Syllabus

Gujarat Technological University, Ahmedabad
B.E. –I

1st Semester

Mathematics-I

Sr. No.	Subject	Teaching scheme	Examination scheme
Theory	Tutorial	Practical	Credits	Exam	Theory Paper	Tutorial	Total
1	Mathematics-I	3	2	0	5	Sessional	30 marks	-	100 marks
University	70 marks	-

Syllabus

• Review of limits, continuity, di.erentiability.

• Mean value theorem, Taylors Theorem, Maxima and Minima.

• Riemann integrals, Fundamental theorem of Calculus, Improper integrals, applications to area, volume.

• Convergence of sequences and series, power series.

• Partial Derivatives, gradient and directional derivatives, chain rule, maxima and minima, Lagrange multipliers.

• Double and Triple integration, Jacobians and change of variables formula. Parametrization of curves and surfaces, vector Fields, line and surface integrals.

• Divergence and curl, Theorems of Green, Gauss, and Stokes.

Texts/References

1.      Hughes-Hallett et al., Calculus – Single and Multivariable (3rd Edition), John-Wiley and Sons (2003).

2.      James Stewart, Calculus (5th Edition), Thomson (2003).

3.      T. M. Apostol, Calculus, Volumes 1 and 2 (2nd Edition), Wiley Eastern 1980.

4.      G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry

B.E. –II

2nd Semester

Mathematics-II

Sr. No.	Subject	Teaching scheme	Examination scheme
Theory	Tutorial	Practical	Credits	Exam	Theory Paper	Tutorial	Total
1	Mathematics-II	3	2	0	5	Sessional	30 marks	-	100 marks
University	70 marks	-

Syllabus

• Vectors in Rn, notion of linear independence and dependence, linear span of a set of vectors, vector subspaces of Rn, basis of a vector subspace.

• Systems of linear equations, matrices and Gauss elimination, row space,null space, and column space, rank of a matrix.

• Determinants and rank of a matrix in terms of determinants.

• Abstract vector spaces, linear transformations, matrix of a linear transformation, change of basis and similarity, rank-nullity theorem.

• Inner product spaces, Gram-Schmidt process, orthonormal bases, projections and least squares approximation.

• Eigenvalues and eigenvectors, characteristic polynomials, eigenvalues of special matrices (orthogonal, unitary, hermitian, symmetric, skew-symmetric, normal). algebraic and geometric multiplicity, diagonalization by similarity transformations, spectral theorem for real symmetric matrices, application to quadratic forms.

Texts/References

1. H. Anton, Elementary linear algebra with applications (8th Edition), John Wiley (1995).

2. G. Strang, Linear algebra and its applications (4th Edition), Thomson(2006).

3. S. Kumaresan, Linear algebra – A Geometric approach, Prentice Hall of India (2000).

4. E. Kreyszig, Advanced engineering mathematics (8th Edition), John Wiley (1999).

B.E.

3rd Semester

Mathematics-III

Topic -I

First order ODE

Methods for solving them, homogeneous equations, exactness, methods for finding integrating factors, Linear and Bernoulli’s equation            [3 Lect/ 2 tut]

Topic -II
Higher order ODE

Linear ODEs (generalities) complimentary function as and particular integrals, linear dependence and independence of functions, Wronskians,  Abel-Liouville formula, use of a known solution (for reduction of order) method of variation of parameter                                                                                                  [4 lect/ 2 tut]

Topic -III

Linear ODEs with constant coefficient and the Cauchy Euler equation. The characteristic and indicial polynomials. Discussion of the case of complex roots and repeated roots. Extracting the real form of the solution via Euler’s formula . Method of undetermined coefficient for finding the particular integral for special right hand sides. (forcing functions) both for const ant coefficient ODEs as well as Cauchy Euler ODEs.                         [5 Lect/3 tut]

Topic -IV

Beta and Gamma functions and their basic properties. Statement of Euler’s reflection formula, duplication formula via the beta-gamma.            [2 Lect/I tut]

Topic -V

Laplace transforms

Definition of functions of exponential type with examples. Definition of the Laplace transform and its basic properties as well as examples of Laplace transforms of exponential function, polynomials and trigonometric functions. Statement of the Riemann Lebesgue lemma. Finding the inverse transform. Laplace transform of  and . The Heaviside unit step function and shifting theorems.  Convolutions  and the convolutions theorem. Beta gamma identity.  Use of Laplace transform for solving initial value problems  for ODEs and systems of ODEs. Computing certain important integrals via Laplace transforms.

[6 Lect/4 tut]

Two Tutorials for Review of the entire portion.

70 Marks External assessment.

Topic I        4  Marks.

Topic II       7 Marks

Topic III      10 Marks

Topic IV       4 Marks

Topic V      10 Marks

Total        35 Marks

Chapters 1, 2 and  5 of Kreyszig’s text.

Chapters 2, 3, 4 and 6 of Boyce Di Prima.

Topic -VI

Series solution of ODEs. Illustrative examples as the equations of   Legendre, Tchebychev etc.,  Legendre polynomials,  their  Orthogonality and completeness.

[5 Lect/ 3 tut]

Topic -VII

Ordinary differential equations  with regular singular points and the method of Frobenious. Detailed discussion of Bessel’s equations and Bessels’ functions of first kind only. Basic properties of , the   recurrence relation between  and . Integral representation of  (where n is a non-negative  integer).                                                                              [5 lect/3 tut]

Topic -VIII

Fourier Series and Fourier transforms Basic formulae in Fourier series.  Statement of the theorem on pointwise convergence of  Fourier series. Parsevals formula (statement only) and Bessel’s inequality with examples. Mean  convergence  of Fourier series.

Fourier transforms and its basic properties.  Fourier transform of the Gaussian and the Fourier inversion theorem (statement only).  Riemann Lebesgue lemma for Fourier series and Fourier transforms (statement only).            [4 lect/ 3 tut]

Topic -IX

Basic partial differential equations of  mathematical physics and  their origins (vibrating strings, vibrating membranes heat conduction in solids etc.,).  Solving PDEs via the method of separation of variables. The Laplace operator in cylindrical and spherical polar coordinates. Brief discussion of Fourier Bessel series. Solution via Fourier series/Fourier-Bessel series for rectangular and circular domains in  and spherical and  cylindrical domains in .                                           [6 Lect/4 tut]

One Review Tutorials on topics VI-IX.

Topic VI        8  Marks.

Topic VII       7 Marks

Topic VIII      10 Marks

Topic IX      10 Marks

Total            35  Marks

The material is contained in chapters  4, 10 and  11  of  Kreyszig’s text.

Or

The material is contained in chapters  5 and 10  of  Boyce and Di Prima (Except for Topic VIII).

B.E. –I

1st Semester

Physics

1) Architectural Acoustics

Classification of Sound : Loudness – Weber – Fechner law Decibel – Absorption Coefficient – Reverberation – Saline’s formula – Factors affecting acoustics of buildings and their remedies.

2) Ultrasonic

Introduction, production, properties and detection of ultrasonics. Determination of velocity and application of ultrasonic in Engineering.

3) Crystal Physics

Introduction and classification of solids-crystal structure – The crystal systems and Bravias Lattice – Space Lattices of cubic systems – Miller Indices – Relation between Interplanner Distance and cubic Edge and Laws Formula.

4) Band theory of Solids

Based theory of Solids – Classification of solids – Energy band structure of conductors, insulator and semi conductions types of diodes (simple diode, Zenerdiode, varactor diode, LED Solar cells, photovoltaic cell, Photo Conductivity, Hall effects.

5) LASERS :

Introduction and properties of Lasers, Stimulated and instantaneous emersion –Relation between Ecienstein’s ‘A’ and ‘B’ Coefficients-Population Inversion – Optical Pumping – Nd-Yag Laser and CO2 Laser – Application of Laser in Material Processing – Holography – Application of Lasers

6) Optical – Fibre Communication

Introduction – Fibre – Optic System – advantages ofFibre optics – Basic principle – Acceptance angle and Numerical Aperture – Types of optics preparation through optical fibre

7) Conducting Materials :

Introduction – conduction in Metals, Electron theory Q.M. treatment – Free electrode theory of metals – Electrical Conductivity – Thermal Conductivity – Wildemann –Franz law – Drawbacks of classical free electrode theory

Super Conducting Materials

Introduction to super conductor – properties of super conductor Type I and Type II super conductor – Comparision between I and II – High T conductors – Application

9) New Engineering Materials

Introduction – Metallic glasses, types, properties, preparation and its application –Introduction to nano technology – method of producing, properties and its application – shape memory alloys – types – shape Memory effect – Pseudo elasticity – properties – application – Bio-materials – General information –Biomedical compatibly of Ti-Al-Nb alloys for implant application.

10) Non-Destructive Testing

Introduction – The objective of NDT – Types of Defects – Methods of NDT (Liquid Penetrate – Dye Penetrate Radiographic) x X-ray Radiography – X-ray Fluoroscopy– Ultrasonic Inspection method – Pulse Echo System – Visual Display units.

Reference Books :

1) Engineering Physics   K. Rajagopal           Prentice-Hall of India Pvt. Ltd.,                                                                                   New Delhi

2) Engg. Physics             G. Vijayakumari       Vikas Publishing House Pvt.Ltd.

3) A Text book of             M.N. Aavadhalula

Engg. Physics              P .G. Kshirsagar     S. Chand

4) Engg. Physics              Abhijit Nayak           S.K. Kataria & Sons.,Delhi.

B.E. –I

1st Semester

Communication Skills

Unit – 1 Communication skills

Process, types and levels of communication.

Technical Communication and General Communication. Factors to be

considered in technical communication.

Unit – 2 Verbal and non-verbal communication (kinesics)

Components of Non-verbal Communication (Kinesics)

Barriers to effective communication. (Noise in oral and written

communication) Communication across cultures.

Unit – 3 Listening skills – Types of Listening Active Listening V/s Passive Listening

Empathetic Listening. Traits of a good listener, barriers in effective listening,

Tips for effective listening.

Unit – 4 Effective presentation strategies. Defining purpose, analysis of audience and

locate, organizing contents. Preparing an outline of the presentation. Visual

aids, nuances of delivery, Body language and effective presentation.

Unit – 5 Interviews

Introduction, General preparations for an interview, Types of questions

generally asked at the interviews. Types of interviews, Importance of nonverbal

aspects.

Unit – 6 Group Discussions

Introduction, Group discussions as a part of the selection process, guidelines

for group discussion. Role functions in group discussion.

Unit – 7 Paragraph Development, Introduction, Topic sentence and supporting

sentences. Attributes of a good paragraph. Types of paragraphs.

Unit – 8 Letter – Writing

Business Letters, Structure and types of a business letter, Letter of Inquiry,

Letters of complaint, regret and adjustment.

Unit – 9 Technical reports

Introduction, types of reports, structure of reports, objectives and

characteristics of reports.

Unit – 10 Technical Proposals

Definition, Purpose, Types, Characteristics, Structure, Style and appearance.

Unit – 11 Technical Descriptions

Introduction, Definition of an object or a process. Guidelines for writing good

description – organization, content, structure.

Unit – 12 Effective Reading Skills

Purpose of reading, skimming and scanning. Tips for improving

comprehension skills.

Unit – 13 Job application

Essential parts – Cover Letter and the ‘resume’. Types of ‘resumes’

(Curriculum Vitae) Chronological ‘resume’, functional ‘resume’.

Unit – 14 Grammar and Vocabulary

Tense and the concept of Time. Passive Voice, Conditionals Prepositions,

Concord. Idioms, Confusables, one-word substitutes, homonyms,

homophones eponyms.

Reference books:

1. Technical Communication

Principles and Practice

- Meenakshi Raman, Sangeeta Sharma (OUP)

2. Personality Development, Harold Wallace and Ann Masters,

Cengage Publishers.

3. Basic Communication Skills for Technology

Andrea J. Rutherford (Pearson Education)

4. Communication Skills for Technical Students

T.M. Farhathullah (Orient Longman)

5. A Textbook of English for Engineers and Technologists.

Prepared by Humanities & Social Sciences Division.

Anna University, Chennai. (Orient Longman)

6. Communication Skills for Engineers

- Sunita Mishra, C, Murali Krishna (Pearson Education)

7. English for Technical Communication

- K.R. Lakshminarayanan

(Scitech Publications, Chennai.)

8. Basics of Management and Communication Skills

- Dr. P.C. Shejwalkar (Everest Publishing House)

1. Technical Communication

Principles and Practice

- Meenakshi Raman, Sangeeta Sharma (OUP)

2. Personality Development, Harold Wallace and Ann Masters,

Cengage Publishers.

3. Basic Communication Skills for Technology

Andrea J. Rutherford (Pearson Education)

4. Communication Skills for Technical Students

T.M. Farhathullah (Orient Longman)

5. A Textbook of English for Engineers and Technologists.

Prepared by Humanities & Social Sciences Division.

Anna University, Chennai. (Orient Longman)

6. Communication Skills for Engineers

- Sunita Mishra, C, Murali Krishna (Pearson Education)

7. English for Technical Communication

- K.R. Lakshminarayanan

(Scitech Publications, Chennai.)

8. Basics of Management and Communication Skills

- Dr. P.C. Shejwalkar (Everest Publishing House)

Introduction, Definition of an object or a process. Guidelines for writing good

description – organization, content, structure.

Unit – 12 Effective Reading Skills

Purpose of reading, skimming and scanning. Tips for improving

comprehension skills.

Unit – 13 Job application

Essential parts – Cover Letter and the ‘resume’. Types of ‘resumes’

(Curriculum Vitae) Chronological ‘resume’, functional ‘resume’.

Unit – 14 Grammar and Vocabulary

Tense and the concept of Time. Passive Voice, Conditionals Prepositions,

Concord. Idioms, Confusables, one-word substitutes, homonyms,

homophones eponyms.

Reference books: