ENGINEERING MATHEMATICS – II -- Diploma Karnataka 2020



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 = (y2y1) (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 typexnexdx

, 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.


Text Box: Course outcome:

 

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.

Text Box: Mapping Course Outcomes with Program Outcomes:

 

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.

6.     E-books:www.mathebook.net

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


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