Mathematics

Department of Mathematics Welcomes You

The department was started with the college in June 1967. Shri V.R. Kulli was appointed as full time lecturer in Mathematics was one of the optional subject for PUC Arts/Science & BA/B.Sc one more lecturer namely Shri B.N. Patil was appointed in August 1968. When Mathematics was made major subject for BA II/B.sc II and element of Mathematics and Statistics as a minor subject for BA II.

Presently the department is working with one full time faculty member and one full time on temporary basis with 29 Theory +8 practical=37  teaching hours per week. In the academic year 2020-21 the dept has a total strength 52+73+51=175 (B.sc I, II, III)

Vision of the department:

Mathematics is bound to gain greater significance with the advancement of Science and technology. L T revolution with further necessiate in strengthening the layman. In the college emphasis is bound to be one those aspect of mathematics, which have greater utilitarian Value. The dept would like to explore the new fields of application and impart education according to the changing needs of our times.

Mission:

It is our mission to engage in the teaching and learning of mathematics that will challenge students to be independent learners and develop sound reasoning, problem- solving, & critical thinking skill necessary to compete in a global society.

OBJECTIVES OF THE DEPARTMENT

Mathematics is supposed to be the mother of all Science. The objective of the department and teachers concerned is to create on atmosphere with students to evolve themselves in understanding stupendously expanded knowledge in mathematics, which should help in future, career.

                The department aims at imparting knowledge of mathematics, so that it will be useful in the examination and a pleasant experience in the classroom. Application of mathematics is a necessity in every walk of life. Teaching the importance of mathematics as a useful tool of calculation in science subjects to the students is also an aim of the faculty members. Conduct seminars  as selective chapters by helping them with proper existence to prepare the subject in detail.

Sl No

Name

Designation

Period

From                      To

1

Shri. V.R. Kulli

Lecturer

1967                  1968

2

Shri. B.N. Patil

Lecturer

1968                  1969

3

Shri. S.S. Chikkagoudar

SGL

1969                  2001

4

Shri. S.K. Bhadrannavar

SGL

2001                  2004

5

Shri L.N. Kulkarni

Asst.  Prof

2004-

Sl No

Name

Designation

Qualification

Date of Joining

1

Shri. L.N. Kulkarni

Asst Prof

M.Sc.  M.Phil.  B.Ed

Ph.D on going

03-09-1994

22-06-2008(Tem)

2

Smt S.B. Amalikoppa

Lecturer(Ad hoc)

M.Sc  B.Ed. Ph.D

17-07-2003

Kumari Mahadevi Jalihal scored 100 marks out of 100 in Mathematics subjects I,II,III,IV & V Sem continuously.

Shri. L.N. Kulkarni published a paper on the topic ‘Inverse Equitable Domination in Graphs’ at Journal of emerging Technologies & Innovative Research (JETIR) ISBN No: 23495162

Shri. L.N. Kulkarni presented a paper on the topic’ Edge equitable connected domination of subdivision of graphs’ at 2nd international online conference on Emerging Trends in Multi-Disciplinary Research ETMDR-2021. Poornima University, Jaipur.

Smt S.B. Amalikoppa completed Ph.D Degree. The title of the thesis is ‘LIE – 2 ALGEBRA’2010.

Shri. L.N. Kulkarni is doing Ph.D on ‘ Recent Results in Various Domination of Different Classes of Graphs’ at Sharnabasva University Kalaburgi Karnataka

*Plan of action of the department  for the next five years. The department has the plan to take up minor research projects.

  1. 1 He is the IQAC Co-cordinator and Member of RUSA
  2. 2 He is the Secretary of Alumni
  3. 3 He was an associate NSS programme officer from 2013-14 to 2015-16
  4. 4. He is the convener of KRVP.
  5. 5. Member of RUCTA 
  6. 6. Member of RCU Mathematics Teachers  Association


S.B.Amalikoppa

  1. She is the convenor of Red cross unit
  2. She is the ranger of Scouts and guider.
  3. She is the convenor of anti Ragging committee
  4. She is the convernor of women empowerment cell.
  5. She was the Chairman of college Magazine (2020-2021)

B.sc I sem

Algebra I & calculus I

1 Gives the idea of finding inverse of a matrix by elementary transformation

2 To understand the greatest lower bound & least upper bond

3 To understand the Idea of the indeterminate forms by using L.Hospital rule

4 Finding the nth derivative of product of two functions by Leibnitz rule

5 Differetiating expansion of Taylors  & Maclaurins theorem

B.sc II sem

 Calculus II & 3 dimensional geometry

Co 1 Finding the angle  between radius vector and  the angle of interaction of two curves

Co 2 Learns the various forms like Cartesian polar, pedal & parametric

Co 3 Concept of limit, continuous of the functions and verification of homogeneous functions by using Eulers theorem

Co 4 To understand the integration of sinx, cosx, tanx  etc.

Co 5 Gives the idea of Sphere, Cone, Cylinder and its equation.

 

B.sc III Sem 

Algebra II Real analysis & differential equations

Co 1: Find the maximum and minimum values

Co 2: To learn the kinds of the sequences and their properties                                                  

C0 3: Verify the given series is convergent or divergent by using different task

Co 4: Test the Abelian group & various  properties  of groups

Co 5: Learns the various  equation like Bernoulli, exact   differential equations clairauts form.

Types of sets  & polynomial equation of nth degree in one variable. Solve the cubic and biquadratic eqations.

B.Sc IV Sem

 Vector calculus, infinite series, differential  equations 

Co  1  Finding the derivatives of dot product,  cross product, and   triple product of vectors and application of dot and cross product of two vectors

Co 2  Verify the given series is convergent or divergent by using different tests.

Co 3 Learns various tests on series

Co 4 Identify the particular integrals of forms

Co 5 To understand the homogeneous linear differential equation

Co 6 Find Fourier series for given function with period 2π and 2l

Co 7 Find finite sine and cosine  series of expansion for given functions

B.Sc V Sem

 5.1 Real analysis

Co 1 To understand the concept Cauchy-Riemann integration. The properties of integrable functions

Co 2 To understand the first and second mean value theorems of integral calculus.

Co 3 Learns the kinds of Improper integrals

Co 4 Explain the properties of Beta functions and relation between Beta and Gamma functions

Co 5 Explain the idea of finding area and volume by double and triple integration

5.2  A  Numerical Analysis 

Co 1 Explain the various method of Algebric and transcedental equations

Co 2 Define basic concept of operative Delta, Del, Shift operate and find intermediate Values  by using Newton’s Gregory forward and backward formulae and Lagranges interpolation formula

Co 3 Compute the first and second order derivatives. Learns the Tropezoibal rule, sinpson’s rules

Co 4 Explain the first order deferential equations by using Taylors, Eulers, Picards Methods.

Co 5 Basic definitions of difference equations

5.2 B (Elective II)

Dynamics and Calculus of Variation 

Co 1 Gives the idea of finding the component of radial, transverse, tangential & normal velocities and accelaration of a particle

Co 2 Discuss  the motion of a particle under a law of force for polar and pedal forms

Co 3 Gains knowledge regarding projectile of a motion

Co 4 Gives the idea of functional and kinds of functionals

Co 5 Finding the smallest distance between  two files for given curve i.s Geodesic. Concept. Isoperimetric problem.

5.3 Number Theory

Co 1 Learns the numbers like prime and composite. Concept of division algorithm and explain the fundamental theorem of arithmetic

Co 2 Explain the theorem on number theory

B.Sc VI Sem

6.1 Complex Analysis and Ring Theory

Co 1 Study about concept of analytic function and Cauchy Riemann equation

Co 2 Explain the various theorems on complex integration

Co 3 Expand complex functions  by using Taylors and Laurents  series. Nature of the singularities

Co 4 Learns about the calculus  of residues and contour integration

Co 5 Gains knowledge in RingTheory

6.2 A( ElectiveIII) 

 Differantial equations

Co 1 Discuss the conditions of integrability and its solution

Co 2 Basic definitions and power series solutions of ODE’s

Co 3 Concept of Legendres polynomial, recurrence formula

Co 4 Solve the Lagranges  linear partial differential equation and standard forms of non linear differential equation

Co 5 Charpits  method and solving different types of differential equation by charpits  method

6.2 B (Elective IV)

Topology and Laplace  Transform

Co 1 Basic definitions of topological space and standard theorems.

Co 2 Definition of Base and Subbase and properties of separation axions    

Co 3 Definitions and results on Laplace Transform  properties

Co 4 Use inverse Laplace transform to solve differential equation.

Co 5 Apply Laplace Transform  to solve first and second order linear  differential equation and simultaneous linear differential equations.

6.3 Graph theory 

Co 1 Basic concepts of graphs

Co 2 Definitions sub graph, walk, trail and bipartite graph and their properties.

For all sems Practicals

Use the Scilab  lab/ Maxima open-source software to execute the practical problems.

Maxima:  is an open source computer Algebra system for solving typical calculus  problems.

 

Program Out comes

        Po 1 The Mathematics students after the completion of UG course will gain through a knowledge in                  preparing competitive  examination conducted by UPSC/KPSC

        Po 2  It is   very helpful to study for higher education

Program specific outcomes 

Pso 1 To understand the concept of algebra which include equations, numbers and algebraic structures

Pso 2 Students are able to understand and view mathematical structures

Pso 3 To understand mathematical ideas from basic axioms

L.N. Kulkarni

H.O.D  Department of Mathematics
       V.M.K.S.R Vastrad Arts, Science and V.S Bellihal Commerce College, Hungund
       E-mail Id: l.n.hungund@gmail .com
       Mobile No: +919448862921

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