Complex Numbers
This chapter introduces complex numbers as numbers of the form a + ib, where i is the imaginary unit (√−1), extending the real number system to solve equations that have no real solutions. It covers the algebraic operations on complex numbers, …
Theory of Equations
This chapter deals with the study of polynomial equations, their roots, and the relationships between the roots and coefficients, providing a comprehensive understanding of algebraic equations of higher degrees. It covers the fundamental theorem of …
Inverse Trigonometric Functions
This chapter introduces inverse trigonometric functions as the inverse operations of trigonometric functions, which are used to find angles corresponding to given trigonometric values, and covers their domains, ranges, and principal value branches. …
Two Dimensional Analytical Geometry-II
This chapter builds upon the fundamentals of analytical geometry, focusing on the study of conic sections—parabola, ellipse, hyperbola—and their standard equations, properties, and geometric interpretations. It covers the concepts of focus, …
Applications of Vector Algebra
This chapter extends vector algebra to solve practical problems in geometry and physics, focusing on the application of vectors in three-dimensional space to find equations of lines and planes, as well as distances and angles between them. It covers …
Applications of Differential Calculus
This chapter explores the practical applications of derivatives in analyzing functions, including finding the slope of tangents and normals, determining intervals of increase and decrease, and identifying maxima and minima of functions. It covers the …
Differentials and Partial Derivatives
This chapter extends the concepts of differentiation to functions of several variables, introducing partial derivatives which measure the rate of change of a function with respect to one variable while keeping others constant. It covers the …
Applications of Integration
This chapter demonstrates the practical applications of definite integrals in computing various geometric and physical quantities, including areas bounded by curves, volumes of solids of revolution, and lengths of plane curves. It covers methods such …
Ordinary Differential Equations
This chapter introduces ordinary differential equations (ODEs), which involve derivatives of a function with respect to a single independent variable, and covers their classification by order and degree along with methods for solving various types. …
Probability Distributions
This chapter introduces the concept of probability distributions, which describe how probabilities are assigned to different possible values of a random variable, and covers both discrete and continuous probability distributions. It discusses …
Discrete Mathematics
This chapter introduces the fundamental concepts of discrete mathematics, which deals with structures that are fundamentally discrete rather than continuous, including topics such as mathematical logic, set theory, and number theory. It covers …