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

Applied Mathematics detailed Syllabus for Chemical Engineering (CH), 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 Chemical Engineering (CH) Syllabus for 2nd Sem I – Scheme MSBTE, do visit Diploma in Chemical Engineering (CH) 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(COs):

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 problem ( s ) 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

1. Suggested Practicals/ ExercisesThe tutorials in this section are sub-components of the COs to be developed and assessed in the student to lead to the attainment of the competency.
2. Solve problems based on finding value of the function at different points.
3. Solve problems to find derivatives of implicit function and parametric function
4. Solve problems to find derivative of logarithmic and exponential functions.
5. Solve problems based on finding equation of tangent and normal
6. Solveproblems based on finding maxima, minima of function and radius of curvature at a given point
7. Solve the problems based on standard formulae of integration.
8. Solve problems based on methods of integration, substitution, partial fractions
9. Solve problems based on integration b\ parts.
10. Solve practice problems based on properties of definite integration.
11. Solve practice problems based on finding area under curve, area between two curves and volume of revolutions
12. Solve the problems based on formation, order and degree of differential equations
13. Develop a model using variable separable method to related engineering problem.
14. Develop a model using the concept of linear differential equation to related engineering problem.
15. Solve problems based on Binomial Distribution related to engineering problems.
16. Solve problems based on Poisson Distribution related to engineering problems
17. Solve problems based on Normal Distribution related to engineering.

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

Major Equipment/ Instruments Required:

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Underpinning Theory Components:

The following topics/subtopics should be taught and assessed in order to develop UOs in cognitive domain for achieving the COs to attain the identified competency.

Unit 1

Differential Calculus

Part -A

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 of given problem

Part -B

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

Unit 2

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Unit 3

Applications of Definite Integration

Part A

1. Solve given simple problems based on properties of definite integration.
2. Apply the concept of definite integration to find the area under the given curve ( s )
3. Utilize the concept of definite integration to find area between given two curves
4. Invoke the concept of definite integration to find the volume of revolution of given surface

Part B

1. Definite Integration:
   1. Simple examples
   2. Properties of definite integral (without proof) and simple examples
2. Applications of integration :
   1. Area under the curve.
   2. Area between two curves.
   3. Volume of revolution

Unit 4

First Order First Degree Differential Equations

Part A

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

Part B

1. Concept of differential equation
2. Order, degree and formation of 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

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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 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 UOs/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 Student Activities:

Other than the classroom and laboratory learning, following are the suggested student-related co-curricular activities which can be undertaken to accelerate the attainment of the various outcomes in this course:

1. Identify engineering problems based on real world problems and solve with the use of free tutorials available on the internet.
2. Use graphical softwares: EXCEL, DPLOT, and GRAPH for related topics.
3. Use Mathcad as Mathematical Tools and solve the problems of Calculus.
4. Identify problems based on applications of differential equations and solve these problems.
5. Prepare models to explain different concepts of applied mathematics.
6. Prepare a seminar on any relevant topic based on applications of integration
7. Prepare a seminar on any relevant topic based on applications of probability distribution to related engineering problems.

Suggested Micro-Projects:

For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.
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Suggested Learning Resources:

1. Higher Engineering Mathematics Grewa], B. S Khanna publications, New Delhi, 2013 ISBN: 8174091955-
2. A Text Book of Engineering Mathematics Dutta, D New Age Publications, New Delhi, 2006, ISBN-978-81-224-1689-3-
3. Advanced Engineering Mathematics Krezig, Ervin Wiley Publications, New Delhi, 2016 ISBN:978-81-265-5423-2,
4. Advanced Engineering Mathematics Das, H.K Chand Publications, New Delhi, 2008, ISBN:9788121903455-
5. Engineering Mathematics, Volume 1 (4 edition. Sastry, S. S PHI Learning, New Delhi, 2009 ISBN-978-81-203-3616-2.
6. Comprehensive Basic Mathematics, Volume 2 Veena, G.R New Age Publications, New Delhi, 2005 ISBN: 978-81-224-1684-8-
7. Getting Started with MATLAB-7 Pratap, Rudra Oxford University Press, New Delhi, 2009, ISBN: 10: 0199731241-
8. Engineering Mathematics (3 ‘edition) Croft, Anthony Pearson Education, New Delhi,2010 ISBN: 978-81-317-2605-1-

Software/Learning Websites:

1. www.scilab.ora/ – SCI Lab
2. www mathworks.com/prodocts/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.easycaleulniion.com
10. www.math-magic.com

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

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