Advanced Calculus-I
Introduction to subject: Advanced Calculus I
Introduction to subject: Advanced Calculus I
Introduction to Function of Several variables
Introduction to Function of Several variables
Spherical Neighborhood & Rectangular Neighborhood
Spherical Neighborhood & Rectangular Neighborhood
Limit of functions of Several Variables
Limit of functions of Several Variables
Part-I
Part-I
Limit of functions of Several Variables
Limit of functions of Several Variables
Part-II
Part-II
Limit of functions of Several Variables
Limit of functions of Several Variables
Part-III
Part-III
Continuity of function of two variables
Continuity of function of two variables
Partial Derivatives and its Geometrical interpretation
Partial Derivatives and its Geometrical interpretation
Partial derivatives and its examples
Partial derivatives and its examples
Partial derivatives and continuity
Partial derivatives and continuity
Differentiability for functions of two variables
Differentiability for functions of two variables
Sufficient condition for differentiability
Sufficient condition for differentiability
Inequality of Mixed Partials
Inequality of Mixed Partials
Schwartz's theorem for Mixed Partials
Schwartz's theorem for Mixed Partials
Young's Theorem for equality of mixed Partials
Young's Theorem for equality of mixed Partials
Directional derivative & It's Geometrical interpretation
Directional derivative & It's Geometrical interpretation
Differential for Two variables
Differential for Two variables
Chain Rules for Derivatives
Chain Rules for Derivatives
Chain Rules for Partial Derivatives
Chain Rules for Partial Derivatives
Examples on Chain Rules for Derivatives
Examples on Chain Rules for Derivatives
Implicit Differentiation
Implicit Differentiation
Jacobian
Jacobian
Which variables treated as constant
Which variables treated as constant
Homogeneous function
Homogeneous function
Euler's Theorem on Homogeneous function
Euler's Theorem on Homogeneous function
Euler's theorem on homogeneous function for n variables
Euler's theorem on homogeneous function for n variables
Corollary on Euler’s Theorem for homogeneous function
Corollary on Euler’s Theorem for homogeneous function
Corollary based on Euler Theorem for homogeneous function (Part-II)
Corollary based on Euler Theorem for homogeneous function (Part-II)
Examples based on Euler's Theorem for Homogeneous function
Examples based on Euler's Theorem for Homogeneous function
Maxima and Minima of Functions of Two variables
Maxima and Minima of Functions of Two variables
Example of Locate all relative extrema and saddle points-I
Example of Locate all relative extrema and saddle points-I
Example on maxima and minima of the function-II
Example on maxima and minima of the function-II
Example of Maxima and Minima of the function-III
Example of Maxima and Minima of the function-III
Example of Maxima and Minima of the function-IV
Example of Maxima and Minima of the function-IV
Example of Maxima and Minima of the function-V
Example of Maxima and Minima of the function-V
Example based on Lagrange's method of undermined multiplies
Example based on Lagrange's method of undermined multiplies
Example based on Lagrange's method of undermined multiplies-II
Example based on Lagrange's method of undermined multiplies-II
Example based on Lagrange's method of undermined multiplies-III
Example based on Lagrange's method of undermined multiplies-III
Example based on Lagrange's method of undermined multiplies-IV
Example based on Lagrange's method of undermined multiplies-IV
Example based on Lagrange's method of undermined multiplies-V
Example based on Lagrange's method of undermined multiplies-V
Taylor's theorem for functions of Two variable
Taylor's theorem for functions of Two variable
Examples on Taylor's Series for Two variables
Examples on Taylor's Series for Two variables
Multiple Points for two dimensional curves
Multiple Points for two dimensional curves
Curvature in Cartesian Form
Curvature in Cartesian Form
Radius of curvature at origin
Radius of curvature at origin
Radius of Curvature in Parametric form
Radius of Curvature in Parametric form
Radius of Curvature in Polar form
Radius of Curvature in Polar form
advanced calculus-I.pdfLecture notes on Advanced calculus-I
Lecture notes on Advanced calculus-I