# 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.

- Roll of HOD’s
- Present Faculty Member
- Achievement
- Publication
- CBCS SYLLABUS
- Research
- Highlights
- Programme outcomes
- SYLLABUS
- Photo Gallery
- Contact Department

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 |

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

**S.B.Amalikoppa**

- She is the convenor of Red cross unit
- She is the ranger of Scouts and guider.
- She is the convenor of anti Ragging committee
- She is the convernor of women empowerment cell.
- 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 n^{th} 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

**Department of Mathematics Syllabus** - https://drive.google.com/file/d/1P9fmhx_zpetxYVEeBCoi312NoiaN79Ia/view

**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