BMATS101 Mathematics for CSE Stream-I syllabus for CSE Stream Physics Group

Introduction to polar coordinates and curvature relating to Computer Science and engineering.

Polar coordinates, Polar curves, angle between the radius vector and the tangent, angle between two curves. Pedal equations. Curvature and Radius of curvature - Cartesian, Parametric, Polar and Pedal forms. Problems.

Self-study: Center and circle of curvature, evolutes and involutes.

Applications: Computer graphics, Image processing.

(RBT Levels: L1, L2 and L3)

Introduction of series expansion and partial differentiation in Computer Science & Engineering applications.

Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems. Indeterminate forms - L’Hospital’s rule-Problems. Partial differentiation, total derivative - differentiation of composite functions. Jacobian and problems. Maxima and minima for a function of two variables. Problems.

Self-study: Euler’s theorem and problems. Method of Lagrange’s undetermined multipliers with single constraint.

Applications: Series expansion in computer programming, Errors and approximations, calculators.

(RBT Levels: L1, L2 and L3)

Introduction to first-order ordinary differential equations pertaining to the applications for Computer Science & Engineering.

Linear and Bernoulli’s differential equations. Exact and reducible to exact differential equations -

Integrating factors on 1⁄𝑁(𝜕𝑀𝜕𝑦⁄𝜕𝑁𝜕𝑥) 𝑎𝑛𝑑 1𝑀(𝜕𝑁𝜕𝑥⁄𝜕𝑀𝜕𝑦). Orthogonal trajectories, L-R & C-R circuits. Problems.

Non-linear differential equations: Introduction to general and singular solutions, Solvable for p only, Clairaut’s equations,reducible to Clairaut’s equations. Problems.

Self-Study: Applications of ODEs, Solvable for x and y.

Applications of ordinary differential equations: Rate of Growth or Decay, Conduction of heat.

(RBT Levels: L1, L2 and L3)

Introduction of modular arithmetic and its applications in Computer Science and Engineering.

Introduction to Congruences, Linear Congruences, The Remainder theorem, Solving Polynomials, Linear Diophantine Equation, System of Linear Congruences, Euler’s Theorem, Wilson Theorem and Fermat’s little theorem. Applications of Congruences-RSA algorithm.

Self-Study: Divisibility, GCD, Properties of Prime Numbers, Fundamental theorem of Arithmetic.

Applications: Cryptography, encoding and decoding, RSA applications in public key encryption.

(RBT Levels: L1, L2 and L3)

Introduction of linear algebra related to Computer Science & Engineering.

Elementary row transformationofa matrix, Rank of a matrix. Consistency and Solution of system of linear equations - Gauss-elimination method, Gauss-Jordan method and approximate solution by Gauss-Seidel method. Eigenvalues and Eigenvectors, Rayleigh’s power method to find the dominant Eigenvalue and Eigenvector.

Self-Study: Solution of system of equations by Gauss-Jacobi iterative method. Inverse of a square matrix by Cayley- Hamilton theorem.

Applications: Boolean matrix, Network Analysis, Markov Analysis, Critical point of a network system. Optimum solution.

(RBT Levels: L1, L2 and L3).

List of Laboratory experiments

(2 hours/week per batch/ batch strength 15)10 lab sessions + 1 repetition class + 1 Lab Assessment

1 2D plots for Cartesian and polar curves

2 Finding angle between polar curves, curvature and radius of curvature of a given curve

3 Finding partial derivatives, Jacobian and plotting the graph

4 Applications to Maxima and Minima of two variables

5 Solution of first-order differential equation and plotting the graphs

6 Finding GCD using Euclid’s Algorithm

7 Applications of Wilson's theorem

8 Numerical solution of system of linear equations, test for consistency and graphical representation

9 Solution of system of linear equations using Gauss-Seidel iteration

10 Compute eigenvalues and eigenvectors and find the largest and smallest eigenvalue by Rayleigh power method.

Suggested software’s: Mathematica/MatLab/Python/Scilab

Course outcome (Course Skill Set)

At the end of the course the student will be able to:

CO1 apply the knowledge of calculus to solve problems related to polar curves and learn the notion of partial differentiation to compute rate of change of multivariate functions

CO2 analyze the solution of linear and nonlinear ordinary differential equations

CO3 get acquainted and to apply modular arithmetic to computer algorithms

CO4 make use of matrix theory for solving for system of linear equations and compute eigenvalues and eigenvectors

CO5 familiarize with modern mathematical tools namely MATHEMATICA/MATLAB/ PYTHON/ SCILAB

Assessment Details (both CIE and SEE)

• The weightage of Continuous Internal Evaluation (CIE) is 50% and for Semester End Exam (SEE) is 50%.
• The minimum passing mark for the CIE is 40% of the maximum marks (20 marks out of 50).
• The minimum passing mark for the SEE is 35% of the maximum marks (18 marks out of 50).
• A student shall be deemed to have satisfied the academic requirements and earned the credits allotted to each subject/ course if the student secures not less than 35% (18 Marks out of 50) in the semester-end examination(SEE), and a minimum of 40% (40 marks out of 100) in the total of the CIE (Continuous Internal Evaluation) and SEE (Semester End Examination) taken together.

Continuous Internal Evaluation(CIE):

Two Unit Tests each of 20 Marks (duration 01 hour)

• First test after the completion of 30-40 % of the syllabus
• Second test after completion of 80-90% of the syllabus One Improvement test before the closing of the academic term may be conducted if necessary. However best two tests out of three shall be taken into consideration.

Two assignments each of 10 Marks

The teacher has to plan the assignments and get them completed by the students well before the closing of the term so that marks entry in the examination portal shall be done in time. Formative (Successive) Assessments include Assignments/Quizzes/Seminars/ Course projects/Field surveys/ Case studies/ Hands-on practice (experiments)/Group Discussions/ others. The Teachers shall 20.11.2022 4choose the types of assignments depending on the requirement of the course and plan to attain the COs and POs. (to have a less stressed CIE, the portion of the syllabus should not be common /repeated for any of the methods of the CIE. Each method of CIE should have a different syllabus portion of the course). CIE methods /test question paper is designed to attain the different levels of Bloom’s taxonomy as per the outcome defined for the course.

The sum of two tests, two assignments, will be out of 60 marks and will be scaled down to 30 marks

CIE for the practical component of the Integrated Course

• On completion of every experiment/program in the laboratory, the students shall be evaluated and marks shall be awarded on the same day. The15 marks are for conducting the experiment and preparation of the laboratory record, the other 05 marks shall be for the test conducted at the end of the semester.
• The CIE marks awarded in the case of the Practical component shall be based on the continuous evaluation of the laboratory report. Each experiment report can be evaluated for 10 marks. Marks of all experiments’ write-ups are added and scaled down to 15 marks.
• The laboratory test (duration 02/03 hours) at the end of the 14th /15th week of the semester /after completion of all the experiments (whichever is early) shall be conducted for 50 marks and scaled down to 05 marks.Scaled-down marks of write-up evaluations and tests added will be CIE marks for the laboratory component of IPCC for 20 marks.

Semester End Examination (SEE):

SEE for IC

Theory SEE will be conducted by University as per the scheduled time table, with common question papers for the course (duration 03 hours)

1.The question paper will have ten questions. Each question is set for 20 marks.

2.There will be 2 questions from each module. Each of the two questions under a module (with a maximum of 3 sub-questions), should have a mix of topics under that module.

3.The students have to answer 5 full questions, selecting one full question from each module.

The theory portion of the Integrated Course shall be for both CIE and SEE, whereas the practical portion will have a CIE component only. Questions mentioned in the SEE paper shall include questions from the practical component).

Passing standard:

• The minimum marks to be secured in CIE to appear for SEE shall be 12 (40% of maximum marks-30) in the theory component and 08 (40% of maximum marks -20) in the practical component. The laboratory component of the IPCC shall be for CIE only. However, in SEE, the questions from the laboratory component shall be included. The maximum of 04/05 questions to be set from the practical component of IPCC, the total marks of all questions should not be more than 30 marks.
• SEE will be conducted for 100 marks and students shall secure 35% of the maximum marks to qualify for the SEE. Marks secured will be scaled down to 50. 20.11.2022 5

Suggested Learning Resources:

Books (Title of the Book/Name of the author/Name of the publisher/Edition and Year)

Text Books

1.B. S. Grewal: “Higher Engineering Mathematics”, Khanna publishers, 44th Ed., 2021.

2.E. Kreyszig: “Advanced Engineering Mathematics”, John Wiley & Sons, 10th Ed., 2018.

Reference Books

1.V. Ramana:“Higher Engineering Mathematics” McGraw-Hill Education, 11th Ed., 2017

2.Srimanta Pal & Subodh C.Bhunia: “Engineering Mathematics” Oxford University Press, 3rd Ed., 2016.

3.N.P Bali and Manish Goyal: “A textbook of Engineering Mathematics” Laxmi Publications, 10th Ed., 2022.

4.C. Ray Wylie, Louis C. Barrett:“Advanced Engineering Mathematics” McGraw – Hill Book Co., Newyork, 6th Ed., 2017.

5.Gupta C.B, Sing S.R and Mukesh Kumar:“Engineering Mathematic for Semester I and II”, Mc-Graw Hill Education(India) Pvt. Ltd 2015.

6.H. K. Dass and Er. Rajnish Verma:“Higher Engineering Mathematics” S. Chand Publication, 3rd Ed., 2014.

7.James Stewart: “Calculus” Cengage Publications, 7th Ed., 2019.

8.David C Lay:“Linear Algebra and its Applications”, Pearson Publishers, 4th Ed., 2018.

9.Gareth Williams:“Linear Algebra with applications”, Jones Bartlett Publishers Inc., 6thEd., 2017.

10.William Stallings:“Cryptography and Network Security” Pearson Prentice Hall, 6th Ed., 2013.

11.David M Burton: “Elementary Number Theory” Mc Graw Hill, 7th Ed.,2010.