Computational methods are numerical techniques used to solve mathematical problems that may not have exact solutions or are too complex for analytical methods. These techniques are widely applied in computer science, engineering, economics, and applied mathematics. 1. Linear Programming Problem (LPP) LPP is a method to maximize or minimize a linear objective function subject to…
Differential equations are equations that involve an unknown function and its derivatives. They are essential in modeling growth, decay, motion, population, economics, and many physical systems. 1. Definition of Differential Equation A differential equation (DE) relates a function with its derivatives. Example: Here, is the unknown function of . 2. Order and Degree of a…
Integration is the reverse process of differentiation. While differentiation deals with the rate of change, integration deals with accumulation — such as finding area under curves, total distance, volume, and surface area. 1. Riemann Integral The Riemann integral defines integration as the limit of sums of areas of rectangles under a curve. If a function…
Differentiation is not just about finding derivatives—it is about applying them to analyze curves, optimize values, and solve real-world problems. This unit focuses on slope, monotonicity, maxima–minima, marginal analysis, and graph sketching. 1. Derivatives and Slope of a Curve The derivative of a function at a point gives the slope of the tangent line at…
Differentiation is one of the core concepts of calculus. It studies how a function changes as its input changes. In simple terms, the derivative represents the rate of change or the slope of a curve at any point. 1. Ordered Pairs and Cartesian Product This idea is the basis for plotting functions on the coordinate…
Calculus begins with the fundamental concepts of limits and continuity. These ideas help us understand how functions behave near certain points and whether they flow smoothly without breaks. 1. Limit of a Function Example 2 (Non-direct substitution): 2. Indeterminate Forms Some limits cannot be evaluated directly and produce forms like: These require algebraic manipulation or…