Multivariable Calculus

Paper Code: 
DMAT 611B
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Understand the concept of functions of several variables.
  2. Introduce 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 (COs):

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

DMAT611B

 

 

 

 

 

 

Multivariate Calculus

 (Theory)

 

 

 

 

 

 

The students will be able to –

 

CO121: Analyze the continuity and differentiability of the functions of several variables.

CO122: Apply the rules of differentiation on multivariable functions.

CO123: Analyze the extreme points of multivariate functions.

CO124: Understand and use the concept of jacobian.

CO125: Describe the different co-ordinate systems and use the concept to calculate areas and volumes of the regions.

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Giving tasks

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

 

 

 

 

Unit I: 
I
18.00

Functions of several variables, limit and continuity of functions. Differentiability of the functions, sufficient conditions for continuity and differentiability.

Unit II: 
II
18.00

Directional derivatives of a function of two variables. Alzebra 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: 
III
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: 
IV
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: 
V
18.00

Co-ordinate system: 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,2 nd Ed., Brooks/Cole, Thomson Learning, USA, 2001.
 
Academic Year: 
2023-2024
  • Printer-friendly version
  • PDF version