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 | N Level | E Level | C Level | Total |
|---|---|---|---|---|---|---|---|---|
| 1 | Determinant and Function | 4 | 7 | 5 | 0 | 0 | 0 | 16 |
| 2 | Trigonometry | 4 | 5 | 5 | 0 | 0 | 0 | 14 |
| 3 | Vectors | 4 | 6 | 4 | 0 | 0 | 0 | 14 |
| 4 | Coordinate Geometry | 4 | 5 | 5 | 0 | 0 | 0 | 14 |
| 5 | Limit | 3 | 4 | 5 | 0 | 0 | 0 | 12 |
| Total | 19 | 27 | 24 | 0 | 0 | 0 | 70 | |
| % | 27 | 39 | 34 | 0 | 0 | 0 | 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#
- YouTube Channel of DTEGUJ
- GeoGebra
- PhET Interactive Simulations
- DPlot
- Wolfram Mathematica
- Khan Academy
- Easy Calculation
- SCI Lab
- NCERT Textbook
- GeeksforGeeks
- Math is Fun - Slope
- Statistics How To - Limit of Functions
- GTU Syllabus Portal
Apps in Google Play Store#
- 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