Stewart Calculus - Multivariable Functions

Explore multivariable calculus concepts in this comprehensive video lecture series on Stewart Calculus Chapter 14. Dive into partial derivatives, visualizing them with examples and learning about Clairaut's Theorem. Tackle advanced partial derivative problems, including derivatives of integrals. Practice finding linear approximations and using differentials for real-world applications. Master the chain rule for partial derivatives in various scenarios. Investigate directional derivatives and gradient vectors. Analyze local extrema and saddle points using the second derivative test. Apply Lagrange multipliers to optimization problems. Conclude by examining multivariable limits using formal definitions. Enhance your understanding of multivariable functions through detailed explanations and practical examples.

Syllabus

What The Heck are Partial Derivatives?? With Visualization, Examples and Clairaut's Theorem!!.
Partial Derivative Examples Advanced (Including Derivative of an Integral).
Find the Linear Approximation of f(x,y) = 1-xycos(pi y) at the Point (1,1).
Use Differentials to Estimate the Amount of Metal in a Cylindrical Can.
Use the Chain Rule to find the Partial Derivatives.
Use the Chain Rule to Find the Partial Derivatives of z = tan(u/v), u-2s+3t, v=3s-2t.
Find all points at which the direction of fastest change of the function is i+j.
Find the Directional Derivative of f(x,y,z) = xy+yz+xz at (1,-1,3) in the direction of (2,4,5).
Local Extrema and Saddle Points of a Multivariable Function. 2nd Derivative Test.
Use Lagrange Multipliers to Find the Maximum and Minimum Values of f(x,y) = x^3y^5.
Multivariable Limit Using the Definition.