Prerequisites:
Engineering MathematicsI, in
First Semester Diploma curriculum.
Course Objectives:
1. Apply the concept of straight
line and conic section in engineering field.
2. Determine derivatives of
functions involving two variables.
3. Apply the concepts of
differentiation in physics and engineering courses.
4. Evaluate the integrals of
functions of two variables.
5. Apply the concepts of
definite integrals and its application over a
region.
6. Solve the ODE of first
degree, first order in engineering field.
Course Contents:
Topic and
Contents 
Hours 
Marks 
Unit1:
COORDINATE GEOMETRY 
08hr 
23 
a. Straight lines: Different forms of equations of straight lines: y = mx + c, y − y_{1} = m(x − x_{1}), y − y_{1} = (^{y}^{2}^{–y}^{1}) (x − x_{1}). x2–x1 General equation of a lineax
+ by + c = o (graphical representation
and statements) and problems on above equations. Equation of lines through a
point and parallel or perpendicular to a given line. Problems. b. Conic Section: Definition of conic section. Definition of axis, vertex,
eccentricity, focus and length of latus rectum. Geometrical representation of
parabola, ellipse and hyperbola: Equations
of parabolay^{2} = 4ax, 
04 hr 04hr 

Equation of ellipse ^{x}2 +
^{y}2 = 1and a2 b2 Equation of hyperbola ^{x}2 −
^{y}2 = 1(without proof of above 3 a2 b2 equations). Equations of parabola, ellipse and hyperbola
with respect to xaxis as axis of
conic. Finding axes, vertices, eccentricity, foci and length of lattice rectum
of conics. Problems on finding the above said equations with direct
substitution. 


UNIT – 2: DIFFERENTIAL
CALCULUS 
15hr 
39 
Differentiation. Definition of increment and increment ratio. Definition of derivative
of a function. Derivatives of functions ofx^{n}, sin x, cos xand tan xwith respect to ‘x’ from first principle method. List
of standard derivatives of cosecx, secx, cotx, log_{e} x, a^{x}, e^{x} etc. Rules of differentiation: Sum, product, quotient rule and problems on
rules. Derivatives of function of a function (Chain rule) and problems.
Inverse trigonometric functions and their derivatives. Derivative of Hyperbolic functions, Implicit functions, Parametric
functions and problems. Logarithmic differentiation of functions of the type u^{v},where u
and v are functions of x.Problems. Successive differentiation
up to second order and problems on all the above types of functions. 


UNIT – 3:
APPLICATIONS OF DIFFERENTIATION. 
07hr 
17 
Geometrical meaning of derivative. Derivative as slope. Equations of
tangent and normal to the curve y = f(x) at a given point (statement only).
Derivative as a rate measure i.e.to find the rate of change of displacement,
velocity, radius, area, volume using differentiation. Definition of
increasing and decreasing function. Maxima and minima of a function. 


UNIT4: INTEGRAL CALCULUS. 
12hr 
30 
Definition
of Integration. List of standard integrals. Rules of integration (only
statement) 1.Ú kf (x)dx = k Ú f (x)dx. 2. Ú{f(x) ± g(x)}dx = Úf(x)dx± Úg(x)dx problems. Integration by substitution method. Problems. Standard
integrals of the type 


1.Ú dx = 1 tan^{1}Ê x ˆ + c 2. Ú dx = sin^{1}Ê x ˆ + c . x^{2}
+ a^{2} a Á a ˜ 2 2 Á a ˜ Ë ¯ a  x Ë ¯ 3. Ú dx = 1 sec^{}^{1}Ê x ˆ + c Á ˜ x x2  a2 a Ë a ¯ (1 to 3 with proof) 4. Ú dx = 1 logÊ x  a ˆ + c if x > a > 0. x^{2}  a^{2} 2a Á x + a ˜ Ë ¯ 5. Ú dx = 1 logÊ a + x ˆ + c if a
> x > 0. ( 4 &
5 without proof) a^{2}  x^{2} 2a Á a  x ˜ Ë ¯ and problems on above results Integration by parts of the type∫
x^{n}e^{x}dx ,∫ xsinxdx, ∫ xcosxdx, ∫ xlogxdx , ∫ logxdx,∫ tan^{–1} x dx, ∫ x sin^{2} x dx , ∫ x cos^{2} x dxwhere n=1, 2. Rule of integration by parts. Problems 


UNIT – 5: DEFINITE
INTEGRALS AND ITS APPLICATIONS 
05 hr 
22 
Definition of Definite integral. Problems
on all types of integration methods. Area, volume, centres of gravity and moment of
inertia by integration method. Simple problems. 


UNIT – 6: DIFFERENTIAL
EQUATIONS. 
05 hr 
14 
Definition, example, order
and degree of differential equation with examples. Formation of differential
equation by eliminating arbitrary constants up to second order. Solution of
O. D. E of first degree and first order by variable separable method. Linear
differential equations and its solution using integrating factor. 


Total 
52 
145 
Course Delivery:
The Course will be
delivered through lectures, class room interaction, exercises, assignments and
selfstudy cases.
On
successful completion of the course, the student will be able to:
1. Formulate
the equation of straight lines and conic sections in different forms.
2. Determine
the derivatives of different types of functions.
3.
Evaluate the successive derivative of functions and its
application in tangent, normal, rate measure, maxima and minima.
4. Evaluate
the integrations of algebraic, trigonometric and exponential function.
5.
Calculate the area under the curve, volume by
revolution, centre of gravity and radius of gyration using definite integration.
6.
Form and solve ordinary differential equations
by variable separable method and linear differential equations.
CO 
Course Outcome 
PO Mapped 
Cognitive Level 
Theory Sessions 
Allotted marks on cognitive levels 
TOTAL 

R 
U 
A 

CO1 
Formulate the equation of straight lines and
conic sections in different forms. 
1,2,3,10 
R/U/A 
08 
6 
5 
12 
23 
CO2 
Determine the derivatives of different types of functions. 
1,2,3,10 
R/U/A 
15 
12 
15 
12 
39 
CO3 
Evaluate the successive
derivative of functions and its application in tangent, normal, rate measure, maxima and minima. 
1,2,3,10 
R/U/A 
07 
6 
5 
6 
17 
CO4 
Evaluate
the integrations of algebraic, trigonometric and exponential function 
1,2,3,10 
R/U/A 
12 
9 
15 
6 
30 
CO5 
Calculate the area under
the curve, volume by revolution, centre of gravity and radius of gyration
using definite integration 
1,2,3,10 
R/U/A 
05 
6 
10 
6 
22 
CO6 
Form and solve ordinary
differential equations by variable separable method and linear differential equations. 
1,2,3,10 
R/U/A 
05 
3 
5 
6 
14 


Total Hours of
instruction 
52 
Total marks 
145 
RRemember;
UUnderstanding; AApplication
Course
outcomes –Program outcomes mapping strength
Course 
Programme Outcomes 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

Engineering MathsII 
3 
3 
3 
 
 
 
 
 
 
3 
Level
3 Highly Addressed, Level 2Moderately Addressed, Level 1Low Addressed.
Method is to relate
the level of PO with
the number of hours devoted
to the COs which address
the given PO. If
>40% of classroom sessions addressing a particular PO, it is considered that
PO is addressed at Level
3
If 25 to 40% of classroom sessions
addressing a particular PO, it is considered that
PO is addressed at Level
2 If 5 to 25% of classroom sessions addressing a particular PO, it is considered that
PO is addressed at Level
1
If < 5% of
classroom sessions addressing a particular PO, it is considered that PO is
considered notaddressed.
Reference Books:
1. NCERT Mathematics Text books
of class XI and XII.
2. Higher Engineering Mathematics
by B.S Grewal, Khanna publishers, New Delhi.
3.
Karnataka State PUC mathematics Text Books of I &
II PUC by H.K. Dass and Dr. Ramaverma published by S.Chand & Co.Pvt. ltd.
4. CBSE Class Xi & XII by
Khattar & Khattar published PHI Learning Pvt. ltd.,
5. First and Second PUC
mathematics Text Books of different authors.
7. www.freebookcentre.net/mathematics/ introductorymathematics books.html
Course Assessment and Evaluation:
Method 
What 
To whom 
When/where (Frequency in the course) 
Max Marks 
Evidence collected 
Contributing
to
course outcomes 

DIRECT ASSMENT 
*CIE 
Internal Assessment Tests 
Student 
Three tests (Average of Three tests to
be computed). 
20 
Blue books 
1 to 6 
Assignment s 
Two
Assignments based on CO’s (Average marks
of Two Assignments shall be rounded
off to the next higher digit.) 
5 
Log of record 
1 to 6 

Total 
25 



*SEE 
Semester End Examinatio n 
End of the course 
100 
Answer
scripts at BTE 
1 to 6 

INDIRECT ASSESSMENT 
Student
feedback 
Student 
Middle of the course 
NA 
Feedback forms 
1 to 3, delivery of the course 

End of Course survey 
End of course 
Questionnaire 
1 to 6, Effectiveness of delivery of
instructions and assessment methods 
*CIE –
Continuous Internal Evaluation *SEE – Semester End
Examination
Note: I.A. test shall be conducted
for 20 marks. Average marks of three tests shall be rounded off to the
next higher digit.
Composition of Educational Components:
Questions for CIE
and SEE will be designed to evaluate the various educational components
(Bloom’s taxonomy) such as:
Sl. No. 
Educational
Component 
Weightage (%) 
1 
Remembering 
31 
2 
Understanding 
41 
3 
Applying
the knowledge acquired from the course 
25 

Analysis
Evaluation 
3 