# Department of Mathematics

## S V M Arts Science and Commerce College Ilkal

# Department of Mathematics

## The department of Mathematics of our college came in to existence in the year 1964, since 1964 the department has been striving to impart the knowledge of Mathematics at UG level to the aspirants of the entire region. Founder HOD of the Department was Prof. S.K Hudedmani. Many of our students score out of out marks in mathematics and many of our students placed in Banking sectors, MNC companies, Educational Institutions and many got Government Jobs and also running coaching institutes.

# COURSES OFFERED

# OUR FACULTY

# DEPARTMENTAL ACTIVITIES

**B.Sc I Semester â€“ (Algebra-1 and calculus-1)**- Learn to solve system of linear equations.
- Solve the system of homogeneous and non-homogeneous linear of m equation sin n variables by using concept of rank of matrix, finding eigen values and eigen vectors.
- Students will be familiar with the techniques of integration and differentiation of function with real variables.
- Identify and apply the intermediate value theorems and Lâ€™Hospitalrule.
- Learn Free and Open Source Software (FOSS) tools for computer programming Solve problem on algebra and calculus theory studied in MATDSCT 1.1by using FOSS software.

**B.Sc II Semester â€“ (Algebra-2 and calculus-2)**- Recognize the mathematical objects called Groups.
- Link the fundamental concepts of groups and symmetries of geometrical objects.
- Explain the significance of the notions of Cosets, normal subgroups and factor groups
- Understand the concept of differentiation and fundamental theorems in differentiation and various rules.
- Find the extreme values of functions of two variables.
- Learn Free and Open Source Software(FOSS) tools for computer programming.
- Solve problem on algebra and calculus by using FOSS softwareâ€™s.

**B.Sc****III****Semester â€“ Algebra II****, Real analysis and Differential Equations**- Assimilate the notions of limit of a sequence and convergence of a series of real number
- Recognize the mathematical objects called groups.
- Understanding concepts of set theory and theory of equation.
- Learn Free and Open Source Software (FOSS) tools for computer programming Solve problem on algebra and calculus theory studied in MATDSCT 1.1by using FOSS software.

**Â****B.Sc****IV****SemesterÂ-Vector Calculus, Infinite series and****Differential Equations**- Know to finding convergence of the infinite series.
- Finding the velocity and acceleration by vector method.
- Able to solve L.D.E. of nth order.
- Able to solve half range series of Sine and Cosine functions using Fourier series
- Learn Free and Open Source Software (FOSS) tools for computer programming Solve problem on algebra and calculus theory studied in MATDSCT 1.1by using FOSS software.

**B.Sc V SemesterÂ â€“Real Analysis**- Recognize bounded, convergent, divergent, Cauchy and monotonic sequences and to calculate their limit superior, limit inferior, and the limit of a bounded sequence.
- Apply the ratio, root, and alternating series and limit comparison tests for convergence and absolute convergence of an infinite series of real numbers.
- Learn some of the properties of Riemann integral functions, and the applications of the fundamental theorems of integration.

**Â****B.Sc V SemesterÂ-Numerical Analysis**- Solving an Algebraic and Transcendental equations by various methods like Bisection and Iteration.
- By estimation method evaluating for the unknown value of y for the function y=f(x).
- Solution of Linear differential equations with constant coefficients using Difference formula.

**B.Sc V SemesterÂ-Dynamics and Calculus of variation**- Understand necessary conditions for the equilibrium of particles acted upon by various forces and learn the principle of virtual work for a system of coplanar forces acting on a rigid body.
- Understand problems, methods and techniques of calculus of variations.
- Familiarize with subject matter, which has been the single centre, to which were drawn mathematicians, physicists, astronomers, and engineers together.
- Deal with the kinematics and kinetics of the rectilinear and planar motions of a particle including the constrained oscillatory motions of particles.

**B.Sc VI SemesterÂ- Differential Equation**- Solving O.D.E. using Power series solutions.
- Formation of P.D.E. by Eliminating Arbitrary constants.
- Solving the Non-Linear P.D.E. by using Char pitâ€™s Method.
- Know to Solve Simultaneous Differential equations with two and three variables.
- Able to solve Total differential equations and condition of Integrability.

**B.Sc****VI****SemesterÂ****-Complex Analysis**- Able to solve bounded area by using Complex Integration method

- Able to solve taylorâ€™s and Laurentâ€™s series expansion by using Equality formula.
- Know the fundamental concepts in ring theory such as the concepts of ideals, quotient rings, integral domains, and fields.

**Â****B.Sc****VI****SemesterÂ****–**- Know about piecewise continuous functions, Dirac delta function, Laplace transforms and its properties.
- Solve ordinary differential equations using Laplace transforms Ability to differentiate between some more Topological spaces.
- Using topological methods to solve Algebraic Problems.

**B.Sc I Semester â€“ (Algebra-I and calculus-I)**- To solve system of linear equations.
- To solve the system of homogeneous and non-homogeneous linear of m equations in n variables by using concept of rank of matrix, finding eigen values and eigen vectors.
- To Identify and apply the intermediate value theorems and Lâ€™Hospitalrule.
- To solve the Problems on algebra and calculus through FOSS Practical/Lab Work to be performed in Computer lab.

**B.Sc II Semester â€“ (Algebra-II and calculus-II)**- To recognize the mathematical objects called groups.
- To link the fundamental concepts of groups and symmetries of geometrical objects.
- To explain the significance of the notions of cosets, normal subgroups and factor groups
- To understand the concept of differentiation and fundamental theorems in differentiation and various rules.
- To find the extreme values of functions of two variables.
- To learn free and open source software (FOSS) tools for computer programming.
- To solve problem on algebra and calculus by using FOSS softwareâ€™s.

**B.Sc****III****Semester â€“ Algebra II****, Real analysis and Differential Equations****Â**- To assimilate the notions of limit of a sequence and convergence of a series of real

number .

- To recognize the mathematical objects called groups.
- To understanding concepts of set theory and theory of equation.
- To Learn Free and Open Source Software (FOSS) tools for computer programming Solve problem on algebra and calculus theory studied in MATDSCT 1.1by using FOSS software.

**B.Sc****IV****SemesterÂ-Vector Calculus, Infinite series and****Differential Equations**- To finding convergence of the infinite series.
- To finding the velocity and acceleration by vector method.
- To able to solve L.D.E. of nth order.
- To able to solve half range series of sine and cosine functions using Fourier series
- To learn Free and Open Source Software (FOSS) tools for computer programming .
- To solve problem on algebra and calculus theory studied in MATDSCT 1.1by using FOSS software.

**B.Sc V SemesterÂ â€“Real Analysis**- To recognize bounded, convergent, divergent, cauchyâ€™s and monotonic sequences and calculate their limit superior, limit inferior, and the limit of a bounded sequence.
- To apply the ratio, root, and alternating series and limit comparison tests for convergence and absolute convergence of an infinite series of real numbers.
- To learn some of the properties of Riemann integral functions, and the applications of the fundamental theorems of integration.

**Â****B.Sc V SemesterÂ-Numerical Analysis**- To solve an Algebraic and Transcendental equations by various methods like Bisection and Iteration.
- To understand the estimation method, evaluating for the unknown value of y for the function y=f(x).
- To solve linear differential equations with constant coefficients using difference formula.

**B.Sc V Semester-Dynamics and Calculus of variation**- To understand necessary conditions for the equilibrium of particles acted upon by various forces and learn the principle of virtual work for a system of coplanar forces acting on a rigid body.
- To understand problems, methods and techniques of calculus of variations.
- To deal with the kinematics and kinetics of the rectilinear and planar motions of a particle including the constrained oscillatory motions of particles.

**B.Sc VI Semester- Differential Equation**- To solve O.D.E. using Power series solutions.
- To formation of P.D.E. by Eliminating Arbitrary constants.
- To solve the Non-Linear P.D.E. by using Char pitâ€™s Method.
- To solve Simultaneous Differential equations with two and three variables.
- To solve Total differential equations and condition of

**B.Sc****VI****SemesterÂ****-Complex Analysis**- To solve bounded area by using complex Integration method
- To solve taylorâ€™s and laurentâ€™s series expansion by using Equality formula.
- To know the fundamental concepts in ring theory such as the concepts of ideals, quotient rings, integral domains, and fields.

**Â****B.Sc****VI****Â****Semester-Topology and Laplace Trnasform**- To know about piecewise continuous functions, delta function, Laplace transforms and its properties.
- To solve ordinary differential equations using laplace transforms Ability to differentiate between some more Topological spaces.
- To solve Algebraic Problems.

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