Calculus through Data & Modeling: Applying Differentiation

Johns Hopkins University

Explore the practical applications of derivatives in the realm of calculus through the course "Calculus through Data & Modeling: Applying Differentiation." This course delves into the utilization of derivatives to find linear approximations for both single-variable and multi-variable functions, offering a straightforward approach to estimating complex and intricate functions. Additionally, learners will harness the power of derivatives to pinpoint the maximum and minimum values of a function, facilitating essential optimization techniques applicable across various fields, encompassing the natural sciences and data analysis.

The topics covered in this course are inherently linked to an array of real-world applications, including machine learning, cost minimization, and profit maximization. Through this course, participants gain the knowledge and skills necessary to tackle optimization challenges, paving the way for practical implementations in diverse industries.

Upon completion of this course, learners will be equipped with a robust understanding of differentiation and its pivotal role in modeling and analyzing real-world data, preparing them for the challenges and opportunities presented by modern data-driven decision-making processes.

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Calculus through Data & Modeling: Applying Differentiation
Course Modules

Calculus through Data & Modeling: Applying Differentiation covers linear approximations, extrema of single-variable functions, multivariable functions, Lagrange multipliers, and a final project on optimization.

Linear Approximations and Tangent Planes

Delve into the world of linear approximations and tangent planes, exploring their applications in estimating single-variable and multi-variable functions. Gain a comprehensive understanding of these fundamental concepts through engaging discussions and practical problem-solving exercises.

Maxima and Minima of Single-Variable Functions

Discover the intricacies of identifying the maxima and minima of single-variable functions, unraveling the impact of derivatives on the shape of their graphs. Engage in insightful discussions and hands-on practice to master essential techniques for analyzing and optimizing single-variable functions.

Maxima and Minima of Multivariable Functions

Uncover the nuances of pinpointing the maxima and minima of multivariable functions, delving into the complexities of optimization in multi-dimensional spaces. Through real-world examples and problem-solving tasks, gain a profound understanding of optimization techniques applicable to multivariable functions.

Lagrange Multipliers

Embark on a journey into the realm of Lagrange multipliers, exploring their pivotal role in solving constrained optimization problems. Dive deep into the applications of Lagrange multipliers through practical examples and problem-solving scenarios, mastering this essential concept in optimization.

Final Project - Optimization

Cap off your learning journey with a final project centered on optimization, applying the knowledge and skills acquired throughout the course to solve real-world optimization challenges. Engage in practical applications and showcase your proficiency in optimization techniques.

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