Engineering Mathematics II

Syllabus

1. Calculus of two or more variables
   1. Introduction: Limit an continuity
   2. Partial derivatives
      1. Homogenous function, Euler’s theorem for the function of two and three variables
      2. Total derivatives
   3. Extrema of functions of two and three variables: Lagrange’s Multiplier
2. Multiple Integrals
   1. Introduction
   2. Double integrals in Cartesian and polar form; change of order of integration
   3. Triple integrals in Cartesian, Cylindrical and Spherical coordinates
   4. Area and volume by double and triple integrals
3. Three dimensional solid geometry
   1. The straight line: symmetric and general form
   2. Coplanar lines
   3. Shortest distance
   4. Sphere
   5. Plane section of a sphere by planes
   6. Tangent planes and lines to the spheres
   7. Right circular cone
   8. Right circular cylinder
4. Solution of Differential equations in series and special Functions
   1. Solution of differential equation by power series method
   2. Legendre’s equation
   3. Legendre polynomial function; Properties and applications
   4. Bessel’s equation
   5. Bessel’s function of first and second kind. Properties and applications
5. Vector Algebra and Calculus
   1. Introduction
   2. Two and three dimensional vectors
   3. Scalar products and vector products
   4. Reciprocal system of vectors
   5. Application of vectors: lines and planes
   6. Scalar and vector fields
   7. Derivatives – Velocity and Acceleration
   8. Directional derivatives
6. Infinite Series
   1. Introduction
   2. Series with positive terms
   3. Convergence and divergence
   4. Alternating series, Absolute convergence
   5. Radius and interval of convergence