Multivariable Calculus (week 9-11)

Introduction To Multivariable Functions

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ "Dive into Multivariable Calculus with Our Introductory Series" Explore the fundamental concepts of functions with multiple variables and their real-world applications in our series. ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Arithmetic Operations on Multivariable functions

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ "Master the arithmetic of multivariable functions in our comprehensive series. Explore operations like addition, subtraction, multiplication, and division applied to functions with multiple variables, unraveling their significance and practical implications." ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Partial Derivatives

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ "Master Partial Derivatives in Our Enlightening Series" Discover the foundational concept of how functions change with respect to individual variables, empowering you to analyze complex systems and optimize solutions. ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Directional Derivatives

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ "Embark on a journey into directional derivatives with our insightful series. Discover how to measure rates of change of multivariable functions in specific directions, unlocking powerful tools for understanding gradients and optimizing in various dimensions." ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Limits of a multivariable function

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ "Explore the limits of multivariable functions in our illuminating series. Delve into the concept of approaching a point from various directions in multiple dimensions, gaining insight into continuity and convergence in higher-dimensional spaces." ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Continuity of a Multivariable function

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ "Dive into the realm of limits and continuity in multivariable functions with our comprehensive series. Uncover the nuances of approaching points in multiple dimensions and understand the conditions for smooth transitions and uninterrupted behavior across various paths." ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Gradient of a Multivariable Function

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ "Unlock the power of gradients in multivariable functions through our insightful series. Delve into the concept of directional derivatives and understand how gradients provide crucial information about the rate and direction of change in multi-dimensional spaces." ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Direction of Steepest Ascent and Descent of a multiariable function

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ "Discover the paths of steepest ascent and descent in multivariable functions with our engaging series. Explore how to navigate through multidimensional landscapes efficiently by understanding the direction that maximizes or minimizes function values, unlocking optimization strategies for various applications." ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Tangents and tangent planes of Multivariable function

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ Tangents and tangent planes play a crucial role in understanding multivariable functions. A tangent line represents the linear approximation of a function at a particular point, while a tangent plane represents the local behavior of a function in three-dimensional space. To find the tangent line at a given point, we use the concept of partial derivatives and evaluate them at that point. Similarly, to find the tangent plane, we use the partial derivatives to find the normal vector and then use it as a slope for the plane. Tangents and tangent planes help us visualize and analyze the behavior of functions in higher dimensions. 00:03 Introduction to tangent planes and tangents of multivariable functions 01:49: Finding the tangent plane and direction derivative 04:42 Understanding the tangent and tangent planes 06:01: Finding tangent planes for multivariable functions 07:17: Derivative and tangent planes of multivariable functions. 08:46 Discussing the equation of tangent plane for a fixed point 09:54 Discussing the equation and finding the tangent plane 11:15 Understanding the linear approximation of a multivariable function. ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Local Maximum, Local Minimum and Critical Points in Multivariable functions

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ Local Maximum, Local Minimum and Critical Points in Multivariable functions In multivariable calculus, local maximum, local minimum, and critical points are concepts related to the behavior of a function of multiple variables. These concepts are extensions of the ideas from single-variable calculus to functions with more than one input variable. Local Maximum and Local Minimum: A local maximum is a point where the function reaches its highest value within a small neighborhood (region) of that point. Formally, a point P is a local maximum if the function's value at P is greater than or equal to the values of the function at all nearby points in some small neighborhood around P. Similarly, a local minimum is a point where the function reaches its lowest value within a small neighborhood of that point. Formally, a point P is a local minimum if the function's value at P is less than or equal to the values of the function at all nearby points in some small neighborhood around P. Critical Points: A critical point of a multivariable function is a point where the partial derivatives of the function are all zero or undefined. In other words, a critical point is where the gradient (vector of partial derivatives) of the function is the zero vector or doesn't exist. Critical points are important because they can correspond to local extrema (maxima or minima) as well as saddle points (points where the function changes direction without reaching a local extremum). It's important to note that not all critical points are local extrema. Some critical points could be saddle points or points where the function takes on neither a maximum nor a minimum value within the given neighborhood. ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu

Second order Partial Derivative and hessian matrix of a Multivariable function

For My Notes ( Fill this Google form ): https://forms.gle/rJYeG4cUhWbX7FeZ9 Connect with me over Instagram for any sort of queries! Instagram: https://www.instagram.com/therealnarad/ Second-order Partial Derivative and hessian matrix of a Multivariable function Second-order partial derivatives involve calculating the rate of change of a function with respect to two different variables. The Hessian matrix, a square matrix of second-order partial derivatives, reveals key information about a function's curvature and can determine whether a critical point is a maximum, minimum, or saddle point. ========================================================== Checkout our Other Playlists Mathematics For Data Science 1: https://youtube.com/playlist?list=PLZd_9NahuB3G7yNvcyVChnSM29oNYTqwO&si=TYZwSXIIHIp2YnaU Linear Algebra For Data Science: https://youtube.com/playlist?list=PLZd_9NahuB3F4w_v1J5oNr3QiQl0cKGQ-&si=l1LEaXFGW6cEwpqD Mathematics 2 for Data Science: https://www.youtube.com/playlist?list=PLZd_9NahuB3EztpCeK9O81agMhePG0hfk Machine Learning Foundation: https://youtube.com/playlist?list=PLZd_9NahuB3HXelMlJvpMBy9LEqzpJALa&si=BEKkFa78WVy6k9Pe ========================================================== ABOUT OUR CHANNEL Join us for educational exploration! We cover topics such as Data Science, Machine Learning, and Coding. Check out our channel: https://www.youtube.com/@Myowncampus Don’t forget to subscribe! ========================================================== GET IN TOUCH Have questions or suggestions? Contact us at Rishujob24@gmail.com ========================================================== FOLLOW US ON SOCIAL Stay updated on our social media profiles! Facebook: https://facebook.com/rishu.rajgautam56 Instagram: https://Instagram.com/rishu_raj_gautam LinkedIn: https://www.linkedin.com/in/rishurajgautam LinkedIn: https://www.linkedin.com/in/rishurajgautam Telegram Group link :- https://t.me/MycampusByRishu