Calculus and Linear Algebra 1st Sem (Physics Group) Syllabus for VTU BE 2017 Scheme

Calculus and Linear Algebra detail syllabus for Physics Group 2017 scheme is selected from VTU official website and presented for VTU students. The course code (18MAT11), and for exam duration, Teaching Hr/week, Practical Hr/week, Total Marks, internal marks, theory marks, duration and credits do visit complete sem subjects post given below.

For all other 1st sem physics group syllabus for be 2017 scheme vtu you can visit 1st Sem Physics Group syllabus for BE 2017 Scheme VTU Subjects. The detail syllabus for calculus and linear algebra is as follows.

Course Objectives:

This course will enable students:

• To familiarize the important tools of calculus and differential equations that are essential in all branches of engineering.
• To develop the knowledge of matrices and linear algebra in a comprehensive manner.

Module 1
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Module 2

Differential Calculus-2: Taylors and Maclaurins series expansions for one variable (statements only), indeterminate forms – LHospitals rule. Partial differentiation; Total derivatives-differentiation of composite functions. Maxima and minima for a function of two variables; Method of Lagrange multipliers with one subsidiary condition. Applications of maxima and minima with illustrative examples. Jacobians-simple problems.

Module 3

Integral Calculus: Review of elementary integral calculus.
Multiple integrals: Evaluation of double and triple integrals. Evaluation of double integrals- change of order of integration and changing into polar coordinates. Applications to find area volume and centre of gravity
Beta and Gamma functions: Definitions, Relation between beta and gamma functions and simple problems.

Module 4
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Module 5

Linear Algebra: Rank of a matrix-echelon form. Solution of system of linear equations – consistency. Gauss-elimination method, Gauss -Jordan method and Approximate solution by Gauss-Seidel method. Eigen values and eigenvectors-Rayleighs power method. Diagonalization of a square matrix of order two.

Text Books:

1. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 43rd Ed., 2015.
2. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 1 Oth Ed.(Reprint), 2016.

Reference Books:

1. C.Ray Wylie, Louis C.Barrett: Advanced Engineering Mathematics”, 6th Edition,
2. McGraw-Hill Book Co., New York, 1995.
3. James Stewart: Calculus -Early Transcendentals, Cengage Learning India Private Ltd., 2017.
4. B.V.Ramana: “Higher Engineering Mathematics” 11th Edition, Tata McGraw-Hill, 2010.
5. Srimanta Pal & Subobh C Bhunia: Engineering Mathematics, Oxford University Press, 3rd Reprint, 2016.
6. Gupta C.B., Singh S.R. and Mukesh Kumar: Engineering Mathematics for Semester I & II, Mc-Graw Hill Education (India) Pvt.Ltd., 2015.

Web links and Video Lectures:

1. http://nptel.ac.in/courses.php?disciplineID=l 11
2. http://www.class-central.com/subject/math(MOOCs)
3. http://academicearth.org/
4. VTUEDUSAT PROGRAMME-20

Course Outcomes:

On completion of this course, students are able to:

1. Apply the knowledge of calculus to solve problems related to polar curves and its applications in determining the bentness of a curve.
2. Learn the notion of partial differentiation to calculate rates of change of multivariate functions and solve problems related to composite functions and Jacobians.
3. Apply the concept of change of order of integration and variables to evaluate multiple integrals and their usage in computing the area and volumes.
4. Solve first order linear/nonlinear differential equation analytically using standard methods
5. Make use of matrix theory for solving system of linear equations and compute eigenvalues and eigenvectors required for matrix diagonalization process.

Question paper pattern:

• The SEE question paper will be set for 100 marks and the marks scored will be proportionately reduced to 60
• The question paper will have ten full questions carrying equal marks.
• Each full question carries 20 marks.
• There will be two full questions (with a maximum of four sub questions) from each module.
• Each full question will have sub questions covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.

For detail syllabus of all other subjects of BE 1st Sem, 2017 scheme do visit Physics Group 1st Sem syllabus for 2017 scheme.

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