Mathematics-I (DI01000021)

Course Information

Institution: Gujarat Technological University

Field	Details
Program Name	Engineering
Level	Diploma
Branch	All
Course Code	DI01000021
Course Name	Mathematics-I
Academic Year	2024
Semester	1st Semester
Category	BSC

Prerequisites

Linear equation in two variables, Factorization, Polynomial, Quadratic Equation, Coordinate Geometry, LCM, GCD, Concept of Set.

Rationale

This course of Mathematics is being introduced for providing a solid foundation in basic mathematics concepts and operations that are crucial for further education and everyday problem-solving. This course is an attempt to include topics which are directly applicable to various fields of engineering, technology, business and sciences and develop logical reasoning and critical thinking abilities. The course is designed focusing on multidisciplinary and competency development to ensure students can effectively use mathematical methods and principles in their vocational and technical fields. The components of course ensure that it is comprehensive, practical and aligned with both academic and professional requirements.

Course Outcomes

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

No	Course Outcomes	RBT Level
01	Interpret the function graphically, numerically and analytically.	A(Application)
02	Demonstrate the ability to algebraically analyse basic functions used in Trigonometry.	A(Application)
03	Demonstrate the ability to crack engineering related problems based on concepts of Vectors.	A(Application)
04	Solve basic engineering problems under given conditions of straight lines and circle.	A(Application)
05	Demonstrate the ability to analyse and illustrate the Functions using the concept of Limit.	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)	Tutorial/Practical PA/CA (I)	Tutorial/Practical ESE (V)	Marks
3	1	0	4	70	30	-	-	100

Course Content

Unit No.	Content	Hours	Weightage (%)
1. Determinant and Function	1.1 Determinant and its value up to 3rd order (Without properties) 1.2 Function and simple examples 1.3 Logarithm as a function 1.4 Laws of Logarithm and related Simple examples	9	23
2. Trigonometry	2.1 Units of Angles (degree and radian) 2.2 Trigonometric Functions 2.3 Allied & Compound Angles, Multiple-Submultiples angles 2.4 Graph of Sine and Cosine 2.5 Periodic Trigonometric function 2.6 Sum and factor formulae 2.7 Inverse Trigonometric function	12	20
3. Vectors	3.1 Introduction to Vectors 3.2 Vector Operations 3.3 Angle between two Vectors 3.4 Applications of Scalar and Vector Product (Work Done and Moment of Force)	9	20
4. Coordinate Geometry	4.1 Straight line (Two-point form) and slope of straight line 4.2 Slope point form, Intercept form, General form of line 4.3 Condition of parallel and perpendicular lines 4.4 Equations of Parallel lines and Perpendicular lines to the given lines 4.5 Angle between two lines 4.6 Equation of circle with center and Radius 4.7 General equation of circle 4.8 Tangent and normal to a circle	8	20
5. Limit	5.1 Limit of a Function 5.2 Standard formulae of Limit and related simple examples	7	17
Total		45	100

Suggested Specification Table with Marks (Theory)

Unit No.	Unit Title	R Level	U Level	A Level	Total
1	Determinant and Function	4	7	5	16
2	Trigonometry	4	5	5	14
3	Vectors	4	6	4	14
4	Coordinate Geometry	4	5	5	14
5	Limit	3	4	5	12
Total		19	27	24	70
%		27	39	34	100

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

References/Suggested Learning Resources

Books

S. No.	Title of Book	Author	Publication with place, year and ISBN
1	Engineering Mathematics (Third edition)	Croft, Anthony	Pearson Education, New Delhi, 2014. ISBN 978-81-317-2605-1
2	A Text Book of Vector Analysis	Narayan Shanti and Mittal P.K	S. Chand Publication, ISBN 978-8121922432
3	Calculus and Analytic Geometry	G. B. Thomas, R. L. Finney	Addison Wesley, 9th Edition, 1995. ISBN 978-8174906168
4	Understanding Engineering Mathematics	John Bird	Routledge; 1st edition ISBN 978-0415662840
5	Advanced Engineering Mathematics	Krezig, Ervin	Wiley Publ., NewDelhi, 2014
6	Mathematics-I	Deepak Singh	Khanna Book Publishing Co ISBN: 978-93-91505-42-4
7	Mathematics-II	Garima Singh	Khanna Book Publishing Co ISBN: 978-93-91505-52-3

Open-source Software and Websites

Android/iOS Apps

National Digital Library
e-Granthalaya
NSDC eBook Reader: Kaushal ePustakalaya
ePathshala
IGNOU e-content

Laboratory/Learning Resources Required

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