Department of Mathematics was established in the year 2008 in order to provide a strong Mathematical foundation through course which cater to the needs of Mathematical applications for the students pertaining to the Engineering skills as well as higher education and research. We have dedicated, experienced and energetic faculty to impart invaluable information that may be used in both academic as well as professional life. At present, the department has one Associate Professor and five Assistant Professors. Our faculties are leaders in the fields of teaching and research activities. The department has more than 12 research publications in reputed national/international journals. The Department adopts various innovative techniques to improve the comprehension and problem solving skills of students.
Designation : Associate Professor
Qualification : B.Sc. M.Sc., M.Phil., Ph.D.
Designation : Assistant. Professor
Qualification : B.Sc., B.Ed. M.Sc., M.Ed.
The department celebrated the National Mathematics Day  2018 0n December 22 of 2018
1st Semester:
Semester : 1 
CIE Marks : 40 

Course Code : 18MAT11 
SEE Marks : 60 

Course Name : Calculus and Linear Algebra 
Credits : 04 

Teaching Hours/week (LTP) : 320 
Exam Hrs. : 03 

Course Learning Objectives: This course Calculus and Linear Algebra (18MAT11) will enable the students : 1. To familiarize the important tools of calculus and differential equation that are essential in all branches of engineering. 2. To develop the knowledge of matrices and linear algebra in a comprehensive manner 

Module No 
Module Name 
Description 
Duration 

1 
Differential Calculus1 
Review of elementary calculus, Polar curves  angle between the radius vector and tangent, angle between two curves, pedal equation. Curvature and radius of curvature Cartesian and polar forms (without proof). Centre and circle of curvature (formulae only) –applications to evolutes and involutes. 
10 Hours 

2 
Differential Calculus2 
Taylor’s and Maclaurin’s series expansions for one variable (statements only), indeterminate forms L’Hospital’s rule. Partial differentiation; Total derivativesdifferentiation of composite functions. Maxima and minima for a function of two variables; Method of Lagrange multipliers with one subsidiary condition. Applications of maxima and minima with illustrative examples. JacobiansSimple problems. 
10 Hours 

3 
Integral Calculus 
Multiple integrals: Evaluation of double and triple integrals. Evaluation of double integrals change of order of integration and changing into polar coordinates. Applications to find area, volume and centre of gravity. Beta and Gamma functions: definitions, Relation between beta and gamma functions and simple problems. 
10 Hours 

4 
Ordinary differential equations(ODE’s)of first order 
Exact and reducible to exact differential equations. Bernoulli’s equation. Applications of ODE’sorthogonal trajectories, Newton’s law of cooling and LR circuits. Nonlinear differential equations: Introduction to general and singular solutions; Solvable for p only; Clairaut’s and reducible to Clairaut’s equation only. 
10 Hours 

5 
Elementary Linear Algebra 
Rank of a matrixechelon form. Solution of system of linear equations – consistency. Gausselimination method, Gauss –Jordan method and GaussSeidel method. Eigen values and eigen vectors Rayleigh’s power method. Diagonalization of a square matrix of order two. 
10 Hours 

Course Outcomes (COs): At the end of this course student will be able to, 1. Apply the knowledge of calculus to solve problems related to polar curves and its applications in determining the bentness of a curve. 2. Learn the notion of partial differentiation to calculate rates of change of multivariate functions and solve problems related to composite functions and Jacobians. 3. Apply the concept of change of order of integration and variables to evaluate multiple integrals and their usage in computing the area and volumes. 4. Solve first order linear/nonlinear differential equation analytically using standard methods. 5. Make use of matrix theory for solving system of linear equations and compute eigen values and eigen vectors required for matrix diagonalization process. 

Text Books: 1. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 43rd Ed., 2015. 2. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed.(Reprint), 2016. Reference books: 1. C.Ray Wylie, Louis C.Barrett : “Advanced Engineering Mathematics", 6th Edition, McGrawHill Book Co., New York, 1995. 2. N.P.Bali and Manish Goyal: A Text Book of Engineering Mathematics, Laxmi Publishers, 7th Ed., 2010. 3. B.V.Ramana: "Higher Engineering Mathematics" 11th Edition, Tata McGrawHill, 2010. 4. Veerarajan T.,” Engineering Mathematics for First year", Tata McGrawHill, 2008. 5. Thomas G.B. and Finney R.L.”Calculus and Analytical Geometry”9th Edition, Pearson, 2012. Web links and Video Lectures: 1. http://nptel.ac.in/courses.php?disciplineID=111 2. http://www.classcentral.com/subject/math(MOOCs) 3. http://academicearth.org/ 
2nd semester
Semester : 2 
CIE Marks : 40 

Course Code : 18MAT21 
SEE Marks : 60 

Course Name : Advanced Calculus and Numerical Method 
Credits : 04 

Teaching Hours/week (LTP) : 320 
Exam Hrs. : 03 

Course Learning Objectives: The purpose of the course 18MAT21 is to facilitate the students with concrete foundation of vector calculus, ordinary and partial differential equations, infinite series and numerical methods enabling them to acquire the knowledge of these mathematical tools. 

Module No 
Module Name 
Description 
Duration 

1 
Vector Calculus 
Vector Differentiation: Scalar and vector fields. Gradient, directional derivative; curl and divergencephysical interpretation; solenoidal and irrotational vector fields Illustrative problems. Vector Integration: Line integrals, Theorems of Green, Gauss and Stokes (without proof). Applications to work done by a force and flux. 
10 Hours 

2 
Differential Equations of higher order 
Second order linear ODE’s with constant coefficientsInverse differential operators, method of variation of parameters; Cauchy’s and Legendre homogeneous equations. Applications to oscillations of a spring and LCR circuits. 
10 Hours 

3 
Partial Differential Equations(PDE’s) 
Formation of PDE’s by elimination of arbitrary constants / functions. Solution of nonhomogeneous PDE by direct integration. Homogeneous PDEs involving derivative with respect to one independent variable only. Solution of Lagrange’s linear PDE. Derivation of one dimensional heat and wave equations and solutions by the method of separation of variables. 
10 Hours 

4 
Infinite Series 
Convergence and divergence of infinite series Cauchy’s root test and D’Alembert’s ratio test(without proof) Illustrative examples. Power series solutionsSeries solution of Bessel’s differential equation leading to Jn(x) Bessel’s function of first kindorthogonality. Series solution of Legendre’s differential equation leading to Pn(x)Legendre polynomials. Rodrigue’s formula (without proof), problems. 
10 Hours 

5 
Elementary Numerical Methods 
Finite differences. Interpolation/extrapolation using Newton’s forward and backward difference formulae, Newton’s divided difference and Lagrange’s formulae (All formulae without proof). Solution of polynomial and transcendental equations – NewtonRaphson and RegulaFalsi methods( only formulae) Illustrative examples. Numerical integration: Simpson’s (1/3)th and (3/8)th rules, Weddle’s rule (without proof ) –Problems. 
10 Hours 

Course Outcomes: On completion of this course, students are able to: 1. Solve first order linear/nonlinear differential equations analytically using standard methods. 2. Explain various physical models through higher order differential equations and solve such linear ordinary differential equations. 3. Understand a variety of partial differential equations and solution by exact methods/method of separation of variables. 4. Describe the applications of infinite series and obtain series solution of ordinary differential equations. 5. Apply the knowledge of numerical methods in the models of various physical and engineering phenomena 

Text Books: 1. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 43rd Ed., 2015. 2. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed.(Reprint), 2016. Reference books: 1. C.Ray Wylie, Louis C.Barrett : “Advanced Engineering Mathematics", 6th Edition, McGrawHill Book Co., New York, 1995. 2. N.P.Bali and Manish Goyal: A Text Book of Engineering Mathematics, Laxmi Publishers, 7th Ed., 2010. 3. B.V.Ramana: "Higher Engineering Mathematics" 11th Edition, Tata McGrawHill, 2010. 4. Veerarajan T.,” Engineering Mathematics for First year", Tata McGrawHill, 2008. 5. Thomas G.B. and Finney R.L.”Calculus and Analytical Geometry”9th Edition, Pearson, 2012. Web links and Video Lectures: 1. http://nptel.ac.in/courses.php?disciplineID=111 2. http://www.classcentral.com/subject/math(MOOCs) 3. http://academicearth.org/ 
3rd semester
4th semester
Semester : 4 
CIE Marks : 40 

Course Code : 17MAT41 
SEE Marks : 60 

Course Name : Engineering Mathematics IV 
Credits : 04 

Teaching Hours/week (LTP) : 400 
Exam Hrs. : 03 

Course Objectives: This course will enable students to: Conversant with numerical methods to solve ordinary differential equations, complex analysis, sampling theory and joint probability distribution and stochastic processes arising in science and engineering. 

Module No 
Module Name 
Description 
Duration 

1 
Numerical Methods1 
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 AdamsBashforth predictor and corrector methods (No proof). 
10 Hours 

2 
Numerical Methods2 and Special Function 
Numerical Methods: Numerical solution of second order ordinary differential equations, RungeKutta method and Milne’s method. Special Functions: Series solutionFrobenious method. Series solutionBessel’s differential equation leading to Jn(x)Bessel’s function of first kind Basic properties and orthogonality.Series solution of Legendre’s differential equation leading to Pn(x)Legendre polynomials. Rodrigue’s formula, problems. 
10 Hours 

3 
Complex Variables 
Complex Variables: Review of a function of a complex variable, limits, continuity, differentiability. Analytic functionsCauchyRiemann equations in cartesian and polar forms. Properties and construction of analytic functions. Complex line integralsCauchy’s theorem and Cauchy’s integral formula, Residue, poles, Cauchy’s Residue theorem ( without proof) and problems. Transformations: Conformal transformations, discussion of transformations: w= _{ } , w=_{ } , w=z+_{ }: and bilinear transformationsproblems. 
10 Hours 

4 
Probability Theory 
Probability Distributions: 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. 
10 Hours 

5 
Sampling Theory 
Sampling Theory: Sampling, Sampling distributions, standard error, test of hypothesis for means and proportions, confidence limits for means, student’s tdistribution, Chisquare 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. 
10 Hours 

Course Outcomes (COs): At the end of this course student will be able to 1. Solve first and second order ordinary differential equations arising in flow problems using single step and multistep numerical methods. 2. Solve problems of quantum mechanics, hydrodynamics and heat conduction by employing Bessel’s function relating to cylindrical polar coordinate systems and Legendre’s polynomials relating to spherical polar coordinate systems. 3. Analyze the analyticity, potential fields, residues and poles of complex potentials in field theory and electromagnetic theory and describe conformal and bilinear transformation arising in aero foil theory, fluid flow visualization and image processing.\ 4. Solve problems on probability distributions relating to digital signal processing, information theory and optimization concepts of stability of design and structural engineering. 5. Draw the validity of the hypothesis proposed for the given sampling distribution in accepting or rejecting the hypothesis and stochastic matrix connected with the multivariable correlation problems for feasible random events. Define transition probability matrix of a Markov chain and solve problems related to discrete parameter random process. 
Semester : 4 
CIE Marks :  

Course Code : 17MATDIP41 
SEE Marks : 60 

Course Name: Additional Mathematics  II 
Credits : 00 

Teaching Hours/week (LTP) : 300 
Exam Hrs. : 03 

Course Objectives: This course will enable students to:


Module No 
Module Name 
Description 
Duration 

1 
Linear Algebra 
Introduction  rank of matrix by elementary row operations – Echelon form. Consistency of system of linear equations  Gauss elimination method. Eigen values and Eigen vectors of a square matrix. Application of CayleyHamilton theorem (without proof) to compute the inverse of a matrixExamples. 
10 Hours 

2 
Higher order ODE’s 
Linear differential equations of second and higher order equations with constant coefficients. Homogeneous /nonhomogeneous equations. Inverse differential operators. Solutions of initial value problems. Method of undetermined coefficients and variation of parameters. 
10 Hours 

3 
Laplace transforms 
Laplace transforms of elementary functions. Transforms of derivatives and integrals, transforms of periodic function and unit step function Problems only. 
10 Hours 

4 
Inverse Laplace transforms 
Definition of inverse Laplace transforms. Evaluation of Inverse transforms by standard methods. Application to solutions of Linear differential equations and simultaneous differential equations. 
10 Hours 

5 
Probability 
Introduction. Sample space and events. Axioms of probability. Addition and multiplication theorems. Conditional probability – illustrative examples. Bayes‘s theoremexamples. 
10 Hours 

Course Outcomes: On completion of the course, students are able to: 1. Solve systems of linear equations in the different areas of linear algebra. 2. Solve second and higher order differential equations occurring in of electrical circuits, damped/undamped vibrations. 3. Describe Laplace transforms of standard and periodic functions. 4. Determine the general/complete solutions to linear ODE using inverse Laplace transforms. 5. Recall basic concepts of elementary probability theory and, solve problems related to the decision theory, synthesis and optimization of digital circuits.. 

Text Books: 1. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 43rd Ed., 2015. Reference books: 1. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed.(Reprint), 2016 2. N.P.Bali and Manish Goyal: A Text Book of Engineering Mathematics, Laxmi Publishers, 7th Ed., 2010. 
Vision
To strive to be recognized for academic excellence in the field of Mathematics through indepth teaching and research, and to play a pivotal role in strengthening the ability of aspirants to solve engineering problems through mathematical problem solving techniques.
Mission
Making Engineers to develop mathematical thinking and applying it to solve complex engineering problems, designing mathematical modeling for systems involving global level technology.