Module numerical sequences and their limit. 12 hours

Module -1. Numerical sequences and their limit. 12 hours
The concept of sequence of numbers. Number of sequences limit. Connection between infinitely small and infinitely large quantities. Properties of converging sequences. Basic theorems about limits. The theorem on the limit of a monotone sequence. The concept of function limit. Properties of a function with a limit. Great limits. Symptoms of Koshe and Dalamber.

Module-2. Derivative. 12 hours

Definition of the derivative. Using the definition of the product, solving examples of the product. Calculation of derivatives of the inverse function according to the definition. differentials. Basic formulas and rule of differentiation. Definition of higher order derivatives. Higher order differentials. Basic theorems of differential calculus. Firm's and Roll's theorems.

Module-3. Integrated account. 12 hours.

Definite Integral. The main methods of integration. Integrating some expressions with quadratic triads. Integrating rational fractions. Integration of trigonometric functions. Basic Properties of the Definite Integral. Improper integrals. Integrals depending on the parameter. Betta function. Gamma function.

Module-4. Differential equations. 12 hours.

Concept of differential equation. Differential equations with separable variables. Homogeneous differential equations. First order linear differential equations. Logrange and Clerot equation. Higher order differential equations. A system of linear homogeneous equations with constant coefficients.

Module-4. Laplace Transforms. 12 hours.

Introduction. Difinition of Laplace transform. Laplace transform of discontinuous Functions.Laplace transform of periodic function. Inverse Laplace Transforms. Inverse transform by completing the square. Inverse transform by the method of partial fractions.

Text Books:

Engineering Mathematics –II. K.B Kavitha & K.B. Adithya.
Advanced Engineering Mathematics. H K DASS.