Pre-requisites:
Engineering Mathematics-I, 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 |
|
Unit-1:
COORDINATE GEOMETRY |
08hr |
23 |
|
a. Straight lines: Different forms of equations of straight lines: y = mx + c, y − y1 = m(x − x1), y − y1 = (y2–y1) (x − x1). 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 parabolay2 = 4ax, |
04 hr 04hr |
|
|
Equation of ellipse x2 +
y2 = 1and a2 b2 Equation of hyperbola x2 −
y2 = 1(without proof of above 3 a2 b2 equations). Equations of parabola, ellipse and hyperbola
with respect to x-axis 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 ofxn, sin x, cos xand tan xwith respect to ‘x’ from first principle method. List
of standard derivatives of cosecx, secx, cotx, loge x, ax, ex 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 uv,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. |
|
|
|
UNIT-4: 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-1Ê x ˆ + c 2. Ú dx = sin-1Ê x ˆ + c . x2
+ a2 a Á a ˜ 2 2 Á a ˜ Ë ¯ a - x Ë ¯ 3. Ú dx = 1 sec-1Ê 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. x2 - a2 2a Á x + a ˜ Ë ¯ 5. Ú dx = 1 logÊ a + x ˆ + c if a
> x > 0. ( 4 &
5 without proof) a2 - x2 2a Á a - x ˜ Ë ¯ and problems on above results Integration by parts of the type∫
xnexdx ,∫ xsinxdx, ∫ xcosxdx, ∫ xlogxdx , ∫ logxdx,∫ tan–1 x dx, ∫ x sin2 x dx , ∫ x cos2 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
self-study 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 |
|||
R-Remember;
U-Understanding; A-Application
Course
outcomes –Program outcomes mapping strength
|
Course |
Programme Outcomes |
|||||||||
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
|
Engineering Maths-II |
3 |
3 |
3 |
- |
- |
- |
- |
- |
- |
3 |
Level
3- Highly Addressed, Level 2-Moderately Addressed, Level 1-Low 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 not-addressed.
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/ introductory-mathematics -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 |
