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Institute-wide Undergrad Courses

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Institute-wide Undergrad Courses

The Department presently offers 10 foundational units of 1 credit each on various topics from basic calculus and linear algebra to differential eqns and probability to the entire community of engineering students of the Institute. These courses have been designed and scheduled in consultation with the different engineering streams so that, as far as possible, a student has the requisite math skills to enrol in any course of his/her choice offered during a particular semester.

Courses Offered

Is B.Tech (M&C) the same as B.Tech (CSE) at IITH?

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.

Elements of Basic Calculus I (MA 1110)

  • 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.

Elements of Basic Calculus II (MA 1220)

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

Series of Functions (MA 1230)

Functional Series:

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

Vector Calculus (MA 1130)

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

Linear Algebra (MA 1140)

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

Differential Equations (MA 1150)

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

Introduction to Probability (MA 2110)

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

Transform Techniques (MA 2120)

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 Variables (MA 2130)

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

Introduction to Statistics (MA 2140)

Random sampling:

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

Institute-wide Undergrad Courses