User Rating: 5 / 5

Course code  :  PMAT 32632

Title               :  Geometry

Pre-requisites :  PMAT 22583

Learning outcomes:

Upon successful completion of the course students should be able to

• develop an intuitive understanding of the nature of general equation of second degree
• define conic sections and their properties
• explain and use various techniques for calculating tangents, normals pair of tangents, pole and polar of conic sections
• compute lines, plane, cone, sphere, ellipsoid and hyperboloid in three dimension
• choose appropriate mathematical functions to model physical phenomena

 Course contents:

Analytical Geometry in Two Dimensions: Pairs of straight lines, General equation of second degree, Translations and rotations of axes,

Conic sections: Parabolas, Ellipses, Hyperbolas, Classifying conic sections by eccentricity.  Equations  of tangents, Pairs of tangents and chords of contact, Harmonic conjugates, Pole and Polar, Invariance, Reduction to standard forms of conic, Parametric treatment, Degenerate conic, Properties of conic, Matrix methods.

Polar equations of straight lines, circles and conics.

Analytical Geometry in Three Dimension: Vector Equations of a line, plane and sphere, Cone ellipsoid and hyperboloid. Tangent plane, Normal, Pole and Polar, Ruled surfaces, General Equation of the second degree.

 Method of Teaching and Learning: A combination of lectures and tutorial discussions.

 Assessment: Based on tutorials, tests and end of course examination.

 Recommended Reading:

1. Chatterjee, D., (2008) Analytical Geometry, Alpha Science International.
2. Thomas, G.B. and Finney, R.L., (2008) Calculus and Analytic Geometry.
3. Maxwell, E.A., (1962) Elementary Coordinate Geometry, Oxford University press.
4. Jain, P.K. & Ahmad, K. (1994) Analytical Geometry of Two Dimensions, Wiley.
5. Kishan, H. (2006) Coordinate Geometry of Two Dimensions. Atlantic Publishers & Dist.
6. Jain, P.K. (2005) A Textbook of Analytical Geometry Of Three Dimensions. New Age International.

User Rating: 5 / 5

Course Code            : PMAT 32612

Title                          : Theory of Riemann Integration

Pre-requisites          : PMAT 12543

 Learning Outcomes:

At the end of the course the student should be able to

• demonstrate knowledge of the basic concepts of Riemann Integration improper integrals
• apply knowledge in solving problems

 Course Contents:

Riemann Integration: The Riemann integral, Properties of the Riemann integral, Intermediate Value Theorem for Integrals, Dominated Convergence Theorem, Monotone Convergence Theorem, Fundamental theorem of calculus.

Improper integrals: Properties of Improper Integrals, Leibnitz’s rule.

 Method of Teaching and Learning: A combination of lectures and tutorial discussions.

 Assessment: Based on tutorials, tests and end of course examination.

 Recommended Reading:

1. Ross, K.A., (2^nd edition, 2015) Elementary Analysis. The Theory of Calculus, Springer.
2. Widder, D.V. (2^nd edition, 2012) Advanced Calculus. Courier Corporation.

User Rating: 5 / 5

Course Code            : PMAT 32622

Title                          : Mathematical Methods

Pre-requisites          : PMAT 22583

 Learning Outcomes:

At the end of this course, the student should be able to solve different types ordinary and partial differential equations using various techniques learned.

 Course Contents:

Special Functions: Legendre Polynomials, Bessel Functions

Laplace Transforms: Laplace Transform. Linearity, Shifting Theorems, Transforms of Derivatives and Integrals, Unit Step Function (Heaviside Function), Differentiation and Integration of Transforms.

Fourier Series: Fourier Series, Even and Odd Functions, Half-Range Expansions, Fourier Integral, Fourier Cosine and Sine Transforms

Partial Differential Equations (PDEs): Basic Concepts of PDEs, Wave Equation

Solution by Separating Variables, Use of Fourier Series, D’Alembert’s Solution of the Wave Equation. Characteristics

 Method of Teaching and Learning: A combination of lectures and tutorial discussions.

 Assessment: Based on tutorials, tests and end of course examination.

 Recommended Reading:

1. Kreyszig, E., (10^th edition, 2011) Advanced Engineering Mathematics, Wiley.

User Rating: 5 / 5

Course Code            : PMAT 31602

Title                          : Abstract Algebra

Pre-requisites          : PMAT 21553

 Learning Outcomes:

At the end of this course, the student should be able to

• define and identify groups & rings
• prove properties of groups & rings

 Course Contents:

Groups: Basic properties of groups; Examples of groups; Subgroups; Normal subgroups; Quotient groups; Group isomorphism.

Rings: Basic properties of rings; Examples of rings; Subrings; Characteristic of a ring; Ideals; Quotient ring; Integral domains; Euclidean domains.

 Method of Teaching and Learning: A combination of lectures and tutorial discussions.

 Assessment: Based on tutorials, tests and end of course examination.

 Recommended Reading:

Dummit, D.S. and Foote, R.M.,  (3^rd edition, 2011) Abstract Algebra, Wiley