MATH101TH: Differential Calculus: -

This course will enable the students to assimilate the notions of limits, continuity, and differentiability of functions at a point. Sketch curves in Cartesian and Polar co-ordinate systems, expansion of functions using Maclurin’s and Taylor’s theorems, curvature, asymptotes, and curve tracing.

 

On Completion of this course the students will be able to:

§  Explain the relationship between the derivative of a function as a function and the notion of the derivative as the slope of the tangent line to a function at a point. 

§  Compare and contrast the ideas of continuity and differentiability.

§  To inculcate to solve algebraic equations and inequalities involving the sequence root and modulus function.

§  To able to calculate limits in indeterminate forms by a repeated use of L’ Hospital rule. To find the roots of algebraic and transcendental equations by using Rolls theorem and Mean value theorem and solve the Taylor's series and Maclarian series.

§  To find maxima and minima, critical points and inflection points of functions of several variables and to determine the concavity and convexity, radius of curvature of curves.

§  To able to evaluate integrals of rational functions by partial fractions and also Jacobian of functions.

 

MATH102TH: Differential Equations: -

It will enable learners to learn various techniques of getting exact solutions of solvable first order differential equations and linear differential equations of higher order. They will be introduced to partial differential equations and their solutions.

 

On successful completion of the course, Students will be able to:

The main aim of the course is to introduce the students to the technique of solving various problems of engineering and science 

§  Distinguish between linear, nonlinear, partial and ordinary differential equations. 

§  Solve basic application problems described by second order linear differential equations with constant coefficients and also with variable coefficient.

§  Find the solutions of first order first degree differential equations, wronskian and its properties.

§  Find the transforms of derivatives and integrals. 

§  Obtain the solution by Variation of parameters method, Cauchy- Euler equation and Legendre differential equations.

§  Find the solutions of simultaneous differential equations and Total differential equations

§  To find the solutions of partial differential equations, Linear partial differential equation of first order, Lagrange’s method. Classification of second order partial differential equations into elliptical, parabolic and hyperbolic.

 

MATH201TH: Real Analysis: -

Learners will get concept of real line, completeness property, real sequences, infinite series, uniform convergence, and power series.

 

After completing the course students are expected to be able to: 

§  Describe the basic difference between the rational and real numbers. Give the definition of concepts related to metric spaces such as countability, compactness, convergent etc. 

§  Give the essence of the proof of Bolzano-Weistrass theorem the contraction theorem as well as existence of convergent subsequence using Cauchy ‘s Criteria.

§  Evaluate the limits of wide class of real sequences. 

§  Determine whether or not real series are convergent by comparison test, p- test, root test and ratio test. We can also discuss the convergence of alternating series by using Leibnitz rule.

§  To find solutions of sequences and series of functions. We can understand the concept of pointwise, and uniform convergence with the help of Mn -test and M test. Results about uniform convergence, power series and radius of convergence.

§  Stude nts will be able to demonstrate basic knowledge of key topics in classical real analysis.

§  The course pervious the basic for further studies with in function analysis, topology & function Theory. 

 

MATH202TH: Algebra: -

Students will learn about algebraic structures, groups, subgroups, their types; They will be also introduced to rings, sub rings, integral domains and fields.

 

On successful completion of the course, students will be able to: 

§  Students will be able to understand definition of group, abelian and non-abelian groups, the groups Zn of integers under addition modulo n and the group U(n), Cyclic group, Normal subgroups, quotient groups.

§  Understand group homomorphism.

§  Understand basic theory of Rings, Commutative and Non-Commutative rings, Polynomial rings, rings of matrices, subring, Ideals, Integral domain, and fields in detail.

 

MATH309TH: Integral Calculus: -

This SEC will lead expertise in integration, rectification, and quadrature. Students will learn to handle double and triple integrals.

 

On successful completion of the course:

 

§  This course will provide understanding of integration by partial fraction, integration of rational and irrational functions, properties of definite integrals, reduction formulae. Areas and lengths of curves in the plane, volumes, and surfaces of solids of revolution, Cartesian, and parametric forms. Double and triple integrals.

 

MATH310TH: Vector Calculus: -

It will teach students to find gradient divergence, curl, and vector integration and provides a peep into the beautiful world of Gauss, Green and Stokes theorem.

 

On successful completion of the course, students will be able to:

 

§ Vector calculus motivates the study of vector differentiation and integration in two- and three-dimensional spaces. 

§  It helps to understand the students about Scalar and vector product of three and product of four vectors. Reciprocal vectors. Vector differentiation, scalar point function and vector point function. Derivative along a curve, directional derivatives. To understand the concept of orthogonal curvilinear coordinates. Gradient, Divergence, Curl, and Laplacian operator in terms of orthogonal curvilinear coordinates system. 

§  It is widely   accepted as a prerequisite in various fields of science and engineering.   It offers important tools for understanding functions (both real & complex) non-Euclidean geometry and topology. 

§ These tools are employed successfully in different branches of engineering and physics (such as electromagnetic fields, fluid flow and gravitational fields). 

 

 

MATH313TH: Probability and Statistics: -

This course will change one’s sight of viewing different experiments by defining sample space, probability, providing in depth knowledge of different probability distributions and joint probability distribution functions.

 

On successful completion of the course, students will be able to: 

 

§  Understand basic theoretical and applied principles of statistics needed to enter the job force.

§  They will have a better informative view on sample space, probability axioms, cumulative distribution functions, probability density function, mathematical expectations, moments, moment generating functions, Binomial, Poisson, continuous distribution. Joint cumulative distribution function & its properties, joint probability density functions, marginal and conditional distributions, expectation of function of two random variables

 

MATH317TH: Transportation and Game Theory: -

No mathematics programme is complete without operations research. Operations research is that branch of mathematics which helps in optical decision making in various business situations. So, this section deals with solution of transportation problems, assignment problems and game theory.

The game theory provides powerful tools for analyzing transport systems and making decisions in situations. The students will be able to thoroughly grasp the topics like transportation problem and its mathematical formulation, optimal solution, Hungarian method for solving assignment problem. In game theory, solving 2-person zero sum games, games with mixed strategies, graphical solution.

 

MATH303TH: Linear Algebra: -

The main aim of the course is to introduce the students:

§  Vector space, subspace sum and Direct sum of subspaces, Linear dependent, Linear independent subset of a vector space, spanning set and basis of a vector space.

§  The homomorphism and isomorphism of a vector space also they can understand the concept of Linear transformation and its matrix representation. Null space and range space of Linear transformation, rank, and nullity with its applications. 

§  The algebra of Linear transformations minimal polynomials of Linear transformation and singular and non-singular transformations.

§  The inner product space, Cauchy- Schwartz inequality. Orthogonal basis and orthonormal sets.  Bessel’s inequality for finite dimensional vector space. Gram Schmidt orthogonalization process.

 

MATH305TH: Complex Analysis: -

The main aim of the course is to introduce the students:

§  Technique of solving various problems of engineering and science.

§  Limits, limits involving the point at infinity continuity, properties of complex numbers, region in a complex plane function of complex variables and their mapping. Cauchy- Reimann equations.

§  The analytic functions, examples of analytic function derivatives and integrals of analytic function.  

§  Understand the concept of contours integration and Cauchy integral formula.

§  Liouville's theorem and the fundamental theorem of algebra. Convergence of series, Taylor series and Laurent series.