# Mathematics

### 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.