Basics of Differential Equations

SEMESTER- II (BMG2CC1B)

​

INDEX

1. Continuity of f(x, y)
2. Differentiability of f(x, y)
3. Stationary Point, Saddle Point & Sufficient Condition for the existence of Extreme Value
4. Extreme Values of Functions of Two variables
5. Examples
6. References

https://www.overleaf.com/2152685167mqxqtbcrrdqk

https://www.geogebra.org/m/xzua6hru

• Differentiability of the given function at (0, 0) :

​

https://www.geogebra.org/m/emebax4j

EXTREME VALUES OF FUNCTIONS OF TWO VARIABLES

• SADDLE POINT:

In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local

extremum of the function.

https://www.overleaf.com/2152685167mqxqtbcrrdqk

https://www.overleaf.com/2152685167mqxqtbcrrdqk

https://www.geogebra.org/m/xzua6hru

https://www.geogebra.org/m/xzua6hru

REFERENCES:

• Advanced Mathematical Analysis (Utpal Chatterjee)
• Mathematical Analysis (Sitansu Bandyopadhyay)
• Saddler, David; Shea, Julia; Ward, Derek (2011), "12 B Stationary Points and Turning Points", Cambridge 2 Unit Mathematics Year 11, Cambridge University Press, p. 318, ISBN 9781107679573.
• W. Fleming (1977). Functions of Several Variables. Undergraduate Texts in Mathematics (2nd ed.). Springer. ISBN 0-387-902-066.
• R. Wrede; M.R. Spiegel (2010). Advanced Calculus (3rd ed.). Schaum's Outline Series. ISBN 978-0-07-162366-7.

​

THANK YOU