Calculus 1

Credit Hours: 3.0

Lecture Contact Hours: 3     Lab Contact Hours: 0

Description:

Cartesian coordinates; polar coordinates; complex numbers; summation, multiplication, radical and geometrical representation of complex numbers; polar representation of complex numbers; function; algebra of functions; limit and related theories; infinite limit and limit at infinity; left-hand and right-hand limit; continuum; derivative; derivative rules; inverse function and its derivative; derivative of trigonometric functions and their inverse functions; Roll's theorem; mean; value theorem; geometrical and physical applications of derivative; curves and acceleration in polar coordinates; application of derivative in approximation of equations roots; definition of integral of continuous and piecewise continuous functions; fundamental theorems of differential and integral calculus; primary function; approximation estimate methods of integral; application of integral in calculation of surface area and volume and curve length and momentum and center of gravity and work, etc. (in Cartesian and polar coordinates); logarithm and exponential function and their derivatives; hyperbolic functions; integration methods such as change of variables and by parts and partial fractions decomposition; special variable replacement of sequence, numerical series and convergence theories; power series and Taylor theorem with residual, Taylor expansion.

Suggested Textbooks: