Engineering Mathematics-II
Course code: MAT201
Credits:(3:1:0)
Prerequisites: Differential calculus, Integral calculus.
Contact hours: 42 + 14 = 56
Course coordinator(s): Dr. V. Ramachandramurthy & Dr. N. L. Ramesh
 Course Objectives:
The student will
1. Learn to determine radius of curvature, power series expansion using Taylor’s and
Maclaurin’s series for function of one/two variables.
2. Learn to solve analytically first order linear and non linear ordinary differential equations.
3. Learn to solve second and higher order linear differential equations with constant /variable
coefficients.
4. Learn to evaluate improper integrals using Beta and Gamma functions.
5. Learn to use Laplace transform method to solve initial and boundary value problems.
 Course contents:
Unit I
Differential Calculus - II: Derivatives of arc length, curvature, radius of curvature.
Taylor’s theorem and Maclaurin’s series (without proof) Indeterminate forms, Taylor’s and
Maclaurin’s theorem for functions of two variables (without proof), maxima and minima of
functions of two variables, Lagrange’s method of undetermined multipliers.
Unit II
First order and first degree differential equations and its applications: Exact differential
equations, Reducible to exact differential equations, application of ODEs to find orthogonal
trajectories and to solve simple problems related to engineering applications.
Nonlinear differential equations: Equations solvable for p, equations solvable for y, equations
solvable for x, general and singular solutions, Clairauit’s equations and equations reducible to
Clairauit’s form.
Unit III
Linear differential equations of higher order: Linear differential equation of second and
higher order with constant co-efficients. Solution of second order linear differential equations
using the
method of variation of parameters. Cauchy’s and Legendre’s linear differential
equations. Initial and boundary value problems. Engineering applications.
Unit IV
Beta and Gamma Function: Definition, Relation between Beta and Gamma Function, Problems.
Laplace transforms I: Definition, transforms of elementary functions, properties of Laplace
transforms, existence conditions, transform of derivatives, integrals, multiplication by t n, division
by t, evaluation of integrals by Laplace transforms, unit–step function, unit–impulse function.
Unit V
Laplace transforms II: Laplace transforms of Periodic function, Inverse transforms, convolution
theorem, solution of linear differential equations differential equations and simultaneous linear
differential equations using Laplace transforms. Engineering applications.
Text Books:
1. Erwin Kreyszig –Advanced Engineering Mathematics, Wiley publication, 10th edition, 2015.
2. B.S. Grewal – Higher Engineering Mathematics, Khanna Publishers, 43rd edition, 2014.
Reference Books:
1. Peter V. O’ Neil – Advanced Engineering Mathematics, Thomson Brooks/Cole, 7th edition, 2011.
2. Glyn James – Advanced Modern Engineering Mathematics, Pearson Education, 4th edition, 2010.
Course Delivery:
The Course will be delivered through lectures, class room interaction and exercises.
Course Assessment and Evaluation:
What
To whom
Direct Assessment Methods
Internal assessment
tests
CIE
Assignments
Indirect Assessment
Methods
Max
Marks
Evidence
collected
Contributing
to course
outcomes
30
Blue books
1 to 5
Twice
10(5+5)
Once
05
Quiz test 2
Once
05
Standard
examination
End of Course
100
Quiz test 1
SEE
When/Where
(Frequency in the
course)
Thrice (Average of
the best two will be
computed)
Students
Middle of the course
Student feedback
Students
End of Course survey
Assignment
reports
Quiz
answers
Quiz
answers
Answer
scripts
1,2,3,4
1,2,3,4
1 to 5
Feedback
forms
1 to 5, delivery
of the course
Questionnaire
1 to 5,
Effectiveness
of delivery of
instructions
and
assessment
methods
End of course
1,2,3,4
Questions for CIE and SEE will be designed to evaluate the various educational components
(Bloom’s taxonomy) such as:



Remembering and Understanding the course contents (Weightage: 25%)
Applying the knowledge acquired from the course (Weightage: 35%)
Analyzing and evaluating the related information (Weightage: 40%)
 Course Outcomes
The students will be able to,
1. Determine the radius of curvature, find extreme values of a given function.
2. Express a function as infinite series using Taylor’s and Maclaurin’s theorems.
3. Solve analytically first order linear and non-linear ordinary differential equations.
4. Solve second order linear differential equations with constant/variable coefficients
5. Solve initial and boundary value problems using Laplace transform method.