Mathematics II

Course Objectives
It is assumed that students have taken Mathematics I or an equivalent introduction to calculus as a prerequisite. Major topics to be covered are
(a) two and three-dimensional vectors and some associated linear algebra
(b) infinite series
(c) first order differential equations.

1. Plane curves and Polar coordinates. (4 hours)
1.1 Plane curves.
1.2 Parametric equations.
1.3 Polar coordinates.
1.4 Integrals in Polar Coordinates.

2. Calculus of Several Variables. (6 hours)
2.1 Calculus of two or more variables.
2.2 Partial derivatives.
2.3 Total differential coefficients.
2.4 Extrema of functions of two or three variables.

3. Multiple integrals. (4 hours)
3.1 Multiple integrals.
3.2 Uses in areas.
3.3 Volumes.
3.4 Centroids.

4. Analytic Geometry of 3-D (7 hours)
4.1 Analytic Geometry of three dimensions-planes.
4.2 Straight lines.
4.3 Standard equations of sphere.
4.4 Cylinder and cone.

5. Infinite series (9 hours)
5.1 Infinite series and sequences.
5.2 Convergence
5.3 Ratio, root, integral tests.
5.4 Absolute convergence
5.5 Power series.
5.6 Radius of convergence.

6. Vectors in two and three dimensions (5 hours)
6.1 Two and three dimensional Vectors.
6.2 Scalar products.
6.3 Vector products
6.4 Linesand planes.

7. Ordinary Linear differential equations (10 hours)
7.1 Homogeneous Linear differential equations of second order.
7.2 General solution.
7.3 Initial value problems.
7.4 Non homogeneous equations.
7.5 Solution in series, Legendre, Bessel equations.

Textbook:
1.0 E.W. Swokowski, "Calculus With Analytic Geometry", Second Alternate Edition, PWS-Kent Publishing Co., Boston.

Reference Books:
1.0 E. Kreyszig, "Advance Engineering Mathematics", Fifth Edition, Wiley, New York.