## GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Diploma in Engineering Level: Diploma Branch: Electrical Engineering, Renewable Energy, Automation and Robotics Instrumentation & Control Engineering, Power Electronics Engineering Course / Subject Code: DI02000021 Course / Subject Name: Engineering Mathematics | w. e. f. Academic Year: | 2024 | |---------------------------|--------| | Semester: | 2 nd | | Category of the Course: | BSC | | Prerequisite: | 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 Engineering 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 Complex numbers. 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 Outcome: After Completion of the Course, Student will able to: | No | Course Outcomes | RBT Level | |-------------------------------------------------------------------------------------------------------------------|-------------------|-------------| | Demonstrate the ability to Crack engineering related problems based on Matrices. | A(Application) | 01 | | Demonstrate the ability to solve engineering related problems based on applications of differentiation. | A(Application) | 02 | | Demonstrate the ability to solve engineering related problems based on applications of integration. | A(Application) | 03 | | Develop the ability to apply differential equations to significant applied problems. | A(Application) | 04 | | Represent complex numbers algebraically and geometrically for solving engineering related problems. | A(Application) | 05 | *Revised Bloom's Taxonomy (RBT) ## GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Diploma in Engineering Level: Diploma Branch: Electrical Engineering, Renewable Energy, Automation and Robotics Instrumentation & Control Engineering, Power Electronics Engineering Course / Subject Code: DI02000021 Course / Subject Name: Engineering Mathematics ## Teaching and Examination Scheme: | Teaching Scheme (in Hours) | Teaching Scheme (in Hours) | Teaching Scheme (in Hours) | Total Credits L+T+ (PR/2) | Assessment Pattern and Marks | Assessment Pattern and Marks | Assessment Pattern and Marks | Assessment Pattern and Marks | Total | |-------------------------------|-------------------------------|-------------------------------|--------------------------------|--------------------------------|--------------------------------|--------------------------------|--------------------------------|---------| | L | | | | Theory | Theory | Tutorial / Practical | Tutorial / Practical | Marks | | | T | PR | C | ESE (E) | PA / CA (M) | PA/CA (I) | ESE (V) | | | 3 | 1 | 0 | 4 | 70 | 30 | 00 | 00 | 100 | ## Course Content: | Unit No. | Content | No. of Hours | % of Weightage | |--------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------|-------------------| | 1. Matrices | 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. Differentiatio n and its Applications | 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 | 11 | 23 | | 3. Integration and its Applications | 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. | 10 | 20 | ## GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Diploma in Engineering Level: Diploma Branch: Electrical Engineering, Renewable Energy, Automation and Robotics Instrumentation & Control Engineering, Power Electronics Engineering Course / Subject Code: DI02000021 Course / Subject Name: Engineering Mathematics | 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. Complex Numbers | 5.1 Concept of Complex number. 5.2 Algebra of Complex numbers. 5.3 Conjugate, Modulus and inverse of Complex numbers. 5.4 Argument and Polar form of a Complex number. 5.5 De Moivre's Theorem and related simple examples. 5.6 Square root of a Complex number and cube root of unity. | 7 | 17 | | | Total | 45 | 100 | ## Suggested Specification Table with Marks (Theory): | Unit No. | Unit Title | Distribution of Theory Marks | Distribution of Theory Marks | Distribution of Theory Marks | Distribution of Theory Marks | Distribution of Theory Marks | Distribution of Theory Marks | Distribution of Theory Marks | |-------------|---------------------------------------|--------------------------------|--------------------------------|--------------------------------|--------------------------------|--------------------------------|--------------------------------|--------------------------------| | Unit No. | Unit Title | R Level | U Level | A Level | N Level | E Level | C Level | Total | | 1 | Matrices | 4 | 6 | 6 | 0 | 0 | 0 | 16 | | 2 | Differentiation and its Applications | 4 | 6 | 6 | 0 | 0 | 0 | 16 | | 3 | Integration and its Applications | 4 | 4 | 6 | 0 | 0 | 0 | 14 | | 4 | Differential Equations | 2 | 4 | 6 | 0 | 0 | 0 | 12 | | 5 | Complex Numbers | 2 | 4 | 6 | 0 | 0 | 0 | 12 | | Total | Total | 16 | 24 | 30 | 0 | 0 | 0 | 70 | | % | % | 23 | 34 | 43 | 0 | 0 | 0 | 100 | Where R: Remember; U: Understanding; A: Application, N: Analyze and 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 | ## GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Diploma in Engineering Level: Diploma Branch: Electrical Engineering, Renewable Energy, Automation and Robotics Instrumentation & Control Engineering, Power Electronics Engineering Course / Subject Code: DI02000021 Course / Subject Name: Engineering Mathematics | 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 | | 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., NewDelhi,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 | ## (b) Open-source software and website: | | ● https://www.youtube.com/channel/UCLJVrQyPYsseCf78QWCDsvA/featured (YouTube Channel of DTEGUJ) ● https://www.geogebra.org/?lang=en ● https://phet.colorado.edu/ ● www.dplot.com/ - DPlot ● www.wolfram.com/mathematica/ ● https://www.khanacademy.org/ ● www.easycalculation.com ● www.scilab.org/ - SCI Lab ● https://ncert.nic.in/textbook/pdf/lemh102.pdf ● https://www.geeksforgeeks.org | |-----------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | Apps in Google Play Store | National Digital Library e-Granthalaya NSDC eBook Reader: KaushalePustakalaya ePathshala IGNOU e-content | ## GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Diploma in Engineering Level: Diploma Instrumentation & Control Engineering, Power Electronics Engineering Branch: Electrical Engineering, Renewable Energy, Automation and Robotics Course / Subject Code: DI02000021 Course / Subject Name: Engineering Mathematics ## List of Laboratory/Learning Resources Required: 1. Computer System, smart phone & LCD Projector 2. Scientific Calculator (Display type: Natural Display Algebraic input logic: Natural V.P.A.M. Significant function: 10+2.) * * * * * * *