Minutes of Meeting

Board of Studies (BOS)

Division of Mathematics

Galgotias University, Greater Noida

Agenda: To review curmicuh1m and syllabus of B.Tech Mathematics courses and M.Sc

Mathematics.

Board of Sudies meeting was conducted by Mathematics division, SBAS at 10:30 am on 21s

July 2016 in Dean's office.

Dr. Bimal Sarkar started mecting and welcomed all members. Dr. B.P.Singh presented B.Tech Mathematics courses and Dr Sharmistha Ghosh presented the

program structure and syllabus for M.Sc Mathematics.

Points discussed

1) B.Tech I Semester course should be renamed as "Differential and Integral Calculus".

2) Module on Matrices should be in II sem and it should be replaced by Function of single real variable.

3) Content on Improper Integral was suggested to add in B.Tech I Semester course.

4) B.Tech II Semester course should be renamed as "Matrices and Ordinary Differential

Equations" 5) It was decided to add Laplace transform in B.Tech II semester course.

6) Detailed discussion and review of M.Sc Mathematics syllabus was done.

7) It has been decided that the program has just been introduced in the session 2016-17, therefore no changes are required in existing curriculum.

Meeting ended with vote of thanks to Chair.

ERSTP OTIAS

.Utt DEAN

School of Basic & Applied Sciences Galgotias University

Uttar Pradesh 5ape

Galgotias University, Greater Noida

List of Members for Board of Studies, Division of Mathematics

S.No BOS Signature Designation &

Organization Professor, SBAS,GUU

Members 1 Dr. Bimal Dean

Sarkar Dr. Sharmistha Professor, Division of

Mathematics, SBAS,GU Program Chair,

M.Sc 2

Ghosh Mathematics,j

Professor, Division of

Mathematics, SBAS,GU Professor, Division of

Mathematics, SBAS,GU Chair,Division L

3 Dr. Babita Member

Tyagi Dr. B.P. Singh 4 Division

of

Mathematics,Associate Professor, External Dr. Piyush

Tiwari Mathematics, BITS

Misra, Noida Campus Associate Professor,

Dutt Jauhari Division of Mathematics,

SBAS,GU Assistant Professor,

Division of Mathematics, SBAS,GU

Expert

6 Dr. Aradhana Member

Dr. Manish Member

Singh

UN AS

DEAN School of Basic & Applied Sciences

Galgotias UniversityUttar Pradesh

GALGO

Ddesh

NIV Ctar P

LTPC Course Code Course Name

MATI13 31 0 4 Differential and Integral Calculus

Course Content

Contact Hours:8 Unit 1: Functions of single real variable Review of limit, continuity and differentiability for functions of single variable, Hyperbolic functions, Successive Differentiation, Leibnitz theorem, Taylor's and Maclaurin's series for functions of one variables (without proof).

Unit I1: Functions of several real variables Contact Hours:9 Limits and continuity of functions of two variables, Partial derivatives, Eulerr's theorem for homogenous functions, Total differential, Derivatives of composite and implicit functions, Jacobian, Taylor's and Maclaurin's series for functions of two variables (without proof), Extreme values and saddle points, Lagrange's method of undetermined multipliers.

Contact Hours:6 Unit Il1: Improper Integrals: Review of integration for one variable, Improper integrals of first and second kind, convergence of Improper integrals Unit IV: Multiple Integrals Double integral in Cartesian and Polar coordinates, Change of order of integration, Applications of double integral to find area and volume, Beta and Gamma functions

Cylindrical and spherical polar coordinate system, Triple integral, volume of solid by triple integral, Change of variables in double and triple integrals.

Contact Hours:9

Text Books TI. R. K. Jain and S. R. K. Iyengar, Advanced Engineering Mathematics, Narosa Publishers.

T2. Roland B. Minton , Calculus Mc Graw Robert T. Smith and

Hill Education.

Reference Books/ Other Study material

R1. Michael D. Greenberg, Advanced Engineering Mathematics , Pearson Education, Asia

R2. B. S. Grewal, Higher Engineering Mathematics,Khanna Publishers.

Mode of Evaluation Quiz, Assignmeqt, Seminar and Written Examination

NERS/ OTIAS

o.U DEAN

School of Basic & Applied Sciences Galgotias University

Uttar Pradesh ttar spe

Course Outcomes for MATI13

At the end of the course, the student will be able to:

1. Apply the concept of limit, continuity and differentiability for functions of one variables. (K3)

2. Understand and evaluate the limit, continuity, and differentiability of a function of two variables. Find and apply a partial derivative of a function of two or three variables. Determine the maximal domain for functions of two variables.(K2) 3. Recognize and evaluate improper integrals of Type I and Type II. (K5) 4. Formulate, evaluate and apply iterated double integrals and triple integrals using two and three dimensional coordinates to f+nd area and volume.(K3)

Course Outcomes (COs) assessment table:

Assessment tools

QUIZ, SEMINAR

CO's Internal test University Assignment Examination

35 25

15 25

25 25

4 5 25

Total 50 50 20 100

It is see that efforts are to be taken to achieve the following level of knowledge i.e., K2, K3 through

this course. (K1-Remembering, K2-Understanding, K3-Applying, K4-Analyzing, K5-Evaluating,

K6-Creating)

Course Outcomes (COs) and Program Outcome Mapping

CO/PO Mapping (1/2/3indicates strength of correlation) 3-Substantial, 2-Moderate, 1-Slight

Programme Outcomes(POs) Cos PO1 PO2 | PO3 PO4 POS PO6 PO7 PO8 PO9 POI PO11 PO12

CO1 CO23

CO4 3

DEAN JNIVE School of Basic & Applied Sciences

Galgotlas University

AS UM

Prade Uttár

Uttar Pradesh

LTP MAT122 Matrices and Ordinary Differential Equations 3 0 0 3

Course Code Course Name

Course Content

12 Lectures Unit 1: Matrices and Eigen value Problems Review of basic operations on matrices, Determinants and it's properties, Elementary transformations and Elementary matrices, Inverse of matrix using elementary transformations, Linear dependence and independence of vectors, Normal form, Rank of a matrix, Solution of system of linear equations, Definition, properties and computation of Eigenvalues and Eigenvectors, Cayley-Hamilton theorem,Matrix diagonalization..

10 Lectures Unit I1:Ordinary Differential Equations Exact differential equations, Linear differential equations of second and higher order with constant coefficients, Complementary function and particular integral, Complete solution, Method of variation of parameters, Cauchy-Euler equation, System of linear differential equations with constant coefficients, Applications of linear differential equations..

12 Lectures Unit Ill: Laplace Transform Definition and existence of Laplace transform, Properties of Laplace transforms, Laplace transform of Periodic, Unit step and Dirac Delta functions, Transforms of derivatives and integrals, multiplication and division by t, Evaluation of integrals by Laplace transforms, Convolution theorem, Inverse Laplace transform, Application of Laplace Transform in solving ordinary differential equations.

8 Lectures Unit IV: Fourier series Periodic functions, Dirichlet's condition for a Fourier expansion of functions (period 2t and arbitrary length). Fourier expansion of odd and even functions, Fourier expansion of some standard waveforms, Half range sine and cosine series, Harmonic analysis.

Text Books Ti. R. K. Jain and S. R. K. Iyengar, Advanced Engineering Mathematics. Narosa Publishers. T2. Peter V. 0'Neil, Advanced Engineering Mathematics, Pearson Education, Asia.

Reference Books/ Other Study material

R1. Michael D. Greenberg, Advanced Engineering Mathematics, Pearson Education, Asia. R2. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons Robert T. Smith and Roland B. Minton, Calculus, McGraw Hill education, R3. 4th Edition.

OTIA GALGO DEAN

School of Basic & Applied Sciences

Galgotias University

Uttar Pradesh de sh

Mode of Evaluation

Quiz, Assignment, Seminar and Written Examination

Course Outcomes for MAT122

At the end of the course, the student will be able to:

1. Apply elementary matrix operations to find rank and solve a system of linear

equations and Utilizeit to solve Inverse problem, Eigen value problem and

Diagonalisation problem. (K4) 2. Solve nth order ordinary differential equation with constant and variable

coefficients and apply it to solve Simple electric circuits. (K4)

3. Apply Laplace transform to solve initial value problems. (K3) 4. Produce the Fourier series of a periodic function.(K3)

Course Outcomes (COs) assessment table:

Assessment tools

QUIZ, SEMINAR/ CO's Internal test University Assignment Examination

2

25 35

15 20 25

25 25

5 25 4

Total 50 50 20 100

It is see that efforts are to be taken to achieve the following level of knowledge i.e., K2, K3 through

this course. (K1-Remembering, K2-Understanding, K3-Applying, K4-Analyzing, K5-Evaluating,

K6-Creating)

Course Outcomes (COs) and Program Outcome Mapping

CO/PO Mapping (1/2/3indicates strength of correlation) 3-Substantial, 2-Moderate, 1-Slight

Programme Outcomes(POs)

Cos PO11 PO12PO1 PO2 | PO3 P04 PO5 PO6 PO7 | PO8 PO9 P010

COI 33 co2 3 C03

G0TI4S GALG DEAN

School of Basic & Applied Sciences Galgotias University

Uttar Pradesh esh de