### Applied Mathematics Course Description

#### Level II – Semester I

**AMT211β : Classical Mechanics-III (Fluid Dynamics) (30 lecture hrs + 15 tutorial hrs) (Credit Value 2.5)**

Equations of stream lines, Equations of vortex lines, Differentiation following the motion of a fluid. Equations of continuity, Euler’s and Bernoulli’s equations, Irrotational motion, uniqueness theorem, Kinetic energy, Sources and sinks, Images, Potential flow, Complex potential.

*Method of assessment: end of semester examination*

AMT212β: Computational Mathematics (30 lecture hrs + 15 tutorial hrs) (Credit Value 2.5)

Numerical computing and computers: Introduction, Using a computer to do numerical analysis, Computer arithmetic and errors.

Solving Non Linear equations: Bisection Method, Newton’s Method, Fixed point Iteration x = g(x) Method, Secant Method, Regular-Falsi Method.

Interpolation and Curve Fitting: Interpolation, Lagrange polynomials, Divided Differences, Interpolating with a Cubic Spline, Least Square Approximation.

Numerical Differentiation and numerical Integration: Getting derivatives and integrals numerically, Trapezoidal rule (composite formula), Simpson’s rules, Applications of cubic splines.

*Method of assessment: end of semester examination*

**Level II – Semester II**

**AMT221β: Mathematical Modelling-II (30 lecture hrs + 15 tutorial hrs) (Credit Value 2.5)**

Introductory Numerical Solutions of Differential Equations, Mathematical Modelling through Difference Equations, Further Study on Systems of Differential Equations with Matrices. Modelling with Partial Differential Equations (PDEs): The concept of a PDE, Method of separation of variables, Mass-Balance equation (The first method of obtaining PDE Models), Momentum-Balance Equation (The second method of obtaining PDE Models), Variational Principles (The third method of obtaining PDE Models), Probability Generating functions (The fourth method of obtaining PDE Models), Nature of PDEs Initial and Boundary Conditions.

*Method of assessment: end of semester examination*

**AMT222β: Applied Analysis (30 lecture hrs + 15 tutorial hrs);Mathematics (Credit Value 2.5)**

The fundamental notion of periodicity and bifurcation. The concepts of chaos and strong chaos for functions of one variables Fractals, Fractal dimensions, Julia sets and Manderbolt sets.

*Method of assessment: end of semester examination*

AMT223β: Applied Probability (Information Theory) (30 lecture hrs + 15 tutorial hrs) Op. for students following Applied Mathematics(Credit Value 2.5)

Event Spaces, probability measure, probability space, sample space, continuity of a probability measure, Defining random variables on probability spaces and their functions, partition theorem, conditional probabilities, Distribution Functions, The law of large numbers, Introduction to Information theory and Claude Shannon’s remarkable work on mathematical formulation of the central problem in telecommunication channels, Error correcting codes for binary symmetric channel and their performances, Shannon’s noisy channel coding theorem, probability and entropy, entropy and mutual information, convex functions and Jensen’s inequality, the data processing theorem, Discrete memoryless channels and their capacity-cost functions, measuring the information content of an ensemble,the Source-Channel Coding Theorem for the Binary Symmetric Channel.

*Method of assessment: end of semester examination*

**AMT224β: Applied Statistics I (30 lecture hrs + 15 tutorial hrs) Op. for students following Applied Mathematics (Credit Value 2.5)**

Collecting and Summarizing data: Constructing tables and graphs, Measures of center of a set of observations, Median, Arithmetic Mean, Mode.

Samples and Populations: Methods of choosing a sample, Measures of variability: Range, Mean deviation, Variance and Standard deviation, Semi-interquartile range, five number summaries, Box and Whisker plots, stem and leaf plots.

Joint distributions of data: The Scatter diagram, the concept of a statistical relation, Quantitative description of a statistical relation, Covariance, Correlation coefficient

Linear regression: Regression equation, Prediction and error, Interpreting regression. Statistical Applications with probability models: Bernoulli, Binomial, Poisson, Normal approximations, Statistical software packages.

*Method of assessment: end of semester examination*