BCA Mathematics - 2

Definition of limit including epsilon-delta condition, right and left hand limit, and its interpretation, Algebraic properties of limit, Definition and conditions of continuity and discontinuity, Continuity of algebraic, Trigonometric, and exponential functions, examples, and counterexamples

Definition and geometrical meaning of derivatives, First principle (or by definition) method to differentiate algebraic, trigonometric, exponential, and logarithmic functions, Rules of derivatives (sum, product, power, chain, and quotient rule), Derivatives of inverse circular, hyperbolic functions and implicit functions, Higher order derivatives, Relation between derivative and continuity, Definition and examples of partial derivatives

Increasing and decreasing functions, Equation of tangents and normals using first derivatives, L'Hospital's rule, Angle between two lines, Maxima and minima, absolute maxima and minima, concavity, stationary points and points of inflection, Statement and geometric interpretation of Rolle's theorem, Cauchy Mean-value theorem and Generalized Mean-value theorem, Taylor's theorem, Maclaurin theorem (without proof) and its use in expansion of some simple functions, Applications of derivatives in Economics, Rate measures.

Definition and geometrical meaning of integration, Basic integration formulas for algebraic, trigonometric, exponential, and logarithmic functions, Trigonometric substitution for basic functions, Integration by parts (Product rule for integration), Partial fractions, Improper integral, Definite integral in terms of Riemann sum, and fundamental theorem of integral calculus, Applications of definite integral (Area under curve, area between curves, Quadrature & rectification), Surface and volume integrals, Trapezoidal and Simpson's Rule for numerical integration.

Definition, order, and degree of differential equations, Differential equations of first order and first degree, Variables separable, homogeneous, exact, and linear differential equations, Reducible to linear form, Partial differential equations with some basic examples

Linear programming problems, Linear inequalities in two variables and their graphical solutions, Simplex Method (up to 3 variables), Duality problems, Matrix inversion method, Gauss Elimination, Gauss-Seidel method, Bisection method and Newton-Raphson Method for non-linear equations