Department of Mathematics strives to be internationally recognized for academic excellence through the depth of its teaching and research, and to be locally relevant through its role in the development of the community it serves.

Making Engineers to develop mathematical thinking and applying it to solve complex engineering problems, designing mathematical modeling for systems involving global level technology.

• | Enhance mathematical knowledge which will enable them to analyze, interpret and optimize any Engineering related problem . | • | To provide the best mathematics education required to strengthen the backbone of all Engineering Departments. |

• | To attract and retain faculty of highest caliber. | • | Continue to give facilities to the faculty to do their research towards Ph.D. |

• | To provide opportunities for faculty to gain knowledge in teaching methodologies. | • | To provide opportunities for faculty to participate in various seminars, workshops, conferences and training programmes. |

• | To conduct National Conferences and Workshops for the benefit of students and faculty. | • | To create an environment that supports outstanding research. |

• | To gain overall development in academic and teaching domains. | • | To help students for their academic excellence to reach global standards. |

#### Curriculum - Syllabus - First Year - 1st semester

Determination of nth order derivatives of Standard functions - Problems. Leibnitz’s theorem (without proof) - problems. Polar Curves - angle between the radius vector and tangent, angle between two curves, Pedal equation of polar curves. Derivative of arc length - Cartesian, Parametric and Polar forms (without proof) - problems. Curvature and Radius of Curvature – Cartesian, Parametric, Polar and Pedal forms (without proof) –problems

Taylor’s and Maclaurin’s theorems for function of one variable(statement only)- problems. Evaluation of Indeterminate forms. Partial derivatives – Definition and simple problems, Euler’s theorem(without proof) – problems, total derivatives, partial differentiation of composite functions-problems. Definition and evaluation of Jacobian

Derivative of vector valued functions, Velocity, Acceleration and related problems, Scalar and Vector point functions. Definition of Gradient, Divergence and Curl-problems. Solenoidal and Irrotational vector fields. Vector identities - div(ɸA), curl (ɸA ), curl( grad ɸ), div(curl A).

Reduction formulae –Sinnx dx, Cosnx dx, SinmxCosnx dx, (m and n are positive integers), evaluation of these integrals with standard limits (0 to π/2) and problems. Differential Equations ; Solution of first order and first degree differential equations – Exact, reducible to exact and Bernoulli’s differential equations .Orthogonal trajectories in Cartesian and polar form. Simple problems on Newton's law of cooling.

Rank of a matrix by elementary transformations, solution of system of linear equations - Gauss-elimination method, Gauss –Jordan method and Gauss-Seidel method Eigen values and Eigen vectors, Rayleigh’s power method to find the largest Eigen value and the corresponding Eigen vector. Linear transformation, diagonalisation of a square matrix . Reduction of Quadratic form to Canonical form

#### Curriculum - Syllabus - First Year - 2nd semester

Linear differential equations with constant coefficients : Solutions ofsecond and higher order differential equations - inverse differential operatormethod, method of undetermined coefficients and method of variation of parameters

Solutions of simultaneous differential equations of first order.Linear differential equations with variable coefficients : Solution ofCauchy’s and Legendre’s linear differential equations.Nonlinear differential equations : Equations solvable for p, equationssolvable for y, equations solvable for x, general and singular solutions,Clairauit’s equations and equations reducible to Clairauit’s form.

Formulation of PDE by elimination of arbitrary constants/functions, solutionof non-homogeneous PDE by direct integration, solution of homogeneousPDE involving derivative with respect to one independent variable only.Derivation of one dimensional heat and wave equations and their solutionsby variable separable method.Double and triple integrals :Evaluation of double integrals. Evaluation by changing the order ofintegration and changing into polar coordinates. Evaluation of tripleintegrals.

Application of double and triple integrals to find area and volume. Betaand Gamma functions, definitions, Relation between beta and gammafunctions and simple problems.Curvilinear coordinates :Orthogonal curvilinear coordinates - Definition, unit vectors and scalefactors. Expressions for gradient, divergence and curl. Cylindrical andspherical coordinate systems.

Definition and Laplace transforms of elementary functions. Laplacetransforms of (without proof), periodic functions, unitstepfunction and Impulse function - problemsInverse Laplace Transform :
Inverse Laplace Transform - problems, Convolution theorem and problems,solution of linear differential equations using Laplace Transforms.

#### Curriculum - Syllabus - Second Year - 3rd semester

Periodic functions, Dirichlet’s condition, Fourier Series of periodic functions with period 2π and with arbitrary period 2c. Fourier series of even and odd functions. Half range Fourier Series, practical harmonic analysis-Illustrative examples from engineering field.

Infinite Fourier transforms, Fourier sine and cosine transforms. Inverse Fourier transform.

**Z-transform :**Difference equations, basic definition, z-transform-definition, Standard z-transforms, Damping rule, Shifting rule, Initial value and final value theorems (without proof) and problems, Inverse z-transform. Applications of ztransforms to solve difference equations. Review of measures of central tendency and dispersion. Correlation-Karl Pearson’s coefficient of correlation-problems.

**Regression analysis-**lines of regression (without proof) –problems Curve Fitting: Curve fitting by the method of least squares- fitting of the curves of the form, y = ax + b, y = ax2 + bx + c and y = aebx .**Numerical Methods:**Numerical solution of algebraic and transcendental equations by Regula- Falsi Method and Newton-Raphson method. Forward and backward differences, Newton’s forward and backward interpolation formulae. Divided differences- Newton’s divided difference formula. Lagrange’s interpolation formula and inverse interpolation formula (all formulae without proof)-Problems. Numerical integration: : Simpson’s (1/3)th and (3/8)th rules, Weddle’s rule (without proof ) –Problems.

Line integrals-definition and problems, surface and volume integralsdefinition, Green’s theorem in a plane, Stokes and Gauss-divergence theorem(without proof) and problems. Calculus of Variations: Variation of function and Functional, variational problems. Euler’s equation, Geodesics, hanging chain, problems.

#### Curriculum - Syllabus - Second Year - 4th semester

Numerical solution of ordinary differential equations of first order and first degree, Taylor’s series method, modified Euler’s method, Runge - Kutta method of fourth order. Milne’s and Adams-Bashforth predictor and corrector methods (No derivations of formulae).

Numerical solution of second order ordinary differential equations, Runge-Kutta method and Milne’s method. Special Functions: Series solution-Frobenious method. Series solution of Bessel’s differential equation leading to Jn(x)-Bessel’s function of first kind. Basic properties, recurrence relations and orthogonality. Series solution of Legendre’s differential equation leading to Pn(x)-Legendre polynomials. Rodrigue’s formula, problems

Review of a function of a complex variable, limits, continuity, differentiability. Analytic functions-Cauchy-Riemann equations in cartesian and polar forms. Properties and construction of analytic functions.

Complex line integrals-Cauchy’s theorem and Cauchy’s integral formula, Residue, poles, Cauchy’s Residue theorem( without proof) and problems.

Transformations: Conformal transformations, discussion of transformations: w=z^2,w=e^z,w=z+1/z and bilinear transformations-problems.

Complex line integrals-Cauchy’s theorem and Cauchy’s integral formula, Residue, poles, Cauchy’s Residue theorem( without proof) and problems.

Transformations: Conformal transformations, discussion of transformations: w=z^2,w=e^z,w=z+1/z and bilinear transformations-problems.

Random variables (discrete and continuous), probability mass/density functions. Binomial distribution, Poisson distribution. Exponential and normal distributions, problems.

Joint probability distribution: Joint Probability distribution for two discrete random variables, expectation, covariance, correlation coefficient.

Joint probability distribution: Joint Probability distribution for two discrete random variables, expectation, covariance, correlation coefficient.

Sampling, Sampling distributions, standard error, test of hypothesis for means and proportions, confidence limits for means, student’s t-distribution, Chi-square distribution as a test of goodness of fit.

Stochastic process: Stochastic processes, probability vector, stochastic matrices, fixed points, regular stochastic matrices, Markov chains, higher transition probabilitysimple problems.

Stochastic process: Stochastic processes, probability vector, stochastic matrices, fixed points, regular stochastic matrices, Markov chains, higher transition probabilitysimple problems.