The objective of the Engineering Mathematics-I course is to enable students to understand concepts of basic mathematical methods for sequences & series, improper integrals, and multivariable calculus. These techniques are vital for solving engineering problems.
At the end of the course, students will be able to:
Sequences, Limits of sequences, Infinite series, series of positive terms, Convergence and divergence of sequence and series, Integral test, Comparison test, Ratio test, Root test, Alternating series, Absolute and Conditional Convergence, Leibnitz test, Power series, radius of convergence of power series.
Length of curves, Volume (disk and washer method) and surface areas of revolution.
Improper integrals of the First kind, Improper integrals of the second kind, Absolute convergence of Improper integrals, Beta and Gamma functions, their properties, relationship among beta and gamma functions.
Concept of limit and continuity of a function of two and three variables, Partial derivatives, total derivative and differentiability, approximation by total differentials, derivatives of composite function and implicit function, chain rule, homogenous functions, Euler's theorem for homogenous functions, Taylor's theorem (statement only), Maclaurin series, Maxima and minima of a function of two and three variables, Lagrange's method of multipliers.
Double and triple integrals, Change of order of integration, Change of variables in integration, Applications to area and volumes.