Syllabus, 1st Sem, B.E/B.Tech

VTU B.E / B.Tech Syllabus for Mathematics-I Engineering CBCS 2015-16

VTU B.E/B.Tech  Syllabus for Mathematics-I Engineering gives you detail information of Mathematics-I syllabus It will be help full to understand you complete curriculum of the year.

Subject Code 15MAT11 IA Marks 20
Number of Lecture Hours/Week 4 Exam Marks 80
Total Number of Lecture Hours 50 Exam Hours 3

Course Objectives:
To enable the students to apply the knowledge of Mathematics in various engineering fields by making them to learn the following:

  • nth derivatives of product of two functions and polar curves.
  • Partial derivatives
  • Vector calculus
  • Reduction formulae of integration; To solve First order differential equations.
  • Solution of system of linear equations , quadratic forms.
Module – 1
Differential Calculus -1: determination of nth order derivatives of Standard functions – Problems. Leibnitz’s theorem (without proof) – problems.

Polar Curves – angle between the radius vector and tangent, angle between two curves, Pedal equation of polar curves. Derivative of arc length – Cartesian, Parametric and Polar forms (without proof) – problems. Curvature and Radius of Curvature – Cartesian, Parametric, Polar and Pedal forms (without proof) -problems

Hours – 10
Module -2
Differential Calculus -2 Taylor’s and Maclaurin’s theorems for function of one variable(statement only)- problems. Evaluation of Indeterminate forms.

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Hours – 10
Module -3  
Vector Calculus: Derivative of vector valued functions, Velocity, Acceleration and related problems, Scalar and Vector point functions. Definition of Gradient, Divergence and Curl-problems. Solenoidal and Irrotational vector fields. Vector identities – div(ɸA), curl (ɸA ), curl( grad ɸ), div(curl A). Hours – 10
Module -4  
Integral Calculus: Reduction formulae – and n are positive integers), evaluation of these integrals with standard limits (0 to π/2) and problems.

Differential Equations ; Solution of first order and first degree differential equations – Exact, reducible to exact and Bernoulli’s differential equations .Orthogonal trajectories in Cartesian and polar form. Simple problems on Newton’s law of cooling.

Hours – 10
Module -5
Linear Algebra : Rank of a matrix by elementary transformations, solution of system of linear equations – Gauss-elimination method, Gauss –Jordan method and Gauss-Seidel method Eigen values and Eigen vectors, Rayleigh’s power method to find the largest Eigen value and the corresponding Eigen vector. Linear transformation, diagonalisation of a square matrix . Reduction of Quadratic form to Canonical form Hours – 10

Course outcomes:
On completion of this course, students are able to

  • Use partial derivatives to calculate rates of change of multivariate functions.
  • Analyze position, velocity, and acceleration in two or three dimensions using the calculus of vector valued functions.
  • Recognize and solve first-order ordinary differential equations, Newton’s law of cooling
  • Use matrices techniques for solving systems of linear equations in the different areas of Linear Algebra.
  • Question paper pattern:
  • The question paper will have ten questions.
  • Each full Question consisting of 16 marks
  • There will be 2 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 5 full questions, selecting one full question from each module.

Text Books:

  • B.S. Grewal, “Higher Engineering Mathematics”, Khanna publishers, 42nd edition, 2013.
  • Erwin Kreyszig, “Advanced Engineering MathematicsI, Wiley, 2013
  • Reference Books:
  • B.V. Ramana, “Higher Engineering M athematics”, Tata Mc Graw-Hill, 2006
  • N.P.Bali and Manish Goyal, “A text book of Engineering mathematics”, Laxmi publications, latest edition.
  • H.K. Dass and Er. RajnishVerma, “Higher Engineerig Mathematics”, S.Chand publishing, 1st edition, 2011.
For all other BE/B.Tech 1st Sem Subject syllabus do follow VTU 1st Sem BE / B.Tech Syllabus CBCS (2015-16) Scheme for Chemistry Group.
For all other BE/B.Tech 2nd Sem Subject syllabus do follow VTU 2nd Sem BE / B.Tech Syllabus CBCS (2015-16) Scheme for Chemistry Group.

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1 Comment

  1. Jasbir

    Which is the best text book to refer..?

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