ENGINEERING  MATHEMATICS - I

2014 Scheme

Subject Code: 14MAT11

IA Marks: 25

Hours/Week: 04

Exam. Hours: 03

Total Hours: 50

Exam. Marks: 100

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 for 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 and problems. 10 Hours

Module – 2

Differential Calculus - 2:

Taylor’s and Maclaurin’s theorems for function of one variable(statement only)- problems.  Evaluation of Indeterminate forms.
Partial derivatives – Definition and simple problems,   Euler’s theorem – problems, total derivatives, partial differentiation of composite functions, Jacobians-definition and problems, extreme values of functions of two variables. 10 Hours

Module – 3

Vector Calculus:

Derivative of  vector valued functions, Velocity,  Acceleration  and related problems, Scalar and Vector point functions, Gradient, Divergence, Curl, Solenoidal and Irrotational vector fields. Vector identities - div (φA), curl (φA), curl (grad φ), div (curl A).
Differentiation under integral sign using   Leibnitz rule   with constant and variable limits.
Curve  Tracing -   General rules to trace   Cartesian, polar and parametric curves.  10 Hours

Module – 4

Integral Calculus:

Reduction formulae   (m 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.
Applications – orthogonal trajectories, Newton’s law of cooling, flow of electricity, laws of decay and growth. 10 Hours

Module – 5

Linear Algebra:

Rank of a matrix by elementary transformations, solution of system of linear equations - Gauss-elimination method, Gauss-Seidel method and L-U decomposition method.
Linear transformation, diagonalisation of a square matrix, Quadratic forms, reduction to Canonical form by orthogonal transformation, Rayleigh’s power method to find the largest Eigen value and the corresponding Eigen vector. 10 Hours

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.
• Trace the curves which are useful in applications of integration in finding the length, area and volume.
• Recognize and solve first-order ordinary differential equations, model simple electrical circuits, projectile motion and Newton’s law of cooling and laws of decay and growth, and
• Use matrices, determinants and techniques for solving systems of linear equations in the different areas of Linear Algebra.

Scheme of examination:

• Two full questions (with a maximum of four sub questions) of twenty marks each to be set from each module. Each question should cover all contents of the respective module.
• Students have to answer five full questions choosing one full question from each module.

Text Books:

1. B.S. Grewal, "Higher Engineering Mathematics", Khanna publishers, 42nd edition, 2013.
2. Erwin Kreyszig, "Advanced Engineering Mathematics"-Vol-I & II, Wiley, 2013

Reference Books:

1. B.V. Ramana, "Higher Engineering Mathematics", Tata Mc Graw-Hill, 2006
2. N.P.Bali and Manish Goyal, "A text book of Engineering mathematics”, Laxmi publications, latest edition.
3. H.K.Dass and Er. RajnishVerma, "Higher Engineerig Mathematics", S.Chand publishing, 1st edition, 2011.

All the Best ..!!