Course Outcomes and Objectives

“ज्ञान ,विज्ञान आणि सुसंस्कार यांसाठी शिक्षण प्रसार”

                                                                        - शिक्षणमहर्षी डॉ.बापूजीसाळुंखे

Shri Swami Vivekanand Shikshan Sanstha, Kolhapur

Lal Bahadur Shastri College Of Arts, Science And Commerce,Satara

Department of Mathematics

Semester - I

Paper – I | 71603/ DSC-5A | Differential Calculus 1. To understand the DeMovier's theorem and employ the theorem 2. Understand the higher derivative and Leibnitz's theorem 3. To find the Maxima and Minima of Function of two variable. 4. to Understand the Langrange's undetermined multipliers method. Paper – II | 71603/ DSC-6A | Calculus 1. To find the intermediate values using MVT. 2. to expand the function in the form of infinite power of x. 3. To find the limit of function. 4. to understand the concept of continuity of function. Semester - II Paper – III | 72842/ DSC-5B | Differential Equation

1. To understand the types of first order differential equation and it's solution 2. To understand the partial differential equaion and its solution. 3. To understand the linear differential equation of higher order and its solution. Paper – IV | 72842/ DSC-6B | Higher order Ordinary differential equation and partial differential equation 1. to understand the methods of solving second order differential equation. 2. To study the different forms of Partial differential equation. 3. To study the Langrange's method to solve partial differential equation. Semester - III Paper – V | 73300/ DSC-5C | Real Analysis –I (1) understand types of functions and how to identify them. (2) use mathematical induction to prove various properties. (3) understand the basic ideas of Real Analysis. (4) prove order properties of real numbers, completeness property and the Archimedean property Paper – VI | 73300/ DSC-6C | Algebra – I

1. understand properties of matrices 2. solve System of linear homogeneous equations and linear non-homogeneous equations. 3. find Eigen values and Eigen vectors. 4. construct permutation group and relate it to other groups. 5. classify the various types of groups and subgroups. Semester - IV Paper – VII | 78907/ DSC-5D | Real Analysis –II 1. understand sequence and subsequence. 2. prove The Bolzano-Weierstrass Theorem. 3. derive Cauchy Convergence Criterion. 4. find convergence of series. 5. apply Leibnitz Test. Paper – VIII | 78907/ DSC-6D | Algebra – II 1. prove Lagrange’s theorem. 2. derive Fermat’s theorem. 3. understand properties of normal subgroups, factor group. 4. define homomorphism and isomorphism's in group and rings. 5. derive basic properties of rings and subrings. Semester - V Paper – IX | 79672/DSE-9E | Mathematical Analysis 1. The integration of bounded function on a closed and bounded interval 2. Some of the families and properties of Riemann integrable functions 3. The applications of the fundamental theorems of integration 4. Extension of Riemann integral to the improper integrals when either the interval of integration is infinite or the integrand has infinite limits at a finite number of points on the interval of integration 5. The expansion of functions in Fourier series and half range Fourier series Paper – X | 79673/DSE-10E | Abstract Algebra

1. Basic concepts of group and rings with examples 2. Identify whether the given set with the compositions form Ring, Integral domain or field. 3. Understand the difference between the concepts Group and Ring. 4. Apply fundamental theorem, Isomorphism theorems of groups to prove these theorems for Ring. 5. Understand the concepts of polynomial rings, unique factorization domain. Paper – XI | 79674/DSE-11E | Optimization Techniques

1. provide student basic knowledge of a range of operation research models and techniques, which can be applied to a variety of industrial and real life applications. 2. Formulate and apply suitable methods to solve problems. 3. Identify and select procedures for various sequencing, assignment, transportation problems. 4. Identify and select suitable methods for various games . 5. To apply linear programming and find algebraic solution to games. Paper – XII | 79675/DSE-12E | Integral Transform 1. understand concept of Laplace Transform. 2. apply properties of Laplace Transform to solve differential equations. 3. understand relation between Laplace and Fourier Transform. 4. understand infinite and finite Fourier Transform. 5. apply Fourier transform to solve real life problems. Semester - VI Paper – XIII | 81662/DSE-9F | Metric Spaces 1. acquire the knowledge of notion of metric space, open sets and closed sets. 2. demonstrate the properties of continuous functions on metric spaces, 3. apply the notion of metric space to continuous functions on metric spaces. 4.understand the basic concepts of connectedness, completeness and compactness of metric spaces, 5. appreciate a process of abstraction of limits and continuity to metric spaces, Paper – XIV | 81663/DSE-10F | Linear Algebra

1. understand notion of vector space, subspace, basis. 2.understand concept of linear transformation and its application to real life situation. 3. work out algebra of linear transformations. 4. appreciate connection between linear transformation and matrices. 5. work out eigen values, eigen vectors and its connection with real life situation. Paper – XV | 81664/DSE-11F | Complex Analysis

1. learn basic concepts of functions of complex variable. 2. be introduced to concept of analytic functions. 3. learn concept of complex integration and basic results thereof. 4. be introduced to concept of sequence and series of complex variable. 5. learn to apply concept of residues to evaluate certain real integrals Paper – XVI | 81665/DSE-12F | Discrete Mathematics 1. use classical notions of logic: implications, equivalence, negation, proof by contradiction, proof by induction, and quantifiers. 2. apply notions in logic in other branches of Mathematics. 3. know elementary algorithms : searching algorithms, sorting, greedy algorithms, and their complexity. 4. apply concepts of graph and trees to tackle real situations. 5. appreciate applications of shortest path algorithms in computer science.