Friday 27 September 2024
Wednesday 25 September 2024
IPS AIML AL302 [CO's, CO-PO Mapping, Justification, Unit Outcomes]
Introduction to Probability and Statistics (AIML) AL 302
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 (COs)
|
Course Name: Introduction to Probability and Statistics
– III (AL302) Year of Study: 2024-25 (III Semester) |
|
|
CO1 |
Understand and apply basic concepts of probability, including probability spaces, conditional probability, independence, and the characteristics of discrete random variables. |
|
CO2 |
Analyze and interpret continuous probability distributions, including understanding and application of distribution functions and densities such as normal, exponential, and gamma. |
|
CO3 |
Understand and evaluate bivariate distributions and their properties, including conditional densities and the use of Bayes' rule. |
|
CO4 |
Apply statistical concepts to measure central tendency, analyze distributions, and perform correlation and regression analysis, including rank correlation. |
|
CO5 |
Use statistical methods, such as curve fitting and tests of significance, to solve practical problems involving large sample sizes. |
|
CO6 |
Conduct hypothesis testing and analyze small samples using tests such as the Chi-square test for goodness of fit, independence of attributes, and other statistical methods. |
|
CO/POs |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PO11 |
PO12 |
|
CO1 |
3 |
3 |
2 |
2 |
2 |
1 |
- |
- |
- |
1 |
- |
2 |
|
CO2 |
3 |
3 |
2 |
3 |
2 |
1 |
- |
- |
- |
1 |
- |
2 |
|
CO3 |
2 |
3 |
2 |
3 |
2 |
1 |
- |
- |
- |
1 |
- |
2 |
|
CO4 |
2 |
3 |
3 |
2 |
3 |
1 |
- |
- |
1 |
2 |
- |
2 |
|
CO5 |
2 |
3 |
2 |
3 |
3 |
2 |
- |
- |
2 |
2 |
- |
2 |
|
CO6 |
2 |
3 |
2 |
3 |
3 |
2 |
- |
2 |
1 |
2 |
1 |
3 |
|
Average |
2.33 |
3 |
2.17 |
2.67 |
2.5 |
1.33 |
- |
2 |
0.67 |
1.5 |
1 |
2.17 |
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. |