Mathematics-I [CO's, CO-PO Mapping, Justification, Unit Outcomes]

 Mathematics-I

Program Outcomes [PO's]

Course Outcomes [CO's]

CO-PO Mapping

Mapping Justification

Unit Outcomes

Programme Outcomes (POs)

 

Engineering Graduates will be able to:

1. Engineering knowledge: Apply the knowledge of mathematics, science, engineering fundamentals, and an engineering specialization to the solution of complex engineering problems.

2. Problem analysis: Identify, formulate, reviewer search literature, and analyze complex engineering problems reaching substantiated conclusions using first principles of mathematics, natural sciences, and engineering sciences.

3.  Design/development of solutions: Design solutions for complex engineering problems and design system components   or processes that meet the specified needs with appropriate consideration for the public health and safety, and the cultural, societal, and environmental considerations.

4.   Conduct investigations of complex problems: Use research-based knowledge and research methods including design of experiments, analysis and interpretation of data, and synthesis of the information to provide valid conclusions.

5.    Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern engineering and IT tools including prediction and modeling to complex Engineering   activities with an understanding of the limitations.

6.    The engineer and society: Apply reasoning informed by the contextual knowledge to assess societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the professional engineering practice.

7.  Environment and sustainability: Understand the impact of the professional engineering solutions in societal and environmental contexts, and demonstrate the knowledge of, and need for sustainable development.

8.   Ethics: Apply ethical principles and commit to professional ethics and responsibilities and norms of the engineering practices.

9.    Individual and teamwork: Function effectively as an individual, and as a member or leader in diverse teams, and in multidisciplinary settings.

10. Communication: Communicate effectively on complex engineering activities with the engineering community and with society at large, such as, being able to comprehend and write effective reports and design documentation, make effective presentations, and give and receive clear instructions.

11. Project management and finance: Demonstrate knowledge and understanding of the engineering and management principles and apply these to one’s own work, as a member and leader in a team, to manage projects and in multidisciplinary environments.

12.   Life-long learning: Recognize the need for, and have the preparation and ability to engage in independent and life-long learning in the broadest context of technological change.

Course Outcomes (CO’s)

CO1	Apply fundamental theorems of calculus in solving Engineering. problems
CO2	Evaluate definite integrals, apply Beta and Gamma functions, and utilize multiple integrals to calculate areas and volumes in various applications.
CO3	Analyze the convergence of sequences and series and apply Fourier series to represent functions.
CO4	Understand and apply concepts of vector spaces, subspaces, linear independence, and basis in the context of linear transformations.
CO5	Solve systems of linear equations, determine the rank of matrices, compute eigenvalues and eigenvectors, and apply the Cayley-Hamilton theorem in matrix theory.

CO vs. PO Mapping

	PO1	PO2	PO3	PO4	PO5	PO6	PO7	PO8	PO9	PO10	PO11	PO12
CO1	3	3	3	2	2	1	2	1	-	-	-	-
CO2	3	3	3	3	2	1	2	1	-	-	-	-
CO3	3	3	2	2	1	1	1	1	-	-	-	-
CO4	3	3	3	3	3	-	2	1	-	-	-	-
CO5	3	3	3	3	2	-	2	1	-	-	-	-
Average	3	3	2.8	2.6	2	1	1.8	1	-	-	-	-

JUSTIFICATION OF CO’S and PO’S Correlation

CO-PO	Correlation level	Justification
CO1-PO1	3	Fundamental theorems of calculus are crucial for the mathematical foundation in engineering disciplines.
CO1-PO2	3	Calculus is vital for solving engineering problems involving rates of change and motion, strongly aligning with PO2
CO1 -PO3	3	The ability to apply calculus in engineering scenarios supports the creation of models and simulations, which are crucial in design and development.
CO1 -PO4	2	Calculus enables the investigation and exploration of engineering phenomena through differentiation and integration, supporting research and experimental analysis.
CO1-PO5	2	Understanding calculus supports the use of modern engineering tools, particularly those that require mathematical input or calculations.
CO1-PO6	1	Although less directly aligned, fundamental knowledge of calculus can indirectly support understanding the societal impacts of engineering solutions.
CO1-PO7	2	Calculus helps in modeling environmental systems and understanding the sustainability of solutions, although the alignment is moderate.
CO1-PO8	1	Ethical considerations in engineering might involve problem-solving scenarios where calculus is applied, although this is a minimal alignment.
CO1-PO9	-	No link in CO1-PO9 is required.
CO1-PO10	-	No link in CO1-PO10 is required.
CO1-PO11	-	No link in CO1-PO11 is required.
CO1-PO12	-	No link in CO1-PO12 is required.
CO2-PO1	3	Mastery of integral calculus and special functions like Beta and Gamma is fundamental to advanced engineering mathematics, aligning strongly with PO1.
CO2-PO2	3	Integral calculus is critical in analyzing continuous systems and phenomena, contributing significantly to PO2.
CO2-PO3	3	The application of integral calculus in series and function analysis is vital in developing mathematical models for engineering problems.
CO2-PO4	3	Integral calculus, especially in evaluating complex integrals and series, is used in investigating engineering problems and research.
CO2-PO5	2	Integral calculus is essential for understanding and utilizing computational tools that involve mathematical computations, which supports PO5.
CO2-PO6	1	Integral calculus can be used to address societal challenges, particularly in areas like economics and environmental modeling.
CO2-PO7	2	Integral calculus plays a role in modeling environmental systems and assessing sustainability, justifying its alignment with PO7.
CO2-PO8	1	Similar to CO1, the ethical application of mathematical solutions may have a minimal but relevant connection.
CO2-PO9	-	No link in CO1-PO9 is required.
CO2-PO10	-	No link in CO1-PO10 is required.
CO2-PO11	-	No link in CO1-PO11 is required.
CO2-PO12	-	No link in CO1-PO12 is required.
CO3-PO1	3	Convergence and Fourier series are fundamental concepts in many branches of engineering, making a strong case for PO1 alignment.
CO3-PO2	3	The ability to determine the convergence of series and apply Fourier series is essential in the analysis of signals, vibrations, and other engineering systems.
CO3-PO3	2	Fourier series are crucial in developing solutions related to signal processing, heat transfer, and other fields, aligning with PO3.
CO3-PO4	2	Understanding convergence and applying Fourier series is key in investigations involving periodic functions and waveforms, supporting PO4.
CO3-PO5	1	The knowledge of series and Fourier transforms is important in using tools for signal processing and system analysis, hence aligned with PO5.
CO3-PO6	1	While this connection is less direct, understanding the behavior of sequences and series could contribute to broader societal applications.
CO3-PO7	1	Fourier analysis can be used in environmental modeling and signal analysis in sustainable systems, providing some alignment.
CO3-PO8	1	Although Fourier series and convergence may not directly relate to ethics, their correct application is crucial in the integrity of engineering solutions.
CO3-PO9	-	No link in CO1-PO9 is required.
CO3-PO10	-	No link in CO1-PO10 is required.
CO3-PO11	-	No link in CO1-PO11 is required.
CO3-PO12	-	No link in CO1-PO12 is required.
CO4-PO1	3	Vector spaces and multivariable functions are core components of engineering mathematics, aligning strongly with foundational engineering knowledge (PO1).
CO4-PO2	3	Analyzing vector spaces and multivariable functions is critical in solving complex engineering problems, justifying the strong alignment with PO2.
CO4 -PO3	3	These concepts are essential in designing systems involving multiple variables, such as in control systems, mechanics, and electronics.
CO4 -PO4	3	Understanding vector spaces aids in exploring multi-dimensional problems, essential for research and advanced investigations in engineering (PO4).
CO4-PO5	3	Knowledge of vector spaces is crucial in many engineering tools that perform vector operations, supporting PO5.
CO4-PO6	-	No link in CO1-PO6 is required
CO4-PO7	2	The application of multivariable calculus and vector analysis in environmental systems justifies alignment with PO7.
CO4-PO8	2	The connection here is minimal, but correct application and interpretation of vector spaces can have ethical implications in certain engineering contexts.
CO4-PO9	-	No link in CO1-PO9 is required.
CO4-PO10	-	No link in CO1-PO10 is required.
CO4-PO11	-	No link in CO1-PO11 is required.
CO4-PO12	-	No link in CO1-PO12 is required.
CO5-PO1	3	Matrices are fundamental in engineering for representing and solving linear systems, justifying a strong alignment with PO1.
CO5-PO2	3	The ability to apply matrices in problem-solving is crucial for analyzing and interpreting engineering data, aligning well with PO2.
CO5-PO3	3	Matrix operations are essential in designing algorithms and systems, particularly in control theory, signal processing, and structural analysis (PO3).
CO5-PO4	3	Matrices are used extensively in modeling and simulation, supporting investigations into engineering systems (PO4).
CO5-PO5	2	Many engineering tools rely on matrix operations, particularly in computational simulations and analysis, aligning well with PO5.
CO5-PO6	-
CO5-PO7	1	Matrices can be applied in modeling environmental systems, contributing to sustainable design practices, supporting PO7.
CO5-PO8	1	The ethical use of matrices in engineering calculations is important, though the connection is minimal.
CO5-PO9	-	No link in CO1-PO9 is required.
CO5-PO10	-	No link in CO1-PO10 is required.
CO5-PO11	-	No link in CO1-PO11 is required.
CO5-PO12	-	No link in CO1-PO12 is required.

Unit-1 Outcomes (UO’s)

UO1	Students will be able to understand the geometric and algebraic significance of Rolle’s theorem and the Mean Value Theorem and apply these concepts to solve related problems.
UO2	Students will learn to expand functions in terms of series using Maclaurin’s and Taylor’s theorems for one variable and apply Taylor’s theorem for functions of two variables.
UO3	Students will be able to differentiate functions of several variables using partial differentiation.
UO4	Students will learn methods to find the maxima and minima of functions of two and three variables, including the use of Lagrange’s multipliers.

Unit-2 Outcomes (UO’s)

UO1	Students will understand the concept of definite integrals as limits of sums and apply this understanding to evaluate series.
UO2	Students will learn the properties of Beta and Gamma functions and apply them to solve related problems.
UO3	Students will apply definite integrals to compute surface areas and volumes of solids of revolution.
UO4	Students will be proficient in performing multiple integrations, changing the order of integration, and applying these techniques to calculate areas and volumes.

Unit-3 Outcomes (UO’s)

UO1	Students will understand the criteria for the convergence of sequences and series and apply various tests for convergence.
UO2	Students will develop skills in working with power series and Taylor series for exponential, trigonometric, and logarithmic functions.
UO3	Students will learn to expand functions as Fourier series, including half-range sine and cosine series, and understand and apply Parseval’s theorem.

Unit-4 Outcomes (UO’s)

UO1	Students will gain a deep understanding of vector spaces, including the concepts of vector subspaces, linear combinations, and basis.
UO2	Students will learn to identify linearly dependent and independent sets of vectors.
UO3	Students will learn to apply linear transformations and understand their properties and significance in vector spaces.

Unit-5 Outcomes (UO’s)

UO1	Students will learn to calculate the rank of a matrix and apply it to determine the solvability of linear systems.
UO2	Students will be proficient in solving simultaneous linear equations using elementary transformations.
UO3	Students will gain an understanding of eigenvalues, eigenvectors, and the process of diagonalizing matrices.
UO4	Students will be able to apply the Cayley-Hamilton theorem to find minimal polynomials and solve matrix-related problems.