# Differential Calculus through Data and Modeling

Johns Hopkins University

This specialization in Differential Calculus through Data and Modeling provides an in-depth exploration of single and multivariable calculus within the context of natural and social sciences. Through scientific computing and mathematical modeling, students learn to process, analyze, and interpret data using the tools of calculus. The course covers functions as models of data, differential and integral calculus of functions, differential equations, and optimization and estimation techniques.

Key learning outcomes include the ability to model data using single and multivariable functions, find maximum and minimum values of functions with and without constraints, and apply differential calculus operations to solve real-world problems. The course emphasizes the understanding and application of different types of functions to model various situations, as well as the performance of operations of differential calculus, such as finding velocity, acceleration, rates of change, and slopes of tangent lines.

• Explore the application of calculus to address questions in natural and social sciences
• Learn to model and analyze data using functions
• Master differentiation techniques for common single and multivariable functions
• Apply differential calculus operations to solve real-world problems

Certificate Available ✔

##### Course Modules

This course comprises four modules that cover precalculus review, limits and derivatives, differentiation rules, and applying differentiation techniques. It emphasizes practical applications in scientific modeling and data analysis.

#### Calculus through Data & Modeling: Precalculus Review

This course, "Calculus through Data & Modeling: Precalculus Review," offers an applications-oriented, investigative approach to the study of mathematical topics needed for further coursework in single and multivariable calculus. The emphasis is on using various functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions, to model and analyze data. Graphing calculators and/or the computer are integral to the course.

#### Calculus through Data & Modeling: Limits & Derivatives

The first course in the specialization, "Calculus through Data & Modeling: Limits & Derivatives," introduces the notions of limits of a function to define the derivative of a function. It applies these fundamental concepts through the modeling and analysis of data, with a focus on understanding how derivatives measure sensitivity to change of a function and their practical applications.

#### Calculus through Data & Modeling: Differentiation Rules

"Calculus through Data & Modeling: Differentiation Rules" continues the study of differentiable calculus by developing new rules for finding derivatives without using the limit definition directly. These differentiation rules enable the calculation of rates of change with relative ease for various types of functions and their application to solve problems related to rates of change and function approximation.

#### Calculus through Data & Modeling: Applying Differentiation

The final course, "Calculus through Data & Modeling: Applying Differentiation," applies the derivative to find linear approximations for single-variable and multi-variable functions. It also explores the use of the derivative to locate the maximum and minimum values of a function, emphasizing their importance in real-world applications such as machine learning, cost minimization, and profit maximization.

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