22201: Applied Mathematics Syllabus for Construction Technology 2nd Sem I – Scheme MSBTE

Applied Mathematics detailed Syllabus for Construction Technology (CS), 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 Construction Technology (CS) Syllabus for 2nd Sem I – Scheme MSBTE, do visit Diploma in Construction Technology (CS) Syllabus for 2nd Sem I – Scheme MSBTE Subjects. The detailed Syllabus for applied mathematics is as follows.

Rationale:

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Rationale:

This course is an extension of Basic Mathematics of first semester namely Applied Mathematics which is designed for its applications in engineering and technology using the techniques of calculus, differentiation, integration, differential equations and in particular numerical integration. Derivatives are useful to find slope of the curve, maxima and minima of the function, radius of curvature Integral calculus helps in finding the area Differential equation is used in finding the curve and its related applications for various engineering models Numerical integration is used to find the area of the functions especially whose integration cannot be evaluated easily with routine methods. This course further develops the skills and understanding of mathematical concepts which underpin the investigative tools used in engineering

Competency

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

• Solve civil engineering related broad-based problems using the principles of applied mathematics

Course Outcomes

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Course Map

(with sample COs, Learning Outcomes i . e LOs and topics)

This course map illustrates an overview of the flow and linkages of the topics at various levels of outcomes (details in subsequent sections) to be attained by the student by the end of the course, in all domains of learning in terms of the industry/einployer identified competency depicted at the centre of this map.

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. IV I
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 Trapezoidal rule
15. Solve problems based on Simpson’s 1/3 u rule and Simpsons 3/8th rule.
16. Make use of concept of numerical integration to solve related civil engineering problems.

Note: The ubove 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 LOs in cognitive domain for achieving the COs to attain the identified competency

Unit 1

Differentia 1 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 function.

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

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Unit 3

Applications of Definite Integration

Part A

Unit Outcomes (UOs)

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 curves ( 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

Topics And Sub-Topics

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 Differentia 1 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 b Linear differential equation
4. Application of differential equations and related engineering problems

Unit V

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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 Malhcad 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 numerical integration to related engineering problems

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 students ( s ) in undertaking micro-projects.

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 Grewal, B S. Khanna publications, New Delhi, 2013 ISBN-8174091955
2. A Text Book of Engineering Mathematics Dutta, D. New Age International 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 S. Chand Publications, New Delhi, 2008, ISBN: 9788121903455
5. Engineering Mathematics, Volume 1 (4 edition. Sastry, 8.S PHI learning, New Delhi, 2014 ISBN-978-81-203-3616-2,
6. Comprehensive Basic Mathematics, Volume 2 Veena, G R. New Age International 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: 0199731241
8. Engineering Mathematics ,_rd … (? edition. Croft, Anthony Pearson Education, New Delhi,2010 ISBN: 978-81-317-2605-1

Software/Learning Websites

1. www.scilab.org/ – SCI Lab
2. www.mathworks.com/products/matlab/ – MATLAB
3. Spreadsheet applications
4. www.dplot.com/ – DPlot
5. www.allmathcad.com/ – MathCAD
6. www.woltTam.com/mathematica/ – Mathematica
7. http://fossee in/
8. www.easycalculation.com
9. www.math-magic.com

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

For all Construction Technology results, visit MSBTE Construction Technology all semester results direct links.