Applied Mathematics (DI02000011)

GUJARAT TECHNOLOGICAL UNIVERSITY

Field	Details
Program Name	Diploma in Engineering
Level	Diploma
Course Code	DI02000011
Course Name	Applied Mathematics
Branches	Automobile, Bio-Medical, Chemical, Civil, Computer, Electronics & Communication, Environmental, Information Technology, Mechanical, Mechatronics, Mining, Textile Processing, Textile Manufacturing, Computer Science & Engineering, ICT, Ceramic, Fabrication, Printing, Textile Designing, Mechanical (CAD/CAM)

Academic Year	Semester	Category
w.e.f. 2024	2nd	BSC

Prerequisites

Function, Logarithm, Determinant, Trigonometry, Limit, Factorization, Polynomial, Quadratic Equation, Coordinate Geometry, LCM, GCD, Concept of Set.

Rationale

This course is an extension of the course Mathematics-I of first semester namely Applied Mathematics. The course is designed to inculcate its applications in relevant branch of engineering and technology using the techniques of Differentiation, Integration, Differential equations, Matrix theory and Statistics.

The course is structured with an emphasis on multidisciplinary learning and skill development, ensuring that students can apply mathematical techniques and concepts effectively in their vocational and technical areas. Its elements are designed to be thorough, hands-on, and aligned with both academic standards and professional expectations.

Course Outcomes

After completion of the course, students will be able to:

No.	Course Outcomes	RBT Level
1	Demonstrate the ability to solve engineering related problems based on Matrices.	A (Application)
2	Demonstrate the ability to solve engineering related problems based on applications of differentiation.	A (Application)
3	Demonstrate the ability to solve engineering related problems based on applications of integration.	A (Application)
4	Develop the ability to apply differential equations to significant applied problems.	A (Application)
5	Solve applied problems using the concept of mean.	A (Application)

RBT: Revised Bloom's Taxonomy

Teaching and Examination Scheme

Teaching Scheme (Hours)			Credits	Assessment Pattern (Marks)				Total
L	T	PR	C	Theory ESE (E)	Theory PA/CA (M)	Practical PA/CA (I)	Practical ESE (V)	Marks
3	1	0	4	70	30	0	0	100

Legends:

L: Lecture
T: Tutorial
PR: Practical
C: Credits
ESE: End Semester Examination
PA/CA: Progressive Assessment/Continuous Assessment

Course Content

Unit No.	Unit Title	Content	Hours	Weightage (%)
1	Matrices	1.1 Concept of Matrix 1.2 Types of Matrices 1.3 Addition, Subtraction and multiplication by scalar of matrices 1.4 Product of two matrices 1.5 Adjoint and Inverse of a matrix of order 2X2 and 3X3 1.6 Solution of Simultaneous linear equations of two variables	10	23
2	Differentiation and its Applications	2.1 Concept and Definition of Differentiation 2.2 Working rules: Sum, Product, Division 2.3 Chain Rule 2.4 Derivative of Implicit functions 2.5 Derivative of Parametric functions 2.6 Logarithmic Differentiation 2.7 Successive Differentiation up to second order 2.8 Applications: Velocity, Acceleration, Maxima & Minima of given simple functions	11	23
3	Integration and its Applications	3.1 Concept and Definition of Integration 3.2 Working rules and Integral of standard functions 3.3 Method of substitution 3.4 Integration by parts 3.5 Definite Integral and its properties 3.6 Applications: Area and volume (Simple problems)	10	20
4	Differential Equations	4.1 Concept and Definition, Order and Degree of differential equation 4.2 Solution of DE of first degree and first order by Variable Separable method 4.3 Solution of linear Differential equation	7	17
5	Statistics	5.1 Mean for ungrouped and grouped data 5.2 Mean deviation and Standard deviation about Mean for ungrouped and grouped data	7	17
	Total		45	100

Suggested Specification Table with Marks (Theory)

Unit No.	Unit Title	R Level	U Level	A Level	Total Marks
1	Matrices	4	6	6	16
2	Differentiation and its Applications	4	6	6	16
3	Integration and its Applications	4	4	6	14
4	Differential Equations	2	4	6	12
5	Statistics	2	4	6	12
Total		16	24	30	70
%		23	34	43	100

Legend: R: Remember, U: Understanding, A: Application, N: Analyze, E: Evaluate, C: Create (as per Revised Bloom's Taxonomy)

References/Suggested Learning Resources

(a) Books

S. No.	Title of Book	Author	Publication with place, year and ISBN
1	Elementary Engineering Mathematics	B. S. Grewal	Khanna Publishers, 15th Edition. ISBN: 978-81-7409-257-1
2	Engineering Mathematics (Third edition)	Croft, Anthony	Pearson Education, New Delhi, 2014. ISBN: 978-81-317-2605-1
3	Calculus and Its Applications	Marvin L. Bittinger, David J. Ellenbogen, Scott A. Surgent	Addison-Wesley, 10th Edition. ISBN-13: 978-0-321-69433-1
4	Calculus and Analytic Geometry	G. B. Thomas, R. L. Finney	Addison Wesley, 9th Edition, 1995. ISBN: 978-8174906168
5	Understanding Engineering Mathematics	John Bird	Routledge; 1st edition. ISBN: 978-0415662840
6	Advanced Engineering Mathematics	Krezig, Ervin	Wiley Publ., New Delhi, 2014, ISBN: 978-0-470-45836-5
7	Mathematics-I	Deepak Singh	Khanna Book Publishing Co. ISBN: 978-93-91505-42-4
8	Mathematics-II	Garima Singh	Khanna Book Publishing Co. ISBN: 978-93-91505-52-3
9	Elementary Mathematical Statistics	S. C. Gupta and V. K. Gupta	Sultan Chand and Sons, Educational Publisher, New Delhi. ISBN: 978-8180547003

(b) Open-source software and websites

Additional Resources

Mobile Apps

Apps available in Google Play Store
National Digital Library e-Granthalaya
ePathshala IGNOU e-content
NSDC eBook Reader: Kaushale Pustakalaya

List of Laboratory/Learning Resources Required

Computer System, smartphone & LCD Projector
Scientific Calculator (Display type: Natural Display, Algebraic input logic: Natural V.P.A.M., Significant function: 10+2)