Practical Course: CCPM –I

CO 1: Apply Leibnitz’s theorem, Euler’s theorem and De Moivre’s Theorem to solve problems.

CO 2: Analyse Maxima and Minima of functions of two variables and trace curves in polar form.

CO 3: Solve problems related to radius of curvature. curve, parametric and polar curve.

CO 4: Apply Lagrange’s Mean Value theorem, Cauchy’s Mean Value theorem and Hospital Rule.

Program Name – B.Sc. II

Course Name/ paper

Course Outcome

By the end of each of the following course, the students will be able to:

Paper V Analysis- I

CO 1: Analyze functions and its properties.

CO 2: Apply mathematical induction to derive specific formulae related to integers. CO 3: Understand the basic ideas countibility of sets.

CO 4: Analyse order properties of real numbers, completeness property and the

Archimedean property.

Paper VI Algebra- I

CO 1: Understand properties of matrices.

CO 2: Solve System of linear homogeneous equations and linear non-homogeneous equations.

CO 3: Extract eigen values and eigen vectors.

CO 4: Verify different binary structures and their properties.

Paper VII – Real Analysis II

CO 1: Understand the concepts and different structures, properties of sequence and subsequence of real numbers .

CO 2: Make use of different properties to check the convergence of sequence. CO 3: Analyze series of real numbers with properties.

CO 4: Make use of different type test to study convergence of series.

Paper VIII Algebra - II

CO 1: Make use of Lagrange’s theorem to study subgroup. CO 2: Make use of Fermat’s theorem to find remainder.

CO 3: Explore properties of normal subgroups, factor group.

CO 4: Form homomorphism and isomorphisms.

Practical Course II CCPM - II

CO 1: Solve problems on Eigen values, Eigen vectors and Cayley Hamilton theorem. CO 2: Analyse functions and apply Mathematical Induction.

CO 3: Discover convergence of series using Comparison test Cauchy’s root test, D’ Alembert’s ratio test and Rabbi’s test.

CO 4: Understand group, cyclic subgroup, permutation group and homomorphism and Kernel.

Practical Course III CCPM - III

CO 1: Understand basic concepts in scilab programming and use Scilab as a calculator.

CO 2: Use looping structures in Scilab programming.

CO 3: Solve linear equations by Gauss Elimination, Gauss Jordan methods.

CO 4: Solve linear differential equations by Euler, Euler modified, Runge Kutta 2nd and 4th order methods.

Program Name – B.Sc. III

Course Name/ paper

Course Outcome

By the end of each of the following course, the students will be able to:

Paper IX – Mathematical Analysis

CO 1: Understand and learn about Riemann integration. CO 2: Find Riemann integral of special types of functions. CO 3: Solve improper integrals of different types.

CO 4: Find Fourier series expansion of given functions over given interval.

Paper X– Algebra

CO 1: Understand concepts of group and rings.

CO 2: Analyze the different structures of Groups and Rings.

CO 3: Understand the different fundamental theorems and its applications.

CO 4: Understand the concepts of polynomial rings, unique factorization domain.

Paper XI – Optimization Techniques

CO 1: Understand range of operation research models and techniques, which can be applied to a variety of industrial and real-life applications.

CO 2: Formulate and apply suitable methods to solve problems.

CO 3: Identify and select procedures for various sequencing, assignment, transportation problems.

CO 4: Identify and select suitable methods for various games.

Paper XII – Integral Transforms

CO 1: Understand the concept of Laplace Transform.

CO 2: Apply properties of Laplace Transform to solve differential equations. CO 3: Understand the relation between Laplace and Fourier Transform.

CO 4: Apply infinite and finite Fourier Transform to solve real life problems.

Paper XIII – Metric Spaces

CO 1: Form different types of metric space.

CO 2: Understand the basic concepts of Open sets, Closed sets and connectedness, completeness and compactness of metric spaces.

CO3: Define homeomorphism to study properties of metric spaces. CO 4: Apply knowledge to study Banach and Hilberts spaces.

Paper XIV – Linear Algebra

CO 1: Form different vector spaces and subspaces. CO 2: Form different norm linear space.

CO 3: Analyse the concept of linear transformation and connection between linear transformation and matrices.

CO 4: Apply concepts of eigenvalues, eigen vectors and its connection with real life situations.

Paper XV – Complex Analysis

CO 1: Understand basic concepts and theorems related to functions of complex variable, its differentiability and integrability.

CO 2: Form an analytic functions.

CO 3: Evaluate complex integration and differentiations.

CO 4: Evaluate real integrals using Cauchy residue theorems.

Paper XVI – Discrete Mathematics

CO 1: Understand classical notations of logic: implications, equivalence, negation, proof by contradiction, proof by induction, and quantifiers.

CO 2: Apply notions in logic in other branches of Mathematics.

CO 3: Analyze elementary algorithms: searching algorithms, sorting, greedy algorithms, and their complexity.

CO 4: apply concepts of graphs and trees to tackle real situations.

Practical Course IV

CCPM – IV

CO 1: Use Graphical method for linear programming problems. CO 2: Solve Transportation Problems.

CO 3: Solve Assignment Problems. CO 4: Solve game strategies problems.