Multivariable Calculus

Paper Code: 
24DMAT615(B)
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Evaluate the concept of functions of several variables.
  2. Explore partial derivatives and several of its consequences.
  3. Introduce double and triple integrals along with line integrals which are fundamental to all streams where calculus can be used.

 

Course Outcomes: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

24DMAT 615(B)

 

 

 

 

Multivariate Calculus

 (Theory)

 

 

 

 

 

 

CO151: Analyze the concept of functions with multiple input variables, continuity for functions, differentiability criterias.

CO152: Explore applications of directional derivatives, differential operators, Partial derivatives.

CO153: Evaluate higher - order differentiation and extrema of functions of two variables.

CO154: Evaluate the concept of implicit functions and jacobian.

CO155: Determine the cartesian coordinate system and integration as a mathematical operation.

CO156: Contribute effectively in course specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Assigned tasks

 

 

 

 

Class Test, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

 

 

 

Unit I: 
Functions of several variables
18.00

Functions of several variables, Limit and continuity of functions, Differentiability of the functions, Sufficient conditions for continuity and differentiability.

 

Unit II: 
Differentiation of Functions of several variables
18.00

Directional derivatives of a function of two variables, Algebra of differential functions, Partial derivatives of higher order, Change in the order of partial derivation, Sufficient condition for the equality of fxy=fyx Schwarz’s theorem, Young’s theorem.

Unit III: 
Mean value theorem and Properties
18.00

Differentials of higher order, Composite function, Differentials of higher order of a composite function, Mean value theorem for two variables, Taylor’s theorem for function of two variables, Extrema of functions of two variables, Method of Lagrange multipliers.

 

Unit IV: 
Implicit functions and Jacobian
18.00

Implicit functions, Existence and derivability of implicit functions, Jacobian, Theorems on Jacobians, Jacobian of implicit function, Necessary and sufficient conditions for a jacobian to vanish.

 

Unit V: 
Co-ordinate system
18.00

Cartesian, cylindrical polar, spherical polar, Integration on R2 and R3, Leibnitz rule.

 

Essential Readings: 
  • David V. Widder, Advanced calculus, PHI, New Delhi, 2007.
  • S C Mallik and S Arora: Mathematical Analysis, New Age International Publications.
  • Dipak Chatterjee, real analysis, phi learning pvt. Ltd, Delhi, 2015.
  • G.B. Thomas and R.L. Finney, Calculus, 9th Ed., Pearson Education, Delhi, 2005.

 

 

References: 
  • Richard Courant, Fritz John, Introduction to calculus and analysis, Springer- 2004.
  • Sudhir k. Pundir, Mathematical Analysis, CBS Publishers and Distributors pvt. Ltd, 2014.
  • E. Marsden, A.J. Tromba and A. Weinstein, Basic Multivariable Calculus, Springer (SIE). Indian reprint, 2005.
  • James Stewart, Multivariable Calculus, Concepts and Contexts, 2nd Ed., Brooks/Cole, Thomson Learning, USA, 2001.

e- RESOURCES

JOURNALS

 

Academic Year: 
2024-2025
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