DIFFERENTIAL & VECTOR CALCULUS

Paper Code: 
CBDA 415
Credits: 
3
Periods/week: 
3
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 (COs).

Course outcome (at course level)

Learning and teaching strategies

Assessment Strategies 

On completion of this course, the students will:

CO186. Understand and use the notion of derivative of the function of one variable.

CO187. Demonstrate a working knowledge and use of mean value theorems in real life.

CO188. Calculate higher order derivatives and able to apply Leibnitz theorem.

CO189. Determine partial derivatives and extreme values of the functions of two or more variables.

CO190. Determine the vector, its magnitude and direction to derive scalar and vector products.

Approach in teaching:

Interactive Lectures, Group Discussion, Tutorials, Case Study

 

Learning activities for the students:

Self-learning assignments, Machine Learning exercises, presentations

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

 

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: 
  • G.B. Thomas- M. D. Weir and J. Hass- Thomas Calculus- 14th ed.- Pearson Education India, 2018
  • Shanti Narayan and P.K. Mittal, Differential Calculus, S. Chand Pub. House, 2018.

 

REFERENCES: 

SUGGESTED READING:

  • F. Ayres and E. Mendelson- Schaum's Outline of Calculus- 10th ed. USA: Mc. Graw Hill.- 2015.
  • J. Stewart- Single Variable Essential Calculus: Early Transcendentals- 2nd ed.:
  • Belmont- USA: Brooks/Cole Cengage Learning.- 2013.
  • M. Spivak- Calculus- 4th ed.- Cambridge University Press- 2008.
  • T.M. Apostol- Calculus- Vol-II- Wiley India Pvt. Ltd.- 2011.linear

 

E RESOURCES:

 

JOURNALS:

 

Academic Year: 
2022-23
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