Differential and Vector Calculus

Paper Code: 
25CBDA415
Credits: 
03
Periods/week: 
03
Max. Marks: 
100.00
Objective: 

This course aims  at  enabling  the  students to  know  various  concepts and  principles of differential calculus and  its applications.

Course Outcomes: 

Course

Learning outcome

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course

Code

Course

Title

CO223.  Compute the derivative of the function  of  one variable.

CO224. Demonstrate a working knowledge and     use     of    mean value      theorems    in real  life.

CO225. Calculate higher   order derivatives  and    able to apply Leibnitz theorem.

CO226.     Determine partial  derivatives and extreme values of the functions   of   two   or more  variables. CO227.     Determine the         vector,       its magnitude              and direction     to     derive scalar       and      vector products. CO228.Contribute effectively  in  course- specific  interaction

Approach in teaching: Interactive Lectures, Group Discussion, Case Study

 

Learning activities for the students: Self-learning assignments, Machine Learning exercises, presentations

Class test, Semester end examinations, Quiz, Practical Assignments, Presentation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

25CBDA

415

 

 

 

 

 

 

 

 

 

 

 

 

 

Differential and Vector Calculus (Theory)

 

9.00
Unit I: 

Functions of single variable  Definition  of  the  limit  of  a  function,  Continuity, Types  of  discontinuities,  Differentiability, Maxima  and  Minima.

9.00
Unit II: 

Mean Value Theorems  Rolle  ’s  Theorem,  Lagrange’s  and   Cauchy’s   Mean   Value  Theorems,  Taylor’s   theorem (Lagrange’s form  and  Cauchy’s  forms  of remainder), Maclaurin’s  theorem and  expansions, Indeterminate forms.

9.00
Unit III: 

Successive and Partial Differentiation  Successive   differentiation,   nth    derivatives   of    functions,   Leibnitz    theorem   and    its applications, Partial  differentiation, First  and  higher order derivatives, Partial  derivatives, Total derivative.

9.00
Unit IV: 

Functions of  two variables  Differentiation of  the  homogeneous  functions, Euler’s  theorem, Taylor’s  theorem for  two variables, Maxima  and  Minima of functions of two  variables, Lagrange’s multipliers for two variables

9.00
Unit V: 
Vector Calculus  Vectors,  Types   of   Vectors,  Operations  on   Vectors,  Addition   of  Vectors   Properties  of Operation of Addition,  Subtraction, Properties of Operation of Subtraction Multiplication  by a scalar, , Product of Two Vectors  (Dot and  Cross  Product) & its properties.
Scalar  and  vector point  function, Gradient, Directional derivatives, Divergence and  curl of a vector point  function.
ESSENTIAL READINGS: 

1.     G.B. Thomas- M. D. Weir and  J. Hass-  Thomas Calculus-  14th  ed.-  Pearson Education India, 2018

2.     Shanti  Narayan and  P.K. Mittal, Differential Calculus,  S. Chand  Pub.  House, 2018.

 

REFERENCES: 

SUGGESTED READINGS:

1.     F.  Ayres  and  E.  Mendelson-  Schaum's Outline  of  Calculus-  10th  ed.  USA:  Mc. Graw Hill.- 2015.

2.     J. Stewart- Single  Variable  Essential Calculus: Early Transcendentals- 2nd  ed.:

3.     Belmont- USA: Brooks/Cole Cengage Learning.- 2013.

4.     M. Spivak-  Calculus-  4th  ed.-  Cambridge University  Press- 2008.

5.     T.M. Apostol-  Calculus-  Vol-II- Wiley India  Pvt. Ltd.- 2011.linear

e RESOURCES

1.    Epathshala, calculus  :http://epathshala.nic.in/eresources.php?id=185

2.    Calculus,  academia: https://www.academia.edu/34706287/Calculus

JOURNALS

1.    International Journal of Mathematics, World Scientific:https://www.worldscientific.com/worldscinet/ijm

 

Academic Year: 
2025-26
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