Calculus

GANPAT UNIVERSITY

FACULTY OF ENGINEERING & TECHNOLOGY

Programme

Bachelor of Technology

Branch/Spec.

Computer Science & Engineering (CSE/CBA/CS/BDA)

Semester

I

Version

1.0.0.1

Effective from Academic Year

2022-23

Effective for the batch Admitted in

June 2022

Subject  code

2HS101

Subject Name

CALCULUS

Teaching scheme

Examination scheme (Marks)

(Per week)

Lecture (DT)

Practical(Lab.)

Total

CE

SEE

Total

L

TU

P

TW

Credit

3

1

0

0

4

Theory

40

60

100

Hours

3

1

0

0

4

Practical

0

0

0

Pre-requisites:

Trigonometry, Limit, Continuity, Integration, Differentiation

Learning Outcome:

After successful completion of this course, students must  be able to:

• Understand fundamentals of Differentiation and Integration.
• Apply above to various mathematical problems.
• Prepare him/her for finding Area and Volume.
• Use differentiation and integration of SCILAB libraries to solve  computational problems.

Theory syllabus

Unit

Content

Hrs

1

Differential Calculus :

Successive differentiation, Leibniz’s theorem (without proof),

Taylor's & Maclaurin's expansion of single variable function, Indeterminate forms.

14

2

Partial differentiation and its applications :

Partial and total differential coefficient, Euler’s theorem, Transformations, Geometrical, interpretation of partial derivatives, Tangent plane and Normal line, Jacobians, Taylor’s expansion for two variable function, Errors and approximations, Maxima and Minima for functions of two variables, Lagrange method of undetermined multipliers to determine stationary values.

16

3

Integral Calculus :

Reduction Formulae of sinn x dx,  cosn x dx, sinn x cosm x dx,  tan n x dxand  cotn x dx,Beta & Gamma function.

8

4

Multiple integrals :

Double integral, change of order of integration, transformation of variables by Jacobian only for double integration, change into polar coordinates in double integrals only, Triple integral.

7

Mooc Course

Course Name: Calculus of One Real Variable

Link: https://www.digimat.in/nptel/courses/video/109104124/L01.html

Practical content

Not Applicable

Text Books

1

Higher Engineering Mathematics by Dr. B. S. Grewal

Reference Books

1

Higher Engineering Mathematics Vol. I & II by Dr. K. R. Kachot.

2

Calculus and analytical geometry by G. B. Thomas and R. L. Finney

Course Outcomes:

COs

Description

CO1

Understand fundamentals of Differentiation and Integration.

CO2

Apply above to various mathematical problem.

CO3

Prepare him/her for finding Area and Volume

CO4

Use differentiation and integration of SCILAB libraries to solve  computational problems.

Mapping of CO and PO