Understand the basic concepts of arithmetic ability, quantitative ability, logical reasoning, business computations and data interpretation and obtain the associated skills.

Acquire competency in the use of verbal reasoning.

Apply the skills and competencies acquired in the related areas

Solve problems pertaining to quantitative ability, logical reasoning and verbal ability inside and outside the campus.

Course Outcomes

After successful completion of the course, the student will be able to

1. Solve exact differential equations, linear equations, Bernoulli’s equations, and equations reducible to exact form using integrating factors.
2. Analyze and solve first-order differential equations that are solvable for p,,and y, including Clairaut’s equations.
3. Solve homogeneous and non-homogeneous linear differential equations of higher order with constant coefficients using operator methods.
4. Compute particular integrals for non-homogeneous equations when the right-hand side is a polynomial, exponential, or trigonometric function.
5. Solve non-homogeneous differential equations using the method of variation of parameters and other applicable techniques.

Course Outcomes

Upon successful completion of this course, students will be able to:

1. Apply convergence tests such as P-test, Cauchy’s root test, D’Alembert’s ratiotest, and Leibnitz test to analyze series.
2. Understand and evaluate limits of real-valued functions, including one-sided and infinite limits, and solve problems involving indeterminate forms.
3. Demonstrate knowledge of continuity, identify types of discontinuities, and apply theorems like Heine’s, Borel’s, and Bolzano’s in analysis.
4. Understand and analyze differentiability, distinguish it from continuity, and apply Rolle’s, Lagrange’s, and Cauchy’s Mean Value Theorems.
5. Evaluate Riemann integrals, verify conditions for integrability, and apply the Fundamental Theorem of Calculus in integration problems.

Upon successful completion of this course, students will be able to: 

1. Compute the determinant of a matrix using expansion and apply various properties for simplification.

 2. Perform elementary row and column operations to simplify determinants and matrix expressions. 

3. Determine the rank of a matrix using echelon and normal forms, and compute matrix inverses via transformations. 

4. Analyze systems of linear equations (homogeneous and non-homogeneous) for consistency, and solve them using methods such as matrix inversion, Cramer’s Rule, Gauss elimination, and LU decomposition.

 5. Define and compute eigenvalues and eigenvectors of square matrices, and use characteristic equations in applications.

Course Outcomes

After successful completion of this course, students will be able to

1.Understand and compute vector derivatives, including gradient, divergence, and curl, and apply vector identities in problem-solving.

2.Evaluate double integrals over various regions and use polar coordinates when appropriate.

3.Compute triple integrals in Cartesian and polar coordinates, and apply them to find volumes of solids.

4.Evaluate line, surface, and volume integrals using the appropriate vector calculus methods and geometric interpretations.

5.Apply Gauss’s, Green’s, and Stokes’s theorem store late different types of integrals and solve physical and geometrical problems

Course Outcomes:

After successful completion of this course, students will be able to 

1. Understand the structure of convex sets, convex combinations, and apply the fundamental theorem of linear programming to real-world problem formulation. 

2. Solve LPPs graphically and represent LP problems in standard, canonical, and matrix forms. 

3. Apply the simplex method to solve linear programming problems and interpret unbounded or multiple solutions. 

4. Use artificial variable techniques such as the Big M-method and the two-phase method to handle constraints with equality and greater-than conditions. 

5. Identify and resolve issues in LPP such as degeneracy, alternative and unbounded solutions, and apply the simplex method to solve systems of simultaneous equations.

Course Outcomes

After successful completion of this course, the student will be able to

1. Find derivatives using various difference formulae
2. Understand the process of Numerical Integration
3. Solve Simultaneous Linear systems of Equations
4. Understand Iterative methods
5. Find Numerical Solution of Ordinary Differential Equations

Course Outcomes

After completing this course, students will be able to

1. Derive and interpret equations of planes and lines in various forms.
2. Compute angles, distances, and intersection conditions between geometric elements (lines, planes, spheres).
3. Determine co-planarity of lines and solve problems involving shortest distances in 3D space.
4. Analyze sphere-related problems, including tangents, intersections, and circle equations in 3D.
5. Apply advanced concepts like polar planes, conjugate points, and orthogonality conditions of spheres.

Apply critical thinking skills to solve complex problems involving complex numbers, trigonometric ratios, vectors, and statistical measures.

To explain the basic principles and concepts underlying a broad range of fundamental areas of physics and to connect their knowledge of physics to everyday situations

To explain the basic principles and concepts underlying a broad range of fundamental areas of chemistry and to connect their knowledge of chemistry to daily life.

Understand the interplay and connections between mathematics, physics, and chemistry in various applications. Recognize how mathematical models and physical and chemical principles can be used to explain and predict phenomena in different contexts.

. To explore the history and evolution of the Internet and to gain an understanding of network security concepts, including threats, vulnerabilities, and countermeasures.

After successful completion of the course, students will be able to

1. Understand the fundamental theorem of arithmetic
2. Understand Mobius function, Euler quotient function, The Man goldt function, Liouville’s  function,        The      divisor functions and the generalized convolutions.
3. Understand Euler’s summation formula, application to the distribution of lattice points and the applications to μ (n) and Λ (n)
4. Understand the concepts of congruencies, residue classes and complete residues systems.
5. Comprehend the concept t of quadratic residues mod p and quadratic non-residues mod p.

Course Outcomes

After successful completion of this course, students will be able to

1. Understand and compute vector derivatives, including gradient, divergence, and curl, and apply vector identities in problem-solving.
2. Evaluate double integrals over various regions and use polar coordinates when appropriate.
3. Compute triple integrals in Cartesian and polar coordinates, and apply them to find volumes of solids.
4. Evaluate line, surface, and volume integrals using the appropriate vector calculus methods and geometric interpretations.
5. Apply Gauss’s, Green’s, and Stokes’s theorem store late different types of integrals and solve physical and geometrical problems

Course Outcomes

After successful completion of this course, the student will be able to

1. Understand the definition and basic properties of groups, including finite and infinite groups, and construct composition tables.
2. Analyze subgroups and cosets, apply Lagrange’s Theorem, and understand the structure of a group through its subgroups.
3. Identify and verify normal subgroups, and understand their role in forming quotient groups.
4. Understand and apply homomorphisms and isomorphisms, including the fundamental homomorphism theorem and its applications.
5. Work with permutations, transpositions, and cyclic groups,and understand their properties and significance in group theory, including Cayley’s Theorem.

Course Outcomes

After successful completion of this course, the student will be able to

1. Understand and apply the definitions and properties of vector spaces, subspaces,linear combinations, and linear span.
2. Determine the basis and dimension of vector spaces and subspaces, and apply related theorems including those on quotient spaces.
3. Define linear transformations and operators, compute rank and nullity, and apply the Rank-Nullity Theorem.
4. Use the Cayley-Hamilton Theorem to verify matrix equations and to compute matrix inverses and higher powers.
5. Understand inner product spaces, verify orthogonality, and apply key inequalities such as Schwarz’s and Triangle inequalities.

Explore the applications of mathematics in various fields of physics and chemistry, to understand how mathematical concepts are used to model and solve real-world problems.

To explain the basic principles and concepts underlying a broad range of fundamental areas of physics and to connect their knowledge of physics to everyday situations.

Understand the different sources of renewable energy and their generation processes and advances in nonmaterial’s and their properties, with a focus on quantum dots. To study the emerging field of quantum communication and its potential applications. To gain an understanding of the principles of biophysics in studying biological systems. Explore the properties and applications of shape memory materials.

Understand the principles and techniques used in computer-aided drug design and drug delivery systems, to understand the fabrication techniques and working principles of nanosensors. Explore the effects of chemical pollutants on ecosystems and human health

Understand the interplay and connections between mathematics, physics, and chemistry in various advanced applications. Recognize how mathematical models and physical and chemical principles can be used to explain and predict phenomena in different contexts 

Understand and convert between different number systems, such as binary, octal, decimal,   and hexadecimal. Differentiate between analog and digital signals and understand their characteristics. Gain knowledge of different types of transmission media, such as wired (e.g., copper cables, fiber optics) and wireless (e.g., radio waves, microwave, satellite)..

Course Outcomes

After successful completion of this course, the student will be able to

1. Understand and apply the definitions and properties of vector spaces, subspaces,linear combinations, and linear span.
2. Determine the basis and dimension of vector spaces and subspaces, and apply related theorems including those on quotient spaces.
3. Define linear transformations and operators, compute rank and nullity, and apply the Rank-Nullity Theorem.
4. Use the Cayley-Hamilton Theorem to verify matrix equations and to compute matrix inverses and higher powers.
5. Understand inner product spaces, verify orthogonality, and apply key inequalities such as Schwarz’s and Triangle inequalities.

Course Outcomes:

After successful completion of this course, the student will be able to

1. Understand the real number system, its axioms, and properties, including completeness, supremum, and infimum.
2. Apply the Archimedean property, denseness, and concepts of neighborhoods, limit points, and derived sets in problem-solving.
3. Analyze sequences for boundedness and convergence using definitions and the Cauchy criterion.
4. Understand the concept of subsequences, apply the Bolzano-Weierstrass theorem, and test convergence using Cauchy’s general principle.
5. Determine the convergence of infinite series using various tests and solve related analytical problems.

Course Outcomes

Upon successful completion of this course, students will be able to:

1. Understand and differentiate between rings, integral domains, and fields, and describe their algebraic properties.
2. Identify and construct subrings and various types of ideals, and determine when a ring qualifies as a field.
3. Analyze quotientrings, build composition tables for finite rings, and distinguishbetween prime and maximal ideals.
4. Applyring homomorphisms and isomorphisms effectively, and interpret the fundamental homomorphism theorems.
5. Solve problems involving polynomial rings over fields, including division algorithms, factorization, and irreducibility criteria.