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Institute-wide Undergrad Courses

Well, the answer is a clear NO. While computing does require knowledge of the fundamental courses of CSE, the focus of the M&C program is on doing the mathematics and essential programming and computational courses.

- 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.

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:

- Sequence of Functions
- Pointwise and uniform convergence
- Basic aspects of Power series
- Fourier series

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

Matrices, Linear equations and solvability:

- Vector spaces
- Basis and dimension
- Linear transforms
- Similarity of matrices

Rank-Nullity theorem and its applications:

- Eigenvalues and eigenvectors
- Cayley-Hamilton theorem and diagonalization
- Inner-product spaces
- Gram-Schmidt process

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

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

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

Complex Functions:

- Limits
- Continuity
- Differentiability
- Analytic functions
- Cauchy-Riemann equations
- Laplace equations
- Harmonic functions
- Conformal mapping

Cauchy Integral Theorem and Cauchy Integral Formula:

- Derivations of an analytic function
- Power series
- Taylor series
- Laurent series
- Zeros
- Singularities
- Residues
- Evaluation of real integrals

Random sampling:

- Estimation of parameters
- Confidence Intervals
- Testing of Hypothesis
- Goodness of fit
- Nonparametric tests
- Correlation Analysis

Department of Mathematics