Calculus III

Description

This course provides the first order ordinary differential equations (Separable, Homogeneous, Exact, Linear and Bernoulli’s equations) –Second order ordinary differential equations with constant coefficients (General solution of homogeneous and Non-homogeneous equations: Method of undetermined coefficients– The Method of variation of parameters)–Second order ordinary differential equations with variable coefficients:[Cauchy- Euler Equation] – Laplace transforms(First Shifting Theorem – Derivatives of Transforms – Transform Integration – Unit Step Function – Second Shifting Theorem – Inverse Laplace Transforms – Applications(Solution of ODEs using Laplace Transforms–Solution of R-L circuit using the Laplace Transforms)–Fourier series of functions of period 2P, Fourier series for even and odd functions, half range expansions and for harmonic functions. Also this course provides an introduction to linear programming, including its basic concepts, unconstrained optimization, and solving system of linear inequalities using the simplex method.

Program

IS -144 CRs

Objectives

• 1. Use the Laplace transform and the theorems (first shift theorem, transform of differentiation and integration theorems, etc….) in solving differential and integral equations.
  2. Understand the Fourier analysis which includes the Fourier series and Fourier transform.
  3. Know the concept of linear programming in order to solve system of linear inequalities using the Simplex method.
  4. Learn some useful algorithms for linear systems
  5. Realize the wide applicability of linear programming