22206: Applied Mathematics Syllabus for Mechanical Engineering 2nd Sem I – Scheme MSBTE

Applied Mathematics detailed Syllabus for Mechanical Engineering (ME), I – scheme has been taken from the MSBTE official website and presented for the diploma students. For Subject Code, Subject Name, Lectures, Tutorial, Practical/Drawing, Credits, Theory (Max & Min) Marks, Practical (Max & Min) Marks, Total Marks, and other information, do visit full semester subjects post given below.

For all other Diploma in Mechanical Engineering (ME) Syllabus for 2nd Sem I – Scheme MSBTE, do visit Diploma in Mechanical Engineering (ME) Syllabus for 2nd Sem I – Scheme MSBTE Subjects. The detailed Syllabus for applied mathematics is as follows.

Rationale:

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Competency

The aim of this course is to help the student to attain the following industry identified competency through various teaching learning experiences:

• Solve mechanical engineering related problems using the principles of applied mathematics

Course Outcomes

The theory, practical experiences and relevant soft skills associated with this course are to be taught and implemented, so that the student demonstrates the following industry oriented COs associated with the above mentioned competency:

1. Calculate the equation of tangent, maxima, minima, radius of curvature by differentiation
2. Solve the given problems of integration using suitable methods
3. Apply the concept of integration to find area and volume.
4. Solve the differential equation of first order and first degree using suitable methods
5. Utilize basic concepts of probability distribution to solve elementary engineering problems

Course Map

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Suggested Practicals/ Exercises

The tutorials in this section are LOs ( i . e sub- components of the COs) to be developed and assessed in the student to lead to the attainment of the competency.

1. Solve problems based on finding value of the function al different points
2. Solve problems to find derivatives of implicit function anc parametric function
3. Solve problems to find derivative of logarithmic anc exponential functions
4. Solve problems based on finding equation of tangent anc normal.
5. Solveproblems based on finding maxima, minima of function and radius of curvature at a given point
6. Solve the problems based on standard formulae of integration.
7. Solve problems based on methods of integration, substitution, partial fractions.
8. Solve problems based on integration by parts
9. Solve practice problems based on properties of definite integration
10. Solve practice problems based on finding area under curve, area between two curves and volume of revolutions
11. Solve the problems based on formation, order and degree of differential equations.
12. Develop a model using variable separable method to related engineering problem
13. Develop a model using the concept of linear differential equation to related engineering problem
14. Solve problems based on Binomial Distribution related to engineering problems
15. Solve problems based on Poisson Distribution related to engineering problems.
16. Solve problems based on Normal Distribution related to engineering

Note: The ubove tutorial sessions are for guideline only. The remaining tutorial hours are for revision and practice.

Major Equipment/ Instruments Required:

– Not applicable –

Underpinning Theory Components

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Unit 1

Differential Calculus

Part A

Unit Outcomes (UOs)

1. Solve the given simple problems based on functions
2. Solve the given simple problems based on rules of differentiation
3. Obtain the derivatives of logarithmic, exponential functions
4. Apply the concept of differentiation to find given equation of tangent and normal
5. Apply the concept of differentiation to calculate maxima and minima and radius of curvature for given problem.

Part B

Topics And Sub-Topics

1. Functions and Limits
   1. Concept of function and simple examples
   2. Concept oflimits without examples
2. Derivatives :
   1. Rules of derivatives such as sum, product, quotient of functions.
   2. Derivative of composite functions (chain Rule), impLcit and parametric functions
   3. Derivatives of inverse, logarithmic and exponential functions.
3. Applications of derivative :
   1. Second order derivative without examples
   2. Equation of tangent and normal
   3. Maxima and minima
   4. Radius of curvature

Unit 2

Integral Calculus

Part A

Unit Outcomes (UOs)

1. Solve the given simple problems ( s ) based on rules of integration
2. Obtain the given simple integrals ( s ) using substitution method.
3. Integrate given simple functions using the integration by parts
4. Evaluate the given simple integral by partial fractions

Part B

Topics And Sub-Topics

1. Simple Integration: Rules of integration and integration of standard functions.
2. Methods of Integration:
   1. Integration by substitution
   2. Integration by parts
   3. Integration by partial fractions

Unit 3

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Unit 4

First Order First Degree Differential Equations

Part A

Unit Outcomes (UOs)

1. Find the order and degree of given differential equations
2. Form simple differential equations for given simple engineering problems ( s )
3. Solve given differential equations using the method of variable separable
4. Solve the given simple problems based on linear differential equations.

Part B

Topics And Sub-Topics

1. Concept of differential equation
2. Order, degree and formation ot differential equation
3. Solution of differential equation
   1. Variable separable form
   2. Linear differential equation
4. Application of differential equations and related engineering problems

Unit V

Probability Distributen

Part A

Unit Outcomes (UOs)

1. Make use of probability distribution to identify discrete and continuous probability distribution
2. Solve given problems based on repeated trials using Binomial distribution.
3. Solve given problems when number of trials are large and probability is very small
4. Utilize the concept of normal distribution to solve related engineering problems

Part B

Topics And Sub-Topics

1. Probability distribution
   1. Discrete Probability distribution
   2. Continuous Probability distribution.
2. Binomial distribution.
3. Poissons distribution.
4. Normal distribution

Note: To attain the COs and competency, above listed Learning Outcomes (LOs) need to he undertaken to achieve the ‘Application Level’ of Bloom’s ‘Cognitive Domain Taxonomy

Suggested Student Activities:

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Suggested Special Instructional Strategies (If Any)

These are sample strategies, which the teacher can use to accelerate the attainment of the various learning outcomes in this course:

1. Massive open online courses (MOOCs) may be used to teach various topics/sub topics.
2. L in item No. 4 does not mean only the traditional lecture method, but different types of teaching methods and media that are to be employed to develop the outcomes.
3. About 15-20% of the topics/sub-topics which is relatively simpler or descriptive in nature is to be given to the students for self-directed learning and assess the development of the LOs/COs through classroom presentations (see implementation guideline for details)
4. With respect to item No.10, teachers need to ensure to create opportunities and provisions for co-curricular activities
5. Guide student( s ) in undertaking micro-projects.

Suggested Micro-Projects:

Only one micro-project is planned to be undertaken by a student assigned to him/her in the beginning of the semester. S/he ought to submit it by the end of the semester to develop the industry oriented COs. Each micro-project should encompass two or more COs which are in fact, an integration of practicals, cognitive domain and affective domain LOs The microproject could be industry application based, internet-based, workshop-based, laboratory-based or field-based. Each student will have to maintain dated work diary consisting of individual contribution in the project work and give a seminar presentation of it before submission. The total duration of the micro-project should not be less than 16 (sixteen) student engagement hours during the course.

In the first four semesters, the micro-project could be group-based However, in higher semesters, it should be individually undertaken to build up the skill and confidence in every student to become problem solver so that s/he contributes to the projects of the industry. A suggestive list is given here. Similar micro-projects could be added by the concerned faculty:

1. Prepare models using the concept of tangent and normal to bending of roads in case of sliding of a vehicle
2. Prepare models using the concept of radius of curvature to bending of railway track.
3. Prepare charts displaying the area of irregular shapes using the concept of integration
4. Prepare charts displaying volume of irregular shapes using concept of integration
5. Prepare models using the concept of differential equations for mixing problem
6. Prepare models using the concept of differential equations for radio carbon decay
7. Prepare models using the concept of differential equations for population growth
8. Prepare models using the concept of differential equations for thermal cooling
9. Prepare a chart of binomial distribution by collection of suitable manufacturing industry base data
10. Prepare a chart of normal distribution by collection of suitable manufacturing industry base data
11. Prepare a chart of Poisson distribution by collection of suitable manufacturing industry base data

Suggested Learning Resources

For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
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Software/Learning Websites

1. www.scilab.ore/ – SCI Lab
2. www.mathworks.com/products/matlab/ – MATLAB
3. Spreadsheet applications
4. www.dplot.com/ – DPlot
5. www.allmathcad.com/ – MathCAD
6. www.wolfram.com/mathematica/ – Mathematica
7. http://fossee.in/
8. https://www.khanacademy.org/math?gclid=CNqHuabCys4CFdOJaAoddHoPig
9. www.easycalculation.com
10. www.math-magic.com.

For detail Syllabus of all other subjects of Mechanical Engineering, I – scheme do visit Mechanical Engineering 2nd Sem Syllabus for I – scheme.

For all Mechanical Engineering results, visit MSBTE Mechanical Engineering all semester results direct links.