#### MATH141

#### Calculus I

**3** Credit Hour Course

Intended For Level **1** Term **1** Students

**Prerequisite: **

**Differential Calculus:** Continuity and differentiability; Successive differentiation: Leibnitz’s forms; Maxima and minima of functions of single variable: Rolle's theorem, mean value theorem; Evaluation of indeterminate forms by L'Hospital's rule; Expansion of functions: Taylor's and Maclaurin’s theorems, Lagrange’s and Cauchy’s forms of remainders; Partial differentiation, Euler’s Theorem; Tangent, normal.

**Integral Calculus:** Definite integrals and its properties; Wallis’ formula; Improper integrals; Beta function and Gamma function; Parametric equations and polar coordinates; Applications of integration: area under a plane curve, area of a region enclosed by two curves and arc lengths in Cartesian and polar coordinates, volume and surface area of solids of revolution; Multiple integrals.

**Ordinary Differential Equations (ODE):** Definition. Formation of differential equations. Solution of first order differential equations by various methods with applications. Solution of general linear equations of second and higher orders with constant coefficient. Solution of Euler's homogeneous linear equations.