PROGRAM SPECIFIC OUTCOMES

COURSE OUTCOMES

SEMESTER-I

Differential and Integral Calculus

• Understanding the derivative as a tool for analyzing the behavior of a function and its slopes.
• Applying differentiation techniques to a variety of functions, including polynomials, exponential, logarithmic, and trigonometric functions.
• Understanding the concept of integrals and how they can be used to find the area under a curve.
• Applying integration techniques to evaluate definite and indefinite integrals, including using substitution, integration by parts, and partial fraction decomposition.
• Understanding the connection between differentiation and integration, and how the two concepts can be used together to solve problems in physics, engineering, and other fields.
• Developing the ability to model real-world situations using mathematical concepts and techniques, and to interpret and communicate the results of mathematical models.

SEMESTER-II

Differential Equations

• Understanding of fundamental concepts and principles of differential equations: Students will gain a comprehensive understanding of the basic concepts, principles, and theories that form the foundation of differential equations.
• Ability to solve ordinary and partial differential equations: Students will develop the skills and techniques to solve various types of differential equations, including ordinary and partial differential equations.
• Knowledge of analytical methods for differential equations: Students will become familiar with analytical methods, such as separation of variables, Laplace transforms, and Fourier series, to solve differential equations.
• Familiarity with applications of differential equations: Students will learn how to apply differential equations to real-world problems, such as modeling physical and biological systems, solving engineering problems, and predicting financial markets.
• Understanding of the behavior of differential equations: Students will become familiar with the qualitative behavior of differential equations, such as stability, asymptotic behavior, and bifurcation.

SEMESTER-III

Real Analysis

• Understanding the basic concepts of real numbers and their properties
• Knowledge of different types of convergence, such as pointwise, uniform, and absolute convergence
• Ability to prove theorems and propositions using mathematical logic and techniques from Real Analysis
• Familiarity with various types of functions, such as continuous, differentiable, and integrable functions
• Understanding of the fundamental theorem of calculus
• Ability to analyze real-valued functions and their properties, including differentiability and integrability.

SEMESTER-IV

Algebra

• Understanding of Group theory: students will have a clear understanding of the theory of groups, including group operations, subgroups, cosets, normal subgroups, factor groups, homomorphisms, and isomorphisms.
• Knowledge of Ring theory: students will learn about rings, ideals, factor rings, ring homomorphisms, and ring isomorphisms.
• Familiarity with Field theory: students will learn about fields, extensions of fields, polynomial rings, and finite fields.
• Familiarity with Algebraic structures: students will learn about algebraic structures such as semi-groups, monoids, and lattices.
• Problem-solving skills: students will develop critical thinking and problem-solving skills by applying the concepts learned in the course to solve mathematical problems.

SEMESTER-V

Linear Algebra

• Understanding of linear systems of equations: Students will be able to solve and analyze systems of linear equations, including eigenvalue and eigenvector computations.
• Matrix algebra: Students will be able to perform matrix operations, including multiplication, inversion, and diagonalization.
• Vector spaces: Students will be able to understand the concept of vector spaces and perform operations within them, including linear combinations and subspaces.
• Orthogonality and Gram-Schmidt process: Students will understand the concepts of orthogonal and orthonormal sets and be able to perform the Gram-Schmidt process.
• Linear transformations: Students will understand linear transformations and be able to perform computations, including computing matrices, eigenvectors, and eigenvalues.
• Inner products and norms: Students will be able to understand and use inner products and norms, and understand the properties of norms and the Cauchy-Schwarz inequality.

SEMESTER-VI

Solid Geometry

• Understanding of the basic principles and concepts of analytical solid geometry.
• Ability to apply mathematical concepts to solve geometric problems.
• Ability to visualize and manipulate 3-dimensional objects and their projections.
• Knowledge of the properties of lines, planes, and intersections of geometric objects.
• Ability to use the Cartesian coordinate system to describe the positions of objects in space.
• Understanding of the applications of solid geometry in engineering, physics, and other scientific fields.
• Improved problem-solving skills and critical thinking abilities.