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Visvesvaraya Technological University VTU
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- Differential Calculus - I - ( 4 - 17 )
- Leibnitz's Theorm - ( 18 - 21 )
- Polar curve - ( 22 - 48 )
- Differential Calculus - II - ( 49 - 50 )
- Taylor's mean value Theorm - ( 51 - 68 )
- Partial Differentiation - ( 69 - 81 )
- Vector Calculus - ( 82 - 83 )
- Vector Function - ( 84 - 104 )
- Integral Calculus - ( 105 - 125 )
- Linear Algebra - ( 126 - 127 )
- Elementary transformation - ( 128 - 140 )
- Gauss -jordan method - ( 141 - 142 )
- Gauss-seidel method - ( 143 - 147 )
- Linear Transformation - ( 148 - 150 )
- Eigen values and Eigen vectors - ( 151 - 156 )
- Quadratic forms - ( 157 - 162 )
- Rayleigh's power method - ( 163 - 165 )

Topic:

ENGINEERING MATHEMATICS-I
15MAT11
SYLLABUS
Engineering Mathematics-I
Subject Code: 15MAT11
IA Marks: 20
Hours/Week: 04
Exam. Hours: 03
Total Hours: 50
Exam. Marks: 80
Course Objectives
To enable students to apply knowledge of Mathematics in various
engineering fields by making hem to learn the following:
• nth derivatives of product of two functions and polar curves.
• Partial derivatives.
• Vectors calculus.
• Reduction formulae of integration to solve First order
differential equations
• Solution of system of equations and 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 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(without proof) and problems.
10hrs
Module –2
Differential Calculus -2
Taylor‟s and Maclaurin‟s theorems for function of o ne variable(statement
only)- problems. Evaluation of Indeterminate forms.
Partial derivatives – Definition and simple problems, Euler‟s
theorem(without proof) – problems, total derivatives, partial differentiation
of composite functions-problems, Jacobians-definition and problems .
10hrs
DEPT OF MATHS, SJBIT
Page 1

ENGINEERING MATHEMATICS-I
15MAT11
Module –3
Vector Calculus:
Derivative of vector valued functions, Velocity, Acceleration and related
problems, Scalar and Vector point functions.Definition Gradient,
Divergence, Curl- problems . Solenoidal and Irrotational vector fields.
Vector identities - div ( F A), curl ( F A),curl (grad F ), div (curl A).
10hrs
Module- 4
Integral Calculus:
Reduction formulae ∫ sinnx dx ∫cosnx dx ∫sinnxcosmxdx,, (m and n are
positive integers), evaluation of these integrals with standard limits (0 to л/2)
and problems.
Differential Equations:
Solution of first order and first degree differential equations – Exact,
reducible to exact and Bernoulli‟s differential equations. Applicationsorthogonal trajectories in Cartesian and polar forms. Simple problems on
Newton‟s law of cooling.
10hrs
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. Rayleigh‟s power method to find the
largest Eigen value and the corresponding Eigen vector. Linear
transformation, diagonalisation of a square matrix, Quadratic forms,
reduction to Canonical form
10hrs
COURSE OUTCOMES
On completion of this course students are able to
Use partial derivatives to calculate rates of change of multivariate
functions
Analyse 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.
DEPT OF MATHS, SJBIT
Page 2

ENGINEERING MATHEMATICS-I
15MAT11
Engineering Mathematics – I
Module I : Differential Calculus- I…………….3 - 48
Module II : Differential Calculus- II……………49 -81
Module III: Vector Calculus………………........82-104
Module IV : Integral Calculus…………………105-125
Module V : Linear Algebra ……………………126-165
DEPT OF MATHS, SJBIT
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ENGINEERING MATHEMATICS-I
15MAT11
MODULE I
DIFFERENTIAL CALCULUS-I
CONTENTS:
Successive differentiation …………………………………………..3
nth derivatives of some standard functions…………………...7
Leibnitz‟s theorem (without proof)………………………..…16
Polar curves
Angle between Polar curves…………………………………….20
Pedal equation for Polar curves………………………………...24
Derivative of arc length………………………………………….28
Radius of Curvature……………………………………………….34
Expression for radius of curvature in case of Cartesian Curve …35
Expression for radius of curvature in case of Parametric
Curve………………………………………………………………..36
Expression for radius of curvature in case of Polar Curve……...41
Expression for radius of curvature in case of Pedal Curve……...43
DEPT OF MATHS, SJBIT
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