### B.Sc. Mathematics

Course Outcome

##### B.Sc. Part-I, Semester-I

###### Paper-I: Differential calculus

- On completion of the course, students are able to:
- Study of Rate of change of vectors is vector calculus.
- It is widely used in Physics and Mechanics.
- To study various operations on vectors.
- To learn about differentiation and integration of vectors.
- To understand the concepts of gradient, divergence and curl

###### Paper II: Calculus

- On completion of the course, students are able to:
- It is used in almost all branches of engineering.
- It is a science that deals with rate of change.
- Understanding the concept of differentiation.
- Understanding the concept of Integration.
- It is used in almost all branches of engineering.
- It deals with calculus of several variables.
- To understand the importance of Taylors series.
- To understand Mean value theorem.

##### Semester-II

###### Paper III: Differential Equations

- On completion of the course, students are able to:
- To understand the necessity of differential equations
- To learn about forming differential equations from physical situations
- To know various types of differential equations
- To practice methods of solution for various types of differential equations.
- It is useful for methods of momentum and energy transfer.
- It is used in all branches of engineering.

###### Paper-IV: Higher order ordinary differential equation and partial order differential equation

- On completion of the course, students are able to:
- It is used in almost all branches of engineering.
- Understanding the concept of differentiation.
- Understanding the concept of Integration.
- It is used in almost all branches of engineering.

##### B.Sc. Part-II, Semester- III

###### Paper-V: Differential calculus

- On completion of the course, students are able to:
- Study of Rate of change of vectors is vector calculus.
- It is widely used in Physics and Mechanics.
- To study various operations on vectors.
- To learn about differentiation and integration of vectors.
- To understand the concepts of gradient, divergence and curl.

###### Paper-VI: Differential Equations

- On completion of the course, students are able to:
- It is used in all branches of engineering.
- It is useful for methods of momentum and energy transfer.
- To study existence and uniqueness about solutions.
- To learn about the simultaneous differential equations.
- To understand the methods of solution for total differential equations

##### B.Sc. Part-II, Semester-IV

###### Paper VII: Integral calculus

- On completion of the course, students are able to:
- To find area by double integration.
- To find volume by triple integration.
- It is useful for measuring areas and volumes.
- It is used in all branches of engineering.
- To study differentiability and integrability.
- To learn mean value theorem of integral calculus.
- To learn how to solve improper integrals.
- To understand the importance of Legendre polynomials.
- To know the Fourier series.
- To study half range series.

###### Paper VIII: Discrete Mathematics

- On completion of the course, students are able to:
- Understand the basics of graph theory.
- To learn operations on graphs.
- To learn about connected graphs.
- To understand various problems related with planar graphs
- It is used in Genomics, networks, etc.
- To know about number system
- To learn division algorithm and its application
- To know about congruence classes

##### B.Sc. Part-III: Semester-V

###### Paper-IX: Real Analysis

- On completion of the course, students are able to:
- It is a branch of pure mathematics.
- It is useful and Statistics, Probability, Operations Research, etc.
- To study sequences.
- To study series of real functions.

###### Paper – X: Modern Algebra

- On completion of the course, students are able to:
- Algebra is science of operations.
- It is widely used in Computer science and Information Technology.
- To understand the concept of groups.
- To learn homomorphism and isomorphism
- To under the structure of ring and integral domain.
- To learn normal subgroups.
- To study permutations.
- To know about quotient and polynomial rings.

###### Paper – XI: Partial Differential Equations

- On completion of the course, students are able to:
- To understand the importance of ordinary and partial differential equations.
- It is used in solving many problems of engineering and physics.
- To learn about exact differential equations and various types.
- To learn about second order linear differential equations.
- To study series method of solution.
- To study about linear partial differential equations.

###### Paper XII: Numerical Methods-I

- On completion of the course, students are able to:
- It is used for solving a system of equations
- It has application in all branches of engineering.
- To know how to find the roots of transcendental equation.
- To learn how to interpolate the given set of values
- To understand the curve fitting for various polynomials
- To learn numerical solution of differential equations.

##### Semester VI

###### Paper – XIII: Metric Spaces

- On completion of the course, students are able to:
- A metric space is a set for which distances between all members of the set are defined
- It is used in fixed point theorem and mapping principles.
- To study continuous functions on metric spaces.
- To learn connected metric spaces.
- To understand complete metric spaces.
- To study compact metric spaces.

###### Paper – XIV: Linear Algebra

- On completion of the course, students are able to:
- It is a branch of Algebra.
- It is used in Computer Science, Electrical engineering, etc.
- To learn about vector spaces.
- To understand theorems on basis and dimension.
- To know about eigenvalues and eigenvector.

###### Paper – XV: Complex Analysis

- On completion of the course, students are able to:
- It is widely used in Fluid Mechanics and Electrical engineering.
- To learn properties of complex numbers.
- To understand the use of complex numbers in the field of Calculus.
- To learn the importance of analytic functions.
- To gain knowledge of singularities and residues.
- To apply the knowledge of residues in complex integration.

###### Paper – XVI: Numerical Methods-II

- On completion of the course, students are able to Understand
- It is a branch of numerical analysis
- It is used for solving a system of equations and used in all branches of engineering.
- To solve a system of linear equations.
- To learn numerical differentiation and integration.
- To learn about interpolation polynomials.
- To apply numerical methods for differential equations.