DOC/LP/O1/28.02.02
LESSON PLAN
Sub Code & Name : MA2161 - MATHEMATICS – II
Year : First Year
Semester: II
UNIT - I
LP- FY-MA2161
LP Rev. No: 00
Date:01.02.2012
Page: 1 of 6
Unit Syllabus:
UNIT I: ORDINARY DIFFERENTIAL EQUATIONS (ODE)
Higher order linear differential equations with constant coefficients – Method of variation of
parameters – Cauchy’s and Legendre’s linear equations – Simultaneous first order linear
equations with constant coefficients.
.
OBJECTIVE:
 To solve differential equations of certain types, including systems of differential
equations that they might encounter in the same or higher semesters.
Session
No.
Topics to be covered
Time
(min.)
Ref
Teaching
Method
1
Solution of second and higher order linear ODE with
constant coefficients
Particular integrals of exponential and trigonometric
functions
Particular integrals of algebraic expression
Tutorial class
Particular integrals of the combinations of exponential and
trigonometric expressions
Particular integrals of the combinations of exponential and
algebraic expressions
Tutorial class
Method of Variation of parameters
Cauchy’s homogeneous linear differential equation
Extra problems
Legendre’s linear differential equation
Tutorial class
Simultaneous first order linear equations with constant
coefficients
Extra problems
CAT I
50
1,2,3,5
BB
50
1,2,3,5
BB
50
50
50
1,2,3,5
1,2,3,5
1,2,3,5
BB
BB
BB
50
1,2,3,5
BB
50
50
50
50
50
50
50
1,2,3,5
1,2,3,5
1,2,3,5
1,2,3,5
1,2,3,5
1,2,3,5
1,2,3,5
BB
BB
BB
BB
BB
BB
BB
50
40
1,2,3,5
BB
2
3
4
5
6
7
8
9
10
11
12
13
14
15
DOC/LP/O1/28.02.02
LESSON PLAN
Sub Code & Name : MA2161 - MATHEMATICS – II
Year : First Year
Semester: II
UNIT - II
LP- FY-MA2161
LP Rev. No: 00
Date: 01.02.2012
Page : 2 of 6
Unit syllabus:
UNIT II: VECTOR CALCULUS.
Gradient Divergence and Curl – Directional derivative – Irrotational and solenoidal vector
fields – Vector integration – Green’s theorem in a plane, Gauss divergence theorem and stokes’
theorem (excluding proofs) – Simple applications involving cubes and rectangular
parallelpipeds.
OBJECTIVE:
 To know the basics of vector calculus comprising of gradient, divergence and
curl and line, surface and volume integrals along with the classical theorems
involving them
Session
No.
Topics to be covered
Time
(min.)
Ref
Teaching
Method
16
Introduction to Gradient ,Divergence ,Curl
50
1,2,3,6
BB
17
18
19
20
21
22
23
24
Problems in Gradient ,Divergence, Curl
Directional derivative
Tutorial class
Irrotational and solenoidal vector fields
50
50
50
50
50
50
50
50
1,2,3,6
1,2,3,6
1,2,3,6
1,2,3,6
1,2,3,6
1,2,3,6
1,2,3,6
1,2,3,6
BB
BB
BB
BB
BB
BB
BB
BB
25
Simple applications involving
parallelpipeds.
Problems on Green’s theorem
50
1,2,3,6
BB
26
Problems on Gauss divergence Theorem
50
1,2,3,6
BB
27
28
29
Problems on Stoke’s Theorem
Verifications and Extra Problems
Tutorial class
50
50
50
1,2,3,6
1,2,3,6
1,2,3,6
BB
BB
BB
30
CAT II
40
Vector integration
Extra Problems
Tutorial class
Green’s Theorem, Gauss divergence Theorem and Stoke’s
Theorem (excluding proof)
cubes
and
rectangular
DOC/LP/O1/28.02.02
LESSON PLAN
Sub Code & Name : MA2161 - MATHEMATICS – II
Year : First Year
Semester: II
UNIT - III
LP- FY-MA2161
LP Rev. No: 00
Date: 01.02.2012
Page: 3 of 6
Unit Syllabus:
UNIT III: ANALYTIC FUNCTIONS
Functions of a complex variable – Analytic functions – Necessary conditions, Cauchy –
Riemann equation and Sufficient conditions (excluding proofs) – Harmonic and orthogonal
properties of analytic function – Harmonic conjugate – Construction of analytic functions –
Conformal mapping : w= z+c, cz, 1/z, and bilinear transformation.
OBJECTIVE:
 To understand analytic functions and their interesting properties.
 To know conformal mappings with a few standard examples that have direct
application
Session
No
Topics to be covered
Time
(min.)
Ref
Teaching
Method
31
Introduction to functions of a complex variable
50
1,2,5,6
BB
32
50
1,2,5,6
BB
50
1,2,5,6
BB
50
50
50
50
50
50
1,2,5,6
1,2,5,6
1,2,5,6
1,2,5,6
1,2,5,6
1,2,5,6
BB
BB
BB
BB
BB
BB
40
41
Definition – Analytic Function, Derivatives of Analytic
Function
Necessary and Sufficient conditions for a function to be
analytic
Problem using Cauchy Riemann Equations
Tutorial class
Properties of Analytic Function
Harmonic Function and Harmonic conjugate
Extra problems
Construction of Analytic Functions by using Milne’s
Thomson Method
Tutorial class
Conformal Mapping
50
50
1,2,5,6
1,2,5,6
BB
BB
42
43
44
45
Transformation: z + a, az ,1/z
Bilinear transformation
Tutorial class
CAT- III
50
50
50
40
1,2,5,6
1,2,5,6
1,2,5,6
BB
BB
BB
33
34
35
36
37
38
39
DOC/LP/O1/28.02.02
LESSON PLAN
Sub Code & Name : MA2161 - MATHEMATICS – II
Year : First Year
Semester: II
UNIT - IV
LP- FY-MA2161
LP Rev. No: 00
Date: 01.02.2012
Page: 4 of 6
Unit Syllabus:
UNIT IV: COMPLEX INTEGRATION
Complex integration – Statement and applications of Cauchy’s integral theorem and Cauchy’s
integral formula – Taylor and Laurent expansions – Singular points – Residues – Residue
theorem – Application of residue theorem to evaluate real integrals – Unit circle and semicircular contour(excluding poles on boundaries).
OBJECTIVE:
 To grasp the basics of complex integration and the concept of contour
integration which is important for evaluation of certain integrals encountered in
practice.
Session
no.
Topics to be covered
Time
(min)
Ref
Teaching
Method
46
Complex Integration
50
1,2,3,5
BB
47
48
49
50
51
52
53
54
Statement and Applications of Cauchy integral Theorem
Tutorial class
Taylor Series expansion
Laurent series expansion
Tutorial class
Singularities and Residues
Cauchy’s Residue Theorem
50
50
50
50
50
50
50
50
1,2,3,5
1,2,3,5
1,2,3,5
1,2,3,5
1,2,3,5
1,2,3,5
1,2,3,5
1,2,3,5
BB
BB
BB
BB
BB
BB
BB
BB
55
56
Tutorial class
Contour integration over unit circle
50
50
1,2,3,5
1,2,3,5
BB
BB
57
50
1,2,3,5
BB
58
Contour integration over semicircular
contours (excluding poles on boundaries)
Extra Problems
50
1,2,3,5
BB
59
Tutorial class
50
1,2,3,5
BB
60
CAT IV
40
Cauchy’s integral formula
DOC/LP/O1/28.02.02
LESSON PLAN
Sub Code & Name : MA2161 - MATHEMATICS – II
Year : First Year
Semester: II
UNIT - V
LP- FY-MA2161
LP Rev. No: 00
Date: 01.02.2012
Page: 5 of 6
Unit Syllabus:
UNIT V:LAPLACE TRANSFORM
Laplace transform – Conditions for existence – Transform of elementary functions – Basic
properties – Transform of derivatives and integrals – Transform of unit step function and
impulse functions – Transform of periodic functions.
Definition of Inverse Laplace transform as contour integral – Convolution theorem (excluding
proof) – Initial and Final value theorems – Solution of linear ODE of second order with
constant coefficients using Laplace transformation techniques.
OBJECTIVE:


To have a sound knowledge of Laplace transform and its properties.
To solve certain linear differential equations using the Laplace transform
technique which have applications in other subjects of the current and higher
semesters.
Session
No.
Topics to be covered
Time
(min.)
Ref
Teaching
Method
61
Definition of laplace transform and conditions for existence
50
1,2,5,6
BB
62
63
64
65
66
67
68
Transform of elementary functions
Basic properties
Extra problems
Transform of derivatives and integrals
Tutorial Class
Transform of unit step function and unit impulse function
Transform of periodic function
50
50
50
50
50
50
50
1,2,5,6
1,2,5,6
1,2,5,6
1,2,5,6
1,2,5,6
1,2,5,6
1,2,5,6
BB
BB
BB
BB
BB
BB
BB
69
Definition of Inverse laplace transform as contour Integral
50
1,2,5,6
BB
70
71
Extra problems using properties of inverse laplace transform
Convolution theorem(excluding proof)
50
50
1,2,5,6
1,2,5,6
BB
BB
72
73
Initial and Final value theorems
50
50
1,2,5,6
1,2,5,6
BB
BB
74
Tutorial class
50
1,2,5,6
BB
75
CAT-V
40
Solution of linear ODE of second order with constant coefficients
using Laplace transformation techniques
DOC/LP/O1/28.02.02
LESSON PLAN
Sub Code & Name : MA2161 - MATHEMATICS – II
Year : First Year
Semester: II
LP- FY-MA2161
LP Rev. No: 00
Date: 01.02.2012
Page: 6 of 6
Course Delivery Plan:
1
Week
I II
2
3
4
5
6
7
8
9
10
11
12
13
14
15
I II I II I II I II I II I II I II I II I II I II I II I II I II
I II
U N I T - 1 U N I T - 2 U N I T - 3 U N I T - 4 U N I T Units
Text book:
rd
1. Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, 3 Edition, Laxmi
Publications (p) Ltd., (2008).
th
2. Grewal. B.S, “Higher Engineering Mathematics”, 40 Edition, Khanna Publications,
Delhi, (2007).
REFERENCES:
3. Ramana B.V, “Higher Engineering Mathematics”,Tata McGraw Hill Publishing Company,
New Delhi, (2007).
rd
4. Glyn James, “Advanced Engineering Mathematics”, 3 Edition, Pearson Education,
(2007).
th
5. Erwin Kreyszig, “Advanced Engineering Mathematics”, 7 Edition, Wiley India, (2007).
rd
6. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”, 3 Edition, Narosa
Publishing House Pvt. Ltd., (2007).
Prepared by
Approved by
Name
SUBHA. E
Dr.R.Muthucumaraswamy
Designation
Assistant Professor
Professor & HOD – AM
Date
01.02.2012
01.02.2012
Signature
5