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6.1 Introduction The derivative of a function gives the rate at which a quantity changes. Beyond slopes of curves, derivatives are used to: Study real-life changes in quantities like velocity,…

13.1 Introduction Probability measures the likelihood of occurrence of an event. Values lie between 0 and 1 0 → Impossible event 1 → Certain event Widely used in statistics, finance,…

12.1 Introduction Linear Programming (L.P.) is a mathematical technique to optimize a linear objective function subject to linear constraints. Widely used in business, economics, engineering, and operations research Helps in…

11.1 Introduction Three Dimensional Geometry (3D Geometry) deals with points, lines, and planes in space. Uses vector and coordinate methods Essential in physics, engineering, and computer graphics Helps visualize and…

10.1 Introduction Vectors are quantities that have both magnitude and direction, unlike scalars which have only magnitude. Widely used in physics, engineering, and computer graphics Useful for representing forces, velocities,…

9.1 Introduction A differential equation is an equation that relates a function with its derivatives. It represents the rate of change of a quantity Widely used in physics, biology, engineering,…

8.1 Introduction Integrals are not just abstract concepts—they are widely used to measure quantities like area, volume, and displacement. This chapter focuses on practical applications of definite integrals. Helps in…

7.1 Introduction Integration is the inverse process of differentiation and is used to calculate areas, volumes, and solve real-life problems involving accumulation. If differentiation measures rate of change, integration measures…

5.1 Introduction Calculus is the study of change and motion, and derivatives are at its core. To study derivatives, we first need the concepts of continuity and differentiability. Continuity tells…