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. | 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.
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