Course No:           Act 318

Course Name:      Mathematics - 2 (Calculas)

Course Description:      

SECTION-A

Differential Calculus: Bounds, limits and continuity. Properties of continuous functions. Derivatives. Loibnitz theorem, Rolle’s theorem, Lagrange‘s Mean value Theorem, Cauchy's Mean Value Theorem, Generalized Mean Value Theorem. Indeterminate forms. Taylor's and Maclaurin’s series.

SECTION - B

Integral Calculus: Antiderivatives. Techniques of integrations. Riemann integral. Properties of definite integrals. Mean Value Theorem. Reduction formulae important integrals, Beta and Gamma Integrals.

Fourier series: Periodic function, periodic extensions, even and odd functions. Fourier coefficients. Expansion of functions in Fourier series. Functions with arbitrary periods. Fourier sine and cosine series.

SECTION – C

Differential Equations-I: Differential equations, formation and solutions, equations of first order. Initial and boundary value problems. Various methods for solving first order differential equations. Orthogonal trajectories. Non linear first order differential equations. Envelopes and singular solutions.

SECTION – D

Differential Equations-II: Higher order differential equations with constant coefficients. Superposition of solutions. Cauchy Euler’s equations System of two first order linear homogenous equations. Non-linear equation discussed with the help of population growth.

Course Review:

This course familiarizes students with such areas like differential calculus, which includes limits and continuity, functions, derivatives, different theorems and series. The subject matter also contains integral calculus, which includes antiderivatives and different techniques of integration, and also depth study on Fourier series, with a look into its functions and extensions, differential equations with a look into linear and non-linear first order differential equations and as well as emphasis on higher order differential equations.