department of applied mathematics 2017-18
TRANSCRIPT
Department of Applied Mathematics 2017-18
Course Number and Title : AMS-1110, Applied Mathematics-I
Credits : 04
Class/Year/Semester : B.Tech./First Year/Autumn
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn the fundamental concepts of matrices, differential and integral calculus, theory of ordinary
differential equations and applications.
Course Outcomes:
After completing this course the students would be able to:
1. apply tools of the theory of matrices to relevant fields of engineering.
2. understand curve tracing,regions between different curves and expansion of functions.
3. apply tools of integration to find length, area and volume.
4. apply differential equation methods to physical problems.
Syllabus:
Unit Contents Contact Hours
Unit-1 Linear Algebra-Matrices:Rank of a matrix,Consistency of a system of linear
equations, Linear dependence and independence of vectors, Eigen-values and Eigen
vectors of a matrix, Cayley-Hamilton theorem, Diagonalization of a matrix,
Introduction of vector spaces, subspaces, finite dimensional vectorspaces and
examples.
11
Unit-2 Curve Tracing and Successive Differentiation: Asymptotes, Tracing of curves
in cartesian, polar and parametric forms, Successive differentiation, Leibnitz theorem,
Taylor and Maclaurintheorems with remainder terms, Infinite series, Ratio,
Comparison andRoot tests of convergence.
11
Unit-3 Integration and its Applications: Improper integrals, Beta and Gamma functions,
Application of integration to length of curves includingintrinsic equation, surface area
and volume of solids of revolution.
11
Unit-4 Ordinary Differential Equation: Exact differential equations,Integrating
factors,Linear differential equations of second and higher order with constant
coefficients, Homogeneous differential equations, Simultaneous linear differential
equations, Applications to physical problems, Method of variation of parameters.
11
Total: 44
Text Books:
1. R.K. Jain and S.R.K. Iyengar; Advanced Engineering Mathematics, Narosa.
2. Thomas and Finney; Calculus and Analytical Geometry, Narosa Publishing House.
Reference Books: 1. Erwin Kreyszig; Advanced Engineering Mathematics, John Wiley & Sons, INC
2. Chandrika Prasad; Mathematics for Engineers, Pothishala Pvt. Ltd., Allahabad
Department of Applied Mathematics
Course Number and Title : AMS-1120, Applied Mathematics-II
Credits : 04
Class/Year/Semester : B.Tech./First Year/Winter
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn partial differentiation, multiple integration and their applications, Laplace transform and its
applications to differential equations, Fourier series and Fourier transforms.
Course Outcomes:
After completing this course the students would be able to:
1. apply the theory of functions of saveral variables in engineering problems.
2. use double and triple integralsto find area and volume.
3. apply Laplace transform methodto solve differential equations.
4. applyFourier series and Fourier transform methods in relavent areas.
Syllabus:
Unit Contents Contact Hours
Unit-1
Partial Differentiation and Applications: Functions of several variables, Partial
differentiation, Euler’s theorem for homogeneous functions, Total differential, Change
of variables, Jacobian, Taylor series for a function of two variables, Maxima and
minima of functions of two variables.
11
Unit-2 Multiple Integration:Double and triple integrals, Change of variables, Change of
order of integration, Applications to area and volume.
11
Unit-3 Laplace Transform:Laplace transform ofelementary functions, Shifting and other
theorems with important properties, Inverse Laplace transforms, Applications to single
and system of linear differential equations.
11
Unit-4 Fourier Series and Fourier Transform:Fourier series, Fourier coefficients, Half
range series, Fourier series of odd and even functions, Fourier seriesof T-periodic
function, Introduction to Fourier transforms.
11
Total: 44
Text Books:
1. R.K. Jain and S.R.K. Iyengar; Advanced Engineering Mathematics, Narosa.
2. Thomas and Finney; Calculus and Analytical Geometry, Narosa Publishing House.
Reference Books: 1. Erwin Kreyszig; Advanced Engineering Mathematics, John Wiley & Sons, INC
2. Chandrika Prasad; Mathematics for Engineers, Pothishala Pvt. Ltd., Allahabad
2017-18
Department of Applied Mathematics
Course Number and Title : AMS-2110, Applied Mathematics-III
Credits : 03
Class/Year/Semester : B.Tech.(Civil) / IIYear/Autumn
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 2-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn vector calculus, functions of complex variable, boundary value problemsin partial
differential equations.
Course Outcomes:
After completing this course the students would be able to:
1. apply tools of vector differentiation and vector integration in engineering disciplines
2. understand and apply fundamental concepts of a functions of complex variable and complex
integration to various problems.
3. solve the solutions of one dimensional heat, and wave equations and two dimentional Laplace
equation. .
Syllabus:
Units Contents Contact Hours
Unit-1
Vector Calculus:Differentiation of vector functions,gradient of a scalar
field,divergence and curl of a vector fields and their physical significance,
solenoidal and irrotational fields, determination of potential functions, line
integrals, surface and volume integrals, Green’s theorem in a plane.
12
Unit-2 Functions of Complex Variable: Analytic functions, Cauchy- Reimann
equations, integration of functions of a complex variable, line integrals,
Cauchy’s theorem, Cauchy’s integral formula.
12
Unit-3 Partial DifferentialEquations: Formation of partial differential equations,
concept of boundary value problems, solution of two dimensional Laplace
equation in cartesian co-ordinates, solution of one dimensional heat and wave
equation by the method of separation of variable.
12
Total: 36
Text Books:
1. Chandrika, Prasad: Advanced Mathematics for Engineers, Pothishala Pvt. Ltd., Allahabad
2. Chandrika, Prasad: Mathematics for Engineers, Pothishala Pvt. Ltd., Allahabad
Reference Books: 3. Jain, R.K. and Iyengar, S.R.K: Advanced Engineering Mathematics, Narosa.
BOS:7.4.18
2018-19
4. Kreyszig, Erwin: Advanced Engineering Mathematics, John Wiley & Sons,Inc.
Department of Applied Mathematics
Course Number and Title : AMS-2120, AppliedMathematics-IV
Credits : 03
Class/Year/Semester : B.Tech. (Civil)/IIYear/Winter
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 2-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn numerical techniques for system of linear equations, non-linear equations, interpolation
problems, numerical differentiation and integration, numerical solution of differential equations.
Course Outcomes: After completing the course the students are expected to be able to:
1. apply numerical methods to solve system of linear equations and non-linear equations.
2. find approximations using interpolation/extrapolations of different problems and find
numerical differentiation and integration.
3. solve numerically the initial value problems and boundary value problesms in ODE. Syllabus:
Units Contents Contact Hours
Unit-1
Numerical Solution of Equation & Finite Difference:Solution of system of
linear equations by Gauss elimination and Gauss-Seidel methods, solution of a
nonlinear equation by general iteration and Newton-Raphson methods, finite
difference operators and tables, detection of errors/ missing values.
12
Unit-2 Interpolation, Differentiation and Integration: Newtons forward and
backward interpolation formulae, Lagrange’s interpolation formula and
Newton’s divided difference formula, Numerical differentiation and
integration, general quadrature formula: Trapezoidal, Simpson’s and Weddle’s
rules.
12
Unit-3 Numerical Solution of O.D.E:Numerical solution of initial value problems
by Taylor series, Euler’s, modified Euler’s and Runge-Kutta fourth order
methods, Solution of two point boundary value problems by finite difference
method.
12
Total: 36
Text Books:
1. Sastry, S.S: “Introductory Methods of Numerical Analysis”., Prentice Hall India .
2. Jain, M.K., Iyenger, S.R.K. and Jain, R.K:“ Numerical Methods for Scientific and Engineering
Computations”, New Age International Publication Pvt. Ltd.
Reference Books: 3. Erwin Kreyszig, Erwin: Advanced Engineering Mathematics, John Wiley & Sons, INC
4. Venkataraman, M.K: Numerical Methods in Science and Engineering, National Publishing Co.Madras
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2230, Higher Mathematics
Credits : 04
Class/Year/Semester : B. Tech. (Electrical) /II Year/Autumn
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn complex analysis and various numerical methods to solve engineering problems.
Course Outcomes:After completing this course the students should be able to:
1. understand and apply fundamental concepts of functions of complex variable and complex
integration to various problems.
2. apply in solving various problems related to real integral by contour integration.
3. apply numerical methods to solve linear, nonlinear equations and interpolation techniques in
scientific computations.
4. obtain numerical solutions of IVP and BVP.
Syllabus:
Units Contents Contact Hours
Unit-1 Functions of Complex Variable: Analytic functions, Cauchy-Reimann
equations, complex integration, Cauchy’s theorem, Cauchy’s integral formula.
12
Unit-2 Series andContourIntegration: Taylor series, Laurent’s series, zeros and
singular points, residues and residue theorem, evaluation of real integrals by
contour integration.
12
Unit-3 Numerical Solutions of Equations& Interpolation: Solution of algebraic and
transcendental equations by Newton-Raphson and general iterative methods,
solution of linear simultaneous equations by Gauss-elimination and Gauss-
Seidel methods, finite difference operators, Newton’s forward and backward
interpolation formulae.
12
Unit-4 Numerical Solutions of ODE: Taylor’s series methods, Euler’s and modified
Euler’s methods,Runge-Kutta fourth order method, solution of two point
boundary value problems by finite difference methods.
12
Total: 48
Text Books:
1. Chandrika, Prasad: “Advanced Mathematics for Engineers.” Pothishala Pvt. Ltd., Allahabad
2. Sastry, S.S: Introductory Methods of Numerical Analysis, Prentice Hall, India.
Reference Books:
3. Jain,M.K, Jain, R.K and. Iyengar, S.R.K: “Numerical Methods for Scientific and Engineering Computation”.,
New Age National Publishing. Madras.
4. Venkataraman,M.K: Engineering Mathematics Third year (Part A & B), National Pub. Co, Madras.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2310, Higher Mathematics
Credits : 04
Class/Year/Semester : B.Tech. (Mechanical) /II Year/Autumn
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn functions of complex variable, vector differentiation &vector integration.
Course Outcomes:After completing this course the students are expected to be able to:
1. understand and apply fundamental concepts of functions of complex variable and complex
integration to various problems.
2. understand the series expansion and evaluate the real integrals by contour integration.
3. apply tools of vector differentiation in the relevant field.
4. apply tools of vector integration in the relevant field.
Syllabus:
Units Contents Contact Hours
Unit-1 Functionsof Complex Variable: Analytic functions, Cauchy-Reimann
equations, complex integration, Cauchy’s theorem, Cauchy integral formula.
12
Unit-2 Series and Contour Integration: Taylor’s series, Laurent’s series, zeros and
singular points, residues and residue theorem, evaluation of real integrals by
contour integration.
12
Unit-3 Vector Differentiation: Scalar field, gradient of a scalar field and its physical
significance, vector field, divergence and curl of a vector field and their
physical significance, solenoidal and irrotational fields, determination of
potential functions.
12
Unit-4 Vector Integration: Line integral, conservative field, surface and volume
integrals, Gauss divergence theorem, Stokes’ theorem, Green’s theorem in a
plane and applications.
12
Total: 48
Text Books:
1. Chandrika, Prasad: Mathematics for Engineers, Pothishala Pvt. Ltd
2. Jain, R.K and. Iyengar, S.R.K:Advanced Engineering Mathematics, Narosa
Reference Books:
3. Kreyszig, Erwin: Advanced Engineering Mathematics, John Wiley & Sons, Inc.
4. Venkataraman, M.K: “Engineering Mathematics”. 3rd
year, National Publishing Co., Madras.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2410, Higher Mathematics
Credits : 04
Class/Year/Semester : B. Tech(Chemical & Petro-Chemical)/II Yr/Autumn
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To study vector calculus, functions of complex variable and boundary value problems.
Course Outcomes:After completing this course the students are expected to be able to:
1. apply methods of vector differentiation in engineering problems.
2. apply tools of vector integration in the relevant field.
3. apply fundamental concepts of a functions of complex variable and complex integration to
various problems.
4. solve two dimensional Laplace equation, one dimensional diffussion and wave equation by
the method of separation of variables.
Syllabus:
Units Contents Contact Hours
Unit-1 Vector Differentiation: Scalar fields, gradient of a scalar field , divergence
and curl of a vector field,solenoidal and irroataional fields determination of
potential functions.
12
Unit-2 Vector Integration:Line integrals, conservative field, surface and volume
integrals, Gauss divergence theorem, Stokes’ theorem, Green’s theorem in a
plane, applications.
12
Unit-3 Functions of Complex Variable: Analytic function, Cauchy-Reimann
equations, complex integration, Cauchy’s theorem, Cauchy integral formula.
12
Unit-4 Boundary Value Problems: Solution of two dimensional Laplace equation in
cartesian and polar coordinates, solution of one dimensional diffussion and
wave equation by the method of separation of variables.
12
Total: 48
Text Books:
1. Chandrika, Prasad: “Advanced Mathematics for Engineers”. Pothishala Pvt. Ltd.
2. Chandrika, Prasad: Mathematics for Engineers, Pothishala Pvt. Ltd.
Reference Books: 3. Kreyszig,,Erwin: “Advanced Engineering Mathematics.”, John Wiley & Sons.
4. Jain, R.K and. Iyengar, S.R.K :Advanced Engineering Mathematics, Narosa
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMO-3510, Numerical Techniques
Credits : 04
Class/Year/Semester : B.Tech./III & IV Year/Autumn
Course Category : Open Elective
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn advanced numerical methods in system of equations, interpolation, approximation and study
oflinear programming problem.
Course Outcomes:After completing this course the students should be able to:
1. solve linear equations and eigen value problems.
2. understand the interpolation techniques of different kind.
3. approximate data, functions by least squares method.
4. formulate linear programming problem and solve it.
Syllabus:
Units Contents Contact Hours
Unit-1 Linear Systems & Eigen Value Problems: Matrices and linear equations:LU
factorization & pivoting, singular value decompositions. Numerical approach
to eigen value problems.
12
Unit-2 Interpolation:Lagrange’s, Newton’s divided difference,Polynomial, Rational
function & spline interpolation with error analysis.
12
Unit-3 Approximation: Least square approximations for discrete and continuous data.
Mini-max techniques for approximations. Random number generations.
12
Unit-4 Linear Programming: Formulation of linear programming problem. Solution
by graphical and simplex methods Duality. Introduction to nonlinear
programming.
12
Total: 48
Text Books:
1. Jain, M.K, Jain, R.K and Iyenger, S.R.K.: “Numerical Methods for Scientific and Engineering
Computations”, New Age International Publication Pvt. Ltd.
2. Sastry, S.S: “Introductory Methods of Numerical Analysis”., Prentice Hall, India.
Reference Books:
3. Kreyszig, Erwin: Advanced Engineering Mathematics, John Wiley & Sons, INC.
4. Venkataraman, M.K:“NumericalMethods in Science &Engineering”, National Pub. Co, Madras.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMO-4430, Advanced Numerical Methods
Credits : 04
Class/Year/Semester : B.Tech./III & IV Year/Winter
Course Category : Open Elective
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn advanced numerical methods and Finite Element Method(FEM).
Course Outcomes:After completing this course the students will be able to:
1. find the roots of polynomials and non-linear equations, eigen values of matrices.
2. evaluate numerical integration and find solution of initial value problems and boundary value
problems.
3. find numerical solution of partial differential equation.
4. use finite element methods and solve the boundary value problems.
Syllabus:
Units Contents Contact Hours
Unit-1 Non-linear Equations& Eigen Value Problems:Rootsof an algebraic
equation by Bairstow’s methods. System of nonlinear equations by iterative
and Newton-Raphson method, Numerical approach to eigen value problem.
12
Unit-2 Numerical Integration& ODE: Romberg Integration, Gaussian quadrature,
system of first order and higher order differential equations by Euler’s
andRunge-Kutta methods, The Chebyshev approximation.
12
Unit-3 Partial Differential Equations:Boundary value problems by finite difference
and shooting methods, Numerical solution of partial differential equations,
parabolic, elliptic and hyperbolic equations.
12
Unit-4 Finite Element Method: Basic concept of the finite element method.
Variational formulation of BVP’s, Rayleigh-Ritz approximation, weighted
residual methods, finite element analysis of one-dimensional problems.
Derivation, assembly of element equations and solution of the equation, post
processing of the results.
12
Total: 48
Text Books:
1. Jain, M.K, Jain, R.K and Iyenger, S.R.K.: “Numerical Methods for Scientific and Engineering
Computations”, New Age International Publication Pvt. Ltd.
2. Sastry, S.S: “Introductory Methodsof Numerical Analysis”., Prentice Hall India.
Reference Books: 3. Gupta , S.K.: “ Numerical Analysis & its Applications”.
4. Reddy, J.N: “ Finite Element Methods”.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2510, Higher Mathematics-I
Credits : 04
Class/Year/Semester : B. Tech.(Electronics)/II Year/Autumn
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn mathematical tools in functions of complex variable, complex integration andvector calculus.
Course Outcomes:After completing this course the students should be able to:
1. understand apply the basic of functions of complex variable and complex integration to
various engineering problems.
2. understand the basic concepts of zeros and singular ponits and evaluate the real integrals by
contour integration.
3. apply tools of vector differentiation in the relevant field.
4. apply tools of vector integration in the relevant field.
Syllabus:
Units Contents Contact Hours
Unit-1 Function of Complex Variable: Analytic functions, Cauchy-Riemann
equations, complex integration, line integrals, Cauchy’s theorem, Cauchy’s
integral formula.
12
Unit-2 Series and Contour Integration: Taylor’s series, Laurent series, zeros and
singular points, residues and residue theorem, evaluation of real integrals by
contour integration.
12
Unit-3 Vector Differentiation: Gradient of a scalar field and its physical significance.
Divergence and curl of a vector fields and their physical significance,
solenoidal and irrotational fields, determination of potential functions.
12
Unit-4 Vector Integration: Line integrals, conservative fields, surface and volume
integrals, Gauss divergence theorem, Stokes’ theorem, Green’s theorem in a
plane, and applications.
12
Total: 48
Text Books:
1. Chandrika, Prasad: “Mathematics for Engineers”.Pothishala Pvt. Ltd., Allahabad
2. Chandrika, Prasad:“ Advanced Mathematics for Engineers”.Pothishala Pvt. Ltd., Allahabad
Reference Books: 3. Kreyszig, Erwin:“Advanced Engineering Mathematics”. John Wiley & Sons, Inc.
4. Jain, R.K..andIyengar, S.R.K.: Advanced Engineering Mathematics, Narosa.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2520, Higher Mathematics-II
Credits : 04
Class/Year/Semester : B. Tech.(Electronics)/II Year/Autumn
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn complex analysis and various numerical methods for solving engineering problems and
probability.
Course Outcomes:After completing this course the students should be able to:
1. apply numerical methods to solvesystem of linear equations, nonlinear equations.
2. find approximation using interpolation and extrapolation of different problems.
3. evaluate numerical differentiation and integration and obtain numerical solutions of
differential equations.
4. understand the basic concepts of probability and use them to engineering problems.
Syllabus:
Units Contents Contact Hours
Unit-1 Numerical Solution of Equations& Finite Difference: Solution of nonlinear
equations by Newton-Raphson and general iteration methods, solution of
system of linear equations by Gauss elimination and Gauss-Seidel methods,
finite-difference operators, detection of error/missing values.
12
Unit-2 Interpolation, Differentiation and Integration: Newton’s forward and
backward interpolation formulae, Newton’s divided difference and Lagrange’s
interpolation formulae, Numerical differentiation and integration, Gaussian
quadrature.
12
Unit-3 Numerical Solution of O.D.E: Solution of first order initial value problems by
Taylor’s series, Euler’s method , modified Euler’s and Runge-Kutta methods,
Numerical solution of two point boundary value problems by finite difference
method.
12
Unit-4 Probability:Sample space, laws of probability, addition and multiplication
theorems, solution of simple problems, conditional probability, dependent and
independent events, random variable, binomial and normal distributions..
12
Total: 48
Text Books:
1. Sastry, S.S: “IntroductoryMethods of Numerical Analysis”. Prentice Hall India Ltd.
2. Meyer, P.L: “Introductory Probability and Statistical application.” Oxford & IBH.
Reference Books: 3. Kreyszig, Erwin: “Advanced Engineering Mathematics”. John Wiley & Sons, INC.
4. Jain, M.K, Jain, R.K and Iyenger, S.R.K.: “Numerical Methods for Scientific and Engineering
Computations”, New Age International Publication.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2610, Higher Mathematics
Credits : 04
Class/Year/Semester : B. Tech.( Computer)/II Year/Autumn
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn mathematical tools in functions of complex variables, complex integration and vector
calculus.
Course Outcomes:After completing this course the students are expected to be able to:
1. understand and apply the basic of complex variables, functions and complex integration to
various engineering problems.
2. understand the basic concepts of zeroes and singular points and evaluate the real integrals by
contour integration.
3. apply tools of vector differentiation in the relevant field.
4. apply tools of vector integration in the relevant field.
Syllabus:
Units Contents Contact Hours
Unit-1 Functions of a complex variable:Analytic functions, Cauchy-Riemann
equations, Complex integration, line integrals, Cauchy’s theorem, Cauchy’s
integral formula.
12
Unit-2 Series and Contour Integration: Taylor’s series, Laurent’s series,
zeros and singular points, residues and residue theorem, evaluation of
real integrals by contour integration.
12
Unit-3 Vector Differentiation: Gradient of a scalar field and its physical
significance. Divergence and curl of vector field and their physical
significance, solenoidal and irrotational fields, determination of potential
functions.
12
Unit-4 Vector Integration:Integration of vector functions, line integrals,
conservative fields, surface and volume integrals, Gauss divergence theorem,
Stokes’ theorem, Green’s theorem, applications.
12
Total: 48
Text Books:
1. Chandrika, Prasad: “Mathematics for Engineers.”Pothishala, Allahabad.
2. Chandrika, Prasad: “Advanced Mathematics for Engineers.” Pothishala , Allahabad..
Reference Books: 3. Kreyszig, Erwin:“Advanced Engineering Mathematics”. John Wiley & Sons, Inc.
4. Jain, R.K and Iyenger, S.R.K: “Numerical Methods for Scientific and Engineering Computations”,
New Age International Publication.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2320, Numerical Methods & Optimization
Credits : 04
Class/Year/Semester : B. Tech.(Mechanical)/II Year/Winter
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn numerical techniques for system of linear equations, non-linear equations, interpolation
problems, numerical differentiation and integration, numerical solution of ordinary differential
equations and linear programming.
Course Outcomes:After completing this course the students are expected to be able to:
1. apply numerical methods to solve system of linear equations, non-linear equations
2. understand interpolation problems and apply it in relevant problems and also numerical
differentiation and integration problems.
3. numerical solutions of IVP and BVP.
4. understand and solve linear programming problems.
Syllabus:
Units Contents Contact Hours
Unit-1 Numerical Solution of Equations & Finite Difference:Solution of
system of linear equations by Gauss-Seidel and Gauss elimination methods,
solution of single nonlinear equations by Newton-Raphson and general
iteration methods and their convergence. Finite difference operators,
difference tables and relations.
12
Unit-2 Interpolation, Differentiation& Integration: Interpolation by Newton’s
forward, backward, central, divided difference formula, Lagrange’s
interpolation formula, Numerical differentiation and integration.General
Quadrature formula: Trapezoidal, Simpson’s and Weddle’s rules.
12
Unit-3 Numerical Solution of O.D.E: Numerical solution of initial value problems by
Taylor’s series, Euler’s method, modified Euler’s and Runge-Kutta methods,
solution of boundary value problems by finite difference method.
12
Unit-4 Optimization: Introduction to linear programming, definitions and some
elementary properties of convex sets, graphical and Simplex method,
degeneracy and duality of linear programming and its simple applications.
12
Total: 48
Text Books:
1. Sastry, S.S: “Introductory Methodsof Numerical; Analysis”. Prentice Hall.
2. Jain, M.K, Jain, R.K and Iyenger, S.R.K.: “Numerical Methods for Scientific and Engineering
Computations”, New Age International Publication.. Reference Books:
3. Kreyszig, Erwin: “Advanced Engineering Mathematics”. John Wiley & Sons,
4. Venkataraman, M.K: “Numerical Methods in Science and Engineering.” National Publishing, Madras.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2420, Applied Numerical Methods
Credits : 04
Class/Year/Semester : B. Tech.(Petro-Chemical)/lI Year/Winter
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn numerical techniques for system of linear equations, non-linear equations, interpolation
problems, numericaldifferentiation and integration, numerical solution of differential equations.
Course Outcomes:After completing this course the students are expected to be able to:
1. solve system of linear equations, non-linear equations
2. understand interpolation and apply it in relevant problems.
3. find numrical differentiation and intergration
4. solve initial value problems and boundary value problems in ODE.
Syllabus:
Units Contents Contact Hours
Unit-1 Numerical Solution of Equations:Solution of algebraic and transcendental
equations by Newton-Raphson and general iteration methods, applications of
Newton-Raphson method, simple problems on order of convergence, solution
of linear simultaneous equations by Gauss elimination and Gauss-
Seidelmethods.
12
Unit-2 Interpolation: Finite difference operators, detection of error and missing
values, Newton’s forward and backward interpolation formulae, Gauss and
Bassel’s central interpolation formulae,Newton’s divided difference and
Lagrange’s interpolation formulae.
12
Unit-3 Numerical Differentiation and Integration: Numerical differentiation for
tabular and non tabular values, Numerical integration, general quadrature
formula: Trapezoidal, Simpson’s rulesand Weddle’s rule, Gaussian quadrature.
12
Unit-4 Numerical Solution of ODE:Numerical solution of ODE by Taylor’s series,
Euler’s, modified Euler’s and Runge-Kutta fourth order methods, Numerical
solution of two point boundary value problems by finite difference method.
12
Total: 48
Text Books:
1. Sastry, S.S: “Introductory Methods of Numerical Analysis,”. Prentice Hall India.
2. Jain, M.K, Jain, R.K and Iyenger, S.R.K.: “Numerical Methods for Scientific and Engineering
Computations”, New Age International Publication Pvt. Ltd.
Reference Books: 3. Kreyszig, Erwin: “Advanced Engineering Mathematics”. John Wiley & Sons, Inc.
4. Venkataraman, M.K: “Numerical Methods in Science and Engineering.” National Publishing, Madras.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2620, Numerical Analysis & Probability
Credits : 04
Class/Year/Semester : B. Tech.(Computer)/II Year/Winter
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
1. To learn tools of Mathematics in numerical techniques and theory of probability.
Course Outcomes:After completing this course the students are expected to be able to:
1. apply numerical methods for solving system of linear and non linear equations.
2. understand interpolation and apply it in relevant problems and also evaluation of
numerical differentiation and integration. 3. numerical solutions of IVP and BVP.
4. understand the basic concepts of probability and apply them in engineering problems.
Syllabus:
Units Contents Contact Hours
Unit-1 Numerical Solution of Equations & Finite Difference: Solution of
nonlinear equations by Newton-Raphson and general iteration methods, solution
of system of linear equations by Gauss elimination and Gauss-Seidel methods,
finite difference operators, detection of error/ missing values.
12
Unit-2 Interpolation, Differentiation and Integration: Newton forward and
backward difference interpolation formulae. Newton’s divided difference
&Lagrange’s interpolation formulas, Numerical differentiation and integration,
general quadrature formula: Trapezoidal, Simpson’s rules,Weddle’s Rules.
12
Unit-3 Numerical Solution of O.D.E:Solution of first order initial value problems by
Taylor’s, Euler’s methods, modified Euler’s and Runge-Kutta methods,
Numerical solution of two point boundary value problems by finite difference
method.
12
Unit-4 Probability:Sample space, laws of probability, addition and multiplication
theorems, conditional probability, Bayes theorems, dependent and independent
events, solution of simple problem of probability, random variable, binomial and
normal distributions.
12
Total: 48
Text Books:
1. Sastry, S.S: “Introductory Methodsof Numerical Analysis”. Prentice Hall India Ltd
2. P.L. Meyer: “Introductory Probability and Statistical Application, ”Oxford and IBH Publishing Reference Books:
3. Kreyszig, Erwin: “Advanced Engineering Mathematics”. John Wiley & Sons, Inc.
4. Jain, M.K, Jain, R.K and Iyenger, S.R.K.: “Numerical Methods for Scientific and Engineering
Computations”, New Age International Publication.
BOS:7.4.18
2018-19
Department of Applied Mathematics
Course Number and Title : AMS-2630, Discrete Mathematics
Credits : 04
Class/Year/Semester : B. Tech. (Computer)/II Year/Winter
Course Category : Departmental Core
Pre-requisite(s) : NIL
Contact Hours (L-T-P) : 3-1-0
Type of Course : Theory
Course Assessment : Course Work (Home Assignment) (15%)
Mid Semester Examination (1 hour) (25%)
End Semester Examination (2 hour) (60%)
Course Objectives:
To learn some discrete algebraic structure such as groups, rings, fields, basics of Graph theory and
combinatorics and also linear programming problems.
Course Outcomes:After completing this course the students shall be able to:
1. understand algebraic structures and apply them in the field of computer engineering. 2. understand the basic of graph theory and some optimization problems such as shortest path
problem, flow problems etc.
3. understand the basic of combinatorics and solve the recurrence relations.
4. understand and solve linear programming problems.
Syllabus:
Units Contents Contact Hours
Unit-1 Algebraic Structures:Relation and functions, monoids, semi groups and
groups, rings and fields. Examples and problems
12
Unit-2 Graph Theory: Formal definition of graphs, directed and undirected graphs,
cycles, chain, path, connectivity, adjacency and incidence matrices, shortest
path algorithm, elements of transport networks, flows in networks,Ford and
Fulkerson algorithm.
12
Unit-3 Combinatorics: Introduction to permutations and combinatorics,
recursion.Introduction to some common recurrence relations, generating
functions, solution of recurrence relations using generating functions.
12
Unit-4 Linear Programming: Formation of linear programming problems and its
solution by graphical method and simplex algorithm, duality.
12
Total: 48
Text Books:
1. Narshing, Deo:“Graph Theory with applications to engineering and computer science”. Prentice-Hall,
New Delhi.
2. Kolman, B.[etal.] :“Discrete Mathematical Structures”. Pearson Education.
3. KantiSwaroop [et al.]: “Operational Research”. Sultan Chand & Sons,New Delhi.
BOS:7.4.18
2018-19