Engineering Mathematics II

Course Title: Engineering Mathematics II

Course No: SH 121

Nature of the Course: THEORY

Semester: 2

Credit Hours: 3

Course Description

The basic objective of the course is to provide a sound knowledge of multivariable function, extreme values of the function of two and three variables, multiple integrals (Double and Triple), ordinary differential equations including their series solutions, Laplace Transform and three dimensional geometry. After learning the course one may enhance the fundamental concepts on Mathematics and able to study the further courses of the subject which are more applicable in Engineering.

Course Objectives

To provide a sound knowledge of multivariable function, extreme values of the function of two and three variables, multiple integrals (Double and Triple), ordinary differential equations including their series solutions, Laplace Transform and three dimensional geometry; and to enhance the fundamental concepts on Mathematics and enable the student to study further courses of the subject which are more applicable in Engineering.

Course Contents

1. Multivariable differential calculus

6 hrs

1.1. Concept of functions of two and more variables, partial derivative of functions of two and three variables, symmetric and homogeneous function, Euler's theorem for partial derivative (two and three variables)

1.2. Extreme values

Review of maxima and minima of a function of single variable

Concept of critical point, saddle point and point of inflection

Maxima and minima (local only) of function of two and three variables including extreme values of these functions under given constraints

Determination of Lagrange's multiplier to obtain extreme values

2. Ordinary differential equations

14 hrs

2.1. Formation of a differential equation, order and degree of a differential equation, first order differential equations and their solutions

Variable separable form

Reducible to separable form

Exactness condition and integrating factor

Linear and Bernoulli's differential equation

2.2. Second order differential equations (homogeneous and nonhomogeneous) with constant coefficient

Complementary function and particular integral

General, particular and initial solution

2.3. Power series solution of a differential equation with constant as well as variable coefficient

Legendre's differential equation with its solution

Bessel's differential equation with its solution

Legendre polynomial

Bessel's function of first and second kind and their properties

3. Laplace transform

9 hrs

3.1. Definition and fundamental formulae of Laplace transform

3.2. Existence and uniqueness theorem

3.3. Linear property

3.4. First and second shifting properties

3.5. Inverse Laplace transform

3.6. Application of Laplace transform (initial value problem)

3.7. Convolution theorem on Laplace transform and its application

4. Double and triple integrals

7 hrs

4.1. Concept and evaluation of double and triple integrals

4.2. Change of order for double integral

4.3. Change of integral in Cartesian form to polar form

4.4. Dirichlet integral

4.5. Area and volume by double integral

5. Three dimensional geometry

9 hrs

5.1. Review of coordinate in space and plane

5.2. Straight line in three dimensions

Equation of straight line in symmetrical form

Reduction of an equation of a straight line from general to symmetrical form

Angle between a line and a plane

Condition for a line to lie in a plane

Coplanar lines

Shortest distance

5.3. Sphere

Standard and general equation of sphere

Plane section of sphere

Great circle

Sphere through the given circle

Sphere through the given four points

Sphere with the given diameter

5.4. Cone and cylinder (definitions and standard equations only)

Reference Books

1.E.Kreyszig, Advanced Engineering mathematics, Wiley- Eastern, Publication.
2.N. P. Bali, Dr. Manish Goyal, A text book of engineering mathematics, Laxmi Publication (P). LTD
3.Thomas, George B. and Finney, Ross L. Calculus and Analytical Geometry. Pearson Education.

Notes:

This syllabus follows the official BE Comp curriculum of Far Western University. In case of any doubt or revision, the university's published syllabus shall be considered authorative.

Mathematics II