derivatives |
| 8.6 Linear Approximation and Differential of a Function of Several Variables |
| 9 Applications of Integration |
| 9.1 Introduction |
| 9.2 Definite Integral as the Limit of a Sum |
| 9.3 Fundamental Theorems of Integral Calculus and their Applications |
| 9.4 Bernoulli’s Formula |
| 9.5 Improper Integrals |
| 9.6 Reduction Formulae |
| 9.7 Gamma Integral |
| 9.8 Evaluation of Bounded Plane Area by Integration |
| 9.9 Volume of a Solid obtained by Revolving Area about an Axis |
| 10 Ordinary Differential Equations |
| 10.1 Introduction |
| 10.2 Differential Equation, Order, and Degree |
| 10.3 Classification of Differential Equations |
| 10.4 Formation of Differential Equations |
| 10.5 Solution of Ordinary Differential Equations |
| |
| 10.6 Solution of First Order and First Degree Differential Equations |
| 10.7 First Order Linear Differential Equations |
| 10.8 Applications of First Order Ordinary Differential Equations |
| 11 Probability Distributions |
| 11.1 Introduction |
| 11.2 Random Variable |
| 11.3 Types of Random Variable |
| 11.4 Continuous Distributions |
| 11.5 Mathematical Expectation |
| 11.6 Theoretical Distributions: Some Special Discrete Distributions |
| 12 Discrete Mathematics |
| 12.1 Introduction |
| 12.2 Binary Operations |
| 12.3 Mathematical Logic |