Department of Applied Mathematics 2017-18

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 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:


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


Course Number and Title : AMS-2110, Applied Mathematics-III

Credits : 03

Class/Year/Semester : B.Tech.(Civil) / IIYear/Autumn








Course Objectives:

To learn vector calculus, functions of complex variable, boundary value problemsin partial

differential equations.

Course Outcomes:


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.

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2018-19

4. Kreyszig, Erwin: Advanced Engineering Mathematics, John Wiley & Sons,Inc.


Course Number and Title : AMS-2120, AppliedMathematics-IV

Credits : 03

Class/Year/Semester : B.Tech. (Civil)/IIYear/Winter








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:


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

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2018-19


Course Number and Title : AMS-2230, Higher Mathematics

Credits : 04

Class/Year/Semester : B. Tech. (Electrical) /II Year/Autumn








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


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:


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



Credits : 04

Class/Year/Semester : B.Tech. (Mechanical) /II Year/Autumn








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


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:


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



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.

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2018-19



Credits : 04

Class/Year/Semester : B. Tech(Chemical & Petro-Chemical)/II Yr/Autumn








Course Objectives:

To study vector calculus, functions of complex variable and boundary value problems.


1. apply methods of vector differentiation in engineering problems.


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:


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


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

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2018-19


Course Number and Title : AMO-3510, Numerical Techniques

Credits : 04

Class/Year/Semester : B.Tech./III & IV Year/Autumn

Course Category : Open Elective







Course Objectives:

To learn advanced numerical methods in system of equations, interpolation, approximation and study

oflinear programming problem.


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:


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


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


Course Number and Title : AMO-4430, Advanced Numerical Methods

Credits : 04

Class/Year/Semester : B.Tech./III & IV Year/Winter

Course Category : Open Elective







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:


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:



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”.

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2018-19


Course Number and Title : AMS-2510, Higher Mathematics-I

Credits : 04

Class/Year/Semester : B. Tech.(Electronics)/II Year/Autumn








Course Objectives:

To learn mathematical tools in functions of complex variable, complex integration andvector calculus.


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




Syllabus:


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



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


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


Course Number and Title : AMS-2520, Higher Mathematics-II

Credits : 04

Class/Year/Semester : B. Tech.(Electronics)/II Year/Autumn








Course Objectives:

To learn complex analysis and various numerical methods for solving engineering problems and

probability.


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:


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.


Computations”, New Age International Publication.

BOS:7.4.18

2018-19



Credits : 04

Class/Year/Semester : B. Tech.( Computer)/II Year/Autumn








Course Objectives:

To learn mathematical tools in functions of complex variables, complex integration and vector

calculus.


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




Syllabus:


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


Course Number and Title : AMS-2320, Numerical Methods & Optimization

Credits : 04

Class/Year/Semester : B. Tech.(Mechanical)/II Year/Winter








Course Objectives:


problems, numerical differentiation and integration, numerical solution of ordinary differential

equations and linear programming.


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:


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.


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


Course Number and Title : AMS-2420, Applied Numerical Methods

Credits : 04

Class/Year/Semester : B. Tech.(Petro-Chemical)/lI Year/Winter








Course Objectives:


problems, numericaldifferentiation and integration, numerical solution of differential equations.


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:


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.



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


Course Number and Title : AMS-2620, Numerical Analysis & Probability

Credits : 04

Class/Year/Semester : B. Tech.(Computer)/II Year/Winter








Course Objectives:

1. To learn tools of Mathematics in numerical techniques and theory of probability.


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:


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.


Computations”, New Age International Publication.

BOS:7.4.18

2018-19


Course Number and Title : AMS-2630, Discrete Mathematics

Credits : 04

Class/Year/Semester : B. Tech. (Computer)/II Year/Winter








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:


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

Documents

Department of Applied Mathematics 2017-18