Basic Mathematics detailed Syllabus for Textile Technology (TC), K – 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 MSBTE 1st Sem Syllabus K – Scheme Textile Technology, do visit MSBTE 1st Sem Syllabus K – Scheme Textile Technology Subjects. The detailed Syllabus for basic mathematics is as follows.
Rationale
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Course Outcomes:
Students will be able to achieve & demonstrate the following COs on completion of course based learning
- Apply the concepts of algebra to solve engineering (discipline) related problems.
- Utilize trigonometry to solve branch specific engineering problems.
- Solve area specific engineering problems under given conditions of straight lines.
- Apply differential calculus to solve discipline specific problems.
- Use techniques and methods of statistics to crack discipline specific problems.
Unit I
Algebra 1.1 Logarithm: Concept and laws of logarithm. 1.2 Matrices: Matrices, algebra of matrices, transpose, value of determinant of matrix of order 3×3, adjoint and inverse of matrices. 1.3 Matrices: Solution of simultaneous equations by matrix inversion method. 1.4 Partial Fractions: Types of partial fraction based on nature of factors and related Problems. 1.5 Algebra in Indian Knowledge System: Solution of simultaneous equations (Indian Mathematics)..
Suggested Learning Pedagogy
Improved Lecture Tutorial Assignment Demonstration Simulation
Unit II
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Unit III
Straight Line 3.1 Straight line and slope of straight line: Angle between two lines, Condition of parallel and perpendicular lines. 3.2 Various forms of straight lines: Slope point form, two-point form, Double intercept form, General form. 3.3 Perpendicular distance from a point on the line. 3.4 Perpendicular distance between two parallel lines. 3.5 Geometry in Sulabasutras in Indian Knowledge System (construction of square, circling the square). (Indian Mathematics). Improved Lecture Tutorial Assignment Demonstration Simulation
Unit IV
Differential Calculus 4.1 Functions and Limits: Concept of function and simple examples. 4.2 Functions and Limits: Concept of limits without examples. 4.3 Derivatives: Rules of derivatives such as sum, Product, Quotient of functions. 4.4 Derivatives: Derivative of composite functions (chain Rule), implicit and parametric functions. 4.5 Derivatives: Derivatives of inverse, logarithmic and exponential functions. 4.6 Applications of derivative: Second order derivative without examples, Equation of tangent and normal, Maxima and minima, Radius of curvature. 4.7 Calculus in Indian Knowledge System: The Discovery of Calculus by Indian Astronomers.(Indian Mathematics).
Suggested Learning Pedagogy
Improved Lecture Tutorial Assignment Demonstration Simulation
Unit V
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Practical / Tutorial Experiences
- Solve simple problems of Logarithms based on given applications.
- Solve elementary problems on Algebra of matrices for branch specific engineering related applications.
- Solve solution of Simultaneous Equation using inversion method.
- Apply Matrix Inversion method to determine currents through various branches of given electrical networks.
- Determine inverse of a non-singular matrix by using open source software.
- Resolve into partial fraction using linear nonrepeated, repeated, and irreducible quadratic factors.
- Solve problems on Compound, Allied, multiple and sub multiple angles for related shapes.
- Practice problems on factorization and de factorization.
- Solve problems on inverse trigonometric ratios based on applications.
- Practice problems on equation of straight lines using different forms.
- Solve problems on perpendicular distance, distance between two parallel lines and angle between two lines.
- Use given form of straight line to calculate the speed, distance and time of moving object.
- Solve problems to find derivatives of implicit function and parametric function.
- Solve problems to find derivative of logarithmic and exponential functions for engineering applications.
- Solve problems based on finding equation of tangent and normal for engineering applications.
- Solve problems based on finding maxima, minima of function and radius of curvature at a given point for engineering applications.
- Use the concept of tangent and normal to solve the given problem of Engineering Drawing.
- Use the concept of Maxima and Minima to obtain optimum value for given engineering problem.
- Use the concept of radius of curvature to solve given branch specific engineering problem.
- Use the concept of derivative to find the slope of a bending curve for given engineering problem.
- Solve problems on finding range, coefficient of range and mean deviation for given applications.
- Solve problems on standard deviation, coefficient of variation and comparison of two sets.
- Calculate the Standard Deviation for Concrete with the given data for given engineering applications.
Micro Project / Self Learning
Micro project
- Create a function that takes a matrix as input and returns its inverse matrix if it exists. Also Implement a program that finds the inverse of a square matrix.
- Collect the Data of Marks obtained by your class in mid sem test. Compute the variance and coefficient of variance of the data and interpret the result using the free open source software ORANGE.
- Prepare models using matrices to solve simple problems based on cryptography.
- Collect Model on quality control analysis, energy efficiency assessment, environmental monitoring, and process optimization, for these models, analyze data and calculate variance and standard deviation, make a presentation including short videos.
- Prepare the model using the concept of tangent and normal bending of roads in case of sliding of a vehicle, express geometrically the same through any open source software.
- Prepare the model using the concept of radius of curvature to bending of railway tracks, express geometrically the same through any open source software.
- A window in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window to admit maximum light through the whole opening, prepare a model using concept of Maxima and Minima for the above problem and verify the result.
- Visualize trigonometric waveforms and create animations utilizing sine or cosine functions and make a presentation.
- Develop a program of trigonometric function calculator that computes sine, cosine, and tangent values.
- Collect applications of the radius of curvature on lens design and optics, mirror and reflective surface properties, road and highway design, structural behavior, roller coaster track design, and composite material manufacturing and make a video of 5-minutes duration.
- Prepare models using trigonometry based on at least 10 engineering problems.
- Apply trigonometric principles to calculate angles, distances, forces, and dimensions relevant to the chosen area and make a poster presentation.
- Prepare charts using determinant to find area of regular shapes.
- Design a puzzle based on matrices. Create a grid of numbers and operations.
- Develop a math game based on operations of matrices.
- Use matrices as a tool for music composition. Assign different musical elements (e.g., notes, chords, rhythms) to matrix elements, and experiment with combining and transforming the matrices to create unique musical compositions. You can use musical notation open software or even traditional instruments to bring your compositions to life.
- Attempt any 10-12 Micro Projects, out of the given list.
Assignment
- Collect examples based on real world applications of logarithm and prepare a pdf file.
- Solve the simultaneous system of equation in two variables by Matrix Inversion Method. Write down a Mathematical programming using any open source software to verify the result.
- Collect an examples on coding theory using applications of matrices and prepare a pdf file.
- Represent the Graph of Trigonometric function, Logarithmic function on Geogebra and interpret the nature of graph and Make a pdf file.
- Measure height of trees in surrounding locations using trigonometry and prepare presentation.
- Find the derivative of y= x^sinx and visualize the graph of the function and its derivative using any open source software geometrically.
- Find height of room or distance between two pillars by using concept of straight line.
- Collect at least 10 examples based on real world applications of standard deviation/variance.
- Collect at least 10 examples based on real world uses of applications of derivative.
- Attempt any 5-7 Assignment, out of the given list.
Laboratory Equipment / Software Required
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..
Learning Materials / Books
- Grewal B. S. Higher Engineering Mathematics Khanna publication New Delhi , 2013 ISBN: 8174091955
- Dutta. D A text book of Engineering Mathematics New age publication New Delhi, 2006 ISBN: 978-81-224-1689-3
- Kreysizg, Ervin Advance Engineering Mathematics Wiley publication New Delhi 2016 ISBN: 978-81-265-5423-2
- Das H.K. Advance Engineering Mathematics S Chand publication New Delhi 2008 ISBN: 9788121903455
- Marvin L. Bittinger David J. Ellenbogen Scott A. Surgent Calculus and Its Applications Addison-Wesley 10th Edition ISBN-13: 978-0-321-69433-1
- C. S. Seshadri Studies in the History of Indian Mathematics Hindustan Book Agency, New Delhi 110016. ISBN 978-93-80250-06-9
- George Gheverghese Joseph Indian Mathematics Engaging with the World from Ancient to Modern Times World Scientific Publishing Europe Ltd. 57 ISBN 978-17-86340-61-0
- Deepak Singh Mathematics-I Khanna Book Publishing Co. (P) Ltd. ISBN: 978-93-91505-42-4
- Garima Singh Mathematics-II Khanna Book Publishing Co. (P) Ltd. ISBN: 978-93-91505-52-3
- Gareth James, Daniela Witten, Trevor Hastie Robert and Tibshirani An Introduction to Statistical Learning with Applications in R Springer New York Heidelberg Dordrecht London ISBN 978-1-4614-7137-0 ISBN 978-1-4614-7138-7 (eBook)
- Gunakar Muley Sansar Ke Mahan Ganitagya First Edition, Rajkamal Prakashan, ISBN-10. 8126703571, ISBN-13. 9788126703579.
- T.S. Bhanumurthy A Modern introduction to Ancient Indian Mathematics New Age International Private Limited, 1 January 2008 ISBN- 10. 812242600X, ISBN- 13. 978-8122426007
- M.P. Trivedi and P.Y. Trivedi Consider Dimension and Replace Pi Notion Press; 1st edition (2018), ISBN-978-1644291795
Learning Websites & Portals
- http://nptel.ac.in/courses/106102064/1 Online Learning Initiatives by IITs and IISc
- www.scilab.org/ -SCI Lab Signal processing, statistical analysis, image enhancement.
- www.mathworks.com/product/matlab/ -MATLAB Applications of concepts of Mathematics to coding.
- Spreadsheet Applications Use of Microsoft Excel, Apple Numbers, Google Sheets.
- https://ocw.mit.edu/ MIT Course ware
- https://www.khanacademy.org/math? gclid=CNqHuabCys4CFdOJaddHo Pig Concept of Mathematics through video lectures and notes
- http://ocw.abu.edu.ng/courses/mathematics/ List of Mathematical Courses.
- https://libguides.furman.edu/oer/subject/mathematics Open Education Resources (OER) in Mathematics.
- https://phet.colorado.edu/en/simulations/filter?subjects=mat h&type=html,prototype Phet Simulation for Mathematics.
- https://libguides.cmich.edu/OER/mathematics Mathematics with OER.
For detail Syllabus of all other subjects of Textile Technology, K – scheme do visit Textile Technology 1st Sem Syllabus for K – scheme.
For all Textile Technology results, visit MSBTE Textile Technology all semester results direct links.