Mathematics for CSE Stream-I detailed syllabus for CSE Stream Physics Group 2022 Scheme curriculum has been taken from the VTUs official website and presented for the CSE Stream Physics Group students. For course code, course name, duration, number of credits for a course and other scheme related information, do visit full semester subjects post given below.

For CSE Stream Physics Group 1st Sem scheme and its subjects, do visit CSE Stream Physics Group 1st Sem 2022 Scheme scheme. The detailed syllabus of mathematics for cse stream-i is as follows.

#### Course Objectives:

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#### Teaching-Learning Process

*Pedagogy (General Instructions):* These are sample Strategies, which teachers can use to accelerate the attainment of the various course outcomes.

- In addition to the traditional lecture method, different types of innovative teaching methods may be adopted so that the delivered lessons shall develop students’ theoretical and applied mathematical skills.
- State the need for Mathematics with Engineering Studies and Provide real-life examples.
- Support and guide the students for self-study.
- You will also be responsible for assigning homework, grading assignments and quizzes, and documenting students’ progress.
- Encourage the students to group learning to improve their creative and analytical skills.
- Show short related video lectures in the following ways:
- As an introduction to new topics (pre-lecture activity).
- As a revision of topics (post-lecture activity).
- As additional examples (post-lecture activity).
- As an additional material of challenging topics (pre-and post-lecture activity).
- As a model solution of some exercises (post-lecture activity).

#### Module 1:

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#### Module 2:

Vector Calculus(8 hours) Introduction to Vector Calculus in Computer Science & Engineering. Scalar and vector fields. Gradient, directional derivative, curl and divergence – physical interpretation, solenoidal and irrotational vector fields. Problems. Curvilinear coordinates: Scale factors, base vectors, Cylindrical polar coordinates, Spherical polar coordinates, transformation between cartesian and curvilinear systems, orthogonality. Problems.

*Self-Study:* Vector integration and Vector line integral.

*Applications:* Conservation of laws, Electrostatics, Analysis of streamlines.

#### Module 3:

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#### Module 4:

Numerical Methods -1(8 hours) Importance of numerical methods for discrete data in the field of computer science & engineering. Solution of algebraic and transcendental equations – Regula-Falsi and Newton-Raphson methods (only formulae). Problems. Finite differences, Interpolation using Newton’s forward and backward difference formulae, Newton’s divided difference formula and Lagrange’s interpolation formula (All formulae without proof). Problems. Numerical integration: Trapezoidal, Simpson’s (1/3)rd and (3/8)th rules(without proof). Problems.

*Self-Study:* Bisection method, Lagrange’s inverse Interpolation.

*Applications:* Estimating the approximate roots, extremum values, Area, volume, and surface area. Errors in finite precision. (RBT Levels: L1, L2 and L3)

#### Module 5:

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#### List of Laboratory Experiments

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

- Program to compute area, surface area, volume and centre of gravity
- Evaluation of improper integrals
- Finding gradient, divergent, curl and their geometrical interpretation
- Computation of basis and dimension for a vector space and Graphical representation of linear transformation
- Computing the inner product and orthogonality
- Solution of algebraic and transcendental equations by Ramanujan’s, Regula-Falsi and Newton-Raphson method
- Interpolation/Extrapolation using Newton’s forward and backward difference formula
- Computation of area under the curve using Trapezoidal, Simpson’s (1/3)rd and (3/8)th rule
- Solution of ODE of first order and first degree by Taylor’s series and Modified Euler’s method
- Solution of ODE of first order and first degree by Runge-Kutta 4th order and Milne’s predictor-corrector method

*Suggested Software’S:* Mathematica/MatLab/Python/Scilab

#### Course Outcomes:

(Course Skill Set) At the end of the course the student will be able to:

- Apply the concept of change of order of integration and variables to evaluate multiple integrals and their usage in computing area and volume.
- Understand the applications of vector calculus refer to solenoidal, and irrotational vectors.Orthogonal curvilinear coordinates.
- Demonstrate the idea of Linear dependence and independence of sets in the vector space, and linear transformation
- Apply the knowledge of numerical methods in analysing the discrete data and solving the physical and engineering problems.
- Get familiarize with modern mathematical tools namely MATHEMATICA/ MATLAB /PYTHON/ SCILAB

#### Text Books:

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#### Reference Books:

- V. Ramana: “Higher Engineering Mathematics” McGraw-Hill Education, 11th Ed., 2017
- Srimanta Pal & Subodh C.Bhunia: “Engineering Mathematics” Oxford University Press, 3rd Ed., 2016.
- N.P Bali and Manish Goyal: “A Textbook of Engineering Mathematics” Laxmi Publications, 10th Ed., 2022.
- C. Ray Wylie, Louis C. Barrett: “Advanced Engineering Mathematics” McGraw – Hill Book Co., New York, 6th Ed., 2017.
- Gupta C.B, Sing S.R and Mukesh Kumar: “Engineering Mathematic for Semester I and II”, Mc-Graw Hill Education(India) Pvt. Ltd 2015.
- H. K. Dass and Er. Rajnish Verma: “Higher Engineering Mathematics” S. Chand Publication, 3rd Ed., 2014.
- James Stewart: “Calculus” Cengage Publications, 7thEd., 2019.
- David C Lay: “Linear Algebra and its Applications”, Pearson Publishers, 4th Ed., 2018.
- Gareth Williams: “Linear Algebra with applications”, Jones Bartlett Publishers Inc., 6th Ed., 2017.
- Gilbert Strang: “Linear Algebra and its Applications”, Cengage Publications, 4th Ed., 2022.

#### Web links and Video Lectures (e-Resources):

- http://nptel.ac.in/courses.php?disciplineID=111
- http://www.class-central.com/subject/math(MOOCs)
- http://academicearth.org/
- VTU e-Shikshana Program
- VTU EDUSAT Program

#### Activity-Based Learning

(Suggested Activities in Class)/ Practical-Based Learning

- Quizzes
- Assignments
- Seminar

For detailed syllabus of all other subjects of CSE Stream Physics Group, 2022 Scheme curriculum do visit CSE Stream Physics Group 1st Sem subject syllabuses for 2022 Scheme.

For all CSE Stream Physics Group results, visit VTU CSE Stream Physics Group all semester results direct link.