The major constraint of this course is to
understand the analytical and numerical techniques of computing solution of
non-linear algebraic system of equations, non-linear equations, ordinary and
partial differential equations. Moreover this also comprises of optimization
theory, approximation theory, interpolation techniques and methods of computing
quadrature. Mathematics software packages like Maple and Mat lab will be used
throughout the course to obtain numerical results/simulations.

- Teacher: Kaleemullah Bhatti

Calculus-III or Calculus of several variables, applies the techniques and theory of
differentiation and integration to vector-valued functions and functions
of more than one variable. The course presents a thorough study of
vectors in two and three dimensions, vector-valued functions, curves and
surfaces, motion in two and three dimensions, and an introduction to
vector fields. Students will be exposed to modern mathematical software
to visually represent these 2D and 3D objects.

- Teacher: Dr. Javed Hussain

The key course contents are, topological spaces; separation axioms; continuity, convergence, connectedness, and compactness; basic notions in homotopy theory; quotient spaces; and paracompactness.

- Teacher: Dr. Javed Hussain

Much of mathematics relies on our ability to be able to solve equations,
if not in explicit exact forms, then at least in being able to
establish the existence of solutions. To do this requires a knowledge of
so-called "analysis", which in many respects is just Calculus in very
general settings. The foundations for this work are commenced in Real
Analysis, a course that develops this basic material in a systematic and
rigorous manner in the context of real-valued functions of a real
variable. Topics covered are: Basic set theory. The real numbers and
their basic properties. Sequences: convergence, sub-sequences, Cauchy
sequences. Open, closed, and compact sets of real numbers. Continuous
functions and uniform continuity. The Riemann integral. Differentiation
and Mean Value theorems. The Fundamental Theorem of Calculus. Series.
Power series and Taylor series. Convergence of sequences and series of
functions.

- Teacher: Dr. Javed Hussain