Multivariate Calculus
This course will enable the students to -
- Understand the concept of functions of several variables.
- Introduce partial derivatives and several of its consequences
- Introduce double and triple integrals along with line integrals which are fundamental to all streams where calculus can be used.
Course Outcomes (COs):
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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|---|---|---|---|---|
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Course Code |
Course Title |
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DMAT 611B |
Multivariate Calculus (Theory)
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The students will be able to –
CO137: Analyse the continuity and differentiability of the functions of several variables. CO138: Apply the rules of differentiation on multivariable functions. CO139: Analyse the extreme points of multivariate functions. CO140: Understand and use the concept of jacobian. CO141: 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
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Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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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.
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.
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.
Co-ordinate system: Cartesian, cylindrical polar, spherical polar. Integration on R2 and R3. Leibnitz rule.
- 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.
- 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.
