Course Code
Course Name & Syllabus
MA 1110
Elements of Basic Calculus I
Sequences and Series : Limit of a sequence, monotone and Cauchy sequences and properties of convergent sequences, examples. Infinite series, positive series, tests for convergence and divergence, integral test, alternating series, Leibnitz test.
Differential Calculus : Continuity and differentiability of a function of single variable, statement of Rolle’s Theorem, Lagrange’s mean value theorem and applications.

MA 1220
Elements of Basic Calculus II
Integral Calculus : Definite Integrals as a limit of sums, Applications of integration to area, volume,
surface area, Improper integrals.
Functions of several variables : Continuity and differentiability,
mixed partial derivatives, local maxima and minima for function of two variables, Lagrange
multipliers.
Functional Series : Pointwise and uniform convergence, basic aspects of Power series,
Fourier series.

MA 1130
Vector Calculus
Double and Triple Integrals : Calculations, Areas, Volumes, change of variables, Applications.
Integrals of Vector Functions : Line integrals, Green’s formula, path independence, Surface integral:
definition, evaluation, Stoke’s formula, Gauss-Ostrogradsky divergence theorem.

MA 1140
Linear Algebra
Matrices, Linear equations and solvability, Vector spaces,
Basis and dimension, Linear transforms, Similarity of matrices, Rank-Nullity theorem and its applications.
Eigen values and eigen vectors. Cayley-Hamilton theorem and diagonalization, Inner-product spaces, Gram-Schmidt process.

MA 1150
Differential Equations
Ordinary Differential Equations : First order linear equations, Bernoulli’s equations, Exact equations
and integrating factor, Higher order linear, differential equations with constant coefficients.
Partial Differential Equations : First order linear PDE, quasi linear PDE, method of characteristics, Cauchy
problem, first order nonlinear PDE’s of special type.

MA 2110
Introduction to Probability
Sample space and events, definitions of probability, properties of probability, conditional
probability.
Random variables : Distribution functions, discrete and continuous random variables,
moments of random variables, conditional expectation, Chebyshev inequality, functions of random
variables.
Special Distributions : Bernoulli, Binomial, Geometric, Pascal, Poisson, Exponential,
Uniform, Normal distributions, Limit Theorems: Law of large numbers

MA 2120
Transform Techniques
Laplace and Inverse Laplace transform, linearity, Laplace transforms of Derivatives and Integrals,
partial fractions, unit step function, shifting on the t-axis, periodic functions, applications of Laplace
transform for solving differential equations. Fourier integral, Fourier Sine and Cosine transform,
convolution, applications of Fourier transform for solving differential equations.

MA 2130
Complex Variables
Complex Functions limits, Continuity, Differentiability, analytic functions, Cauchy -Riemann
equations, Laplace equations, Harmonic functions, conformal mapping, Cauchy integral theorem,
Cauchy integral formula, derivations of an analytic function,Power series, Taylor series, Laurent
series, zeros, singularities, residues, evaluation of real integrals.

MA 2140
Introduction to Statistics
Random sampling, Estimation of parameters, Confidence Intervals, Testing of Hypothesis,
Goodness of fit, Nonparametric tests, Correlation Analysis.