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Differential Calculus through Data and Modeling

This specialization provides an introduction to topics in single and multivariable calculus, and focuses on using calculus to address questions in the natural and social sciences. Students will learn to use the tools of calculus to process, analyze, and interpret data, and to communicate meaningful results, using scientific computing and mathematical modeling. Topics include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.

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What's inside

Four courses

Calculus through Data & Modeling: Precalculus Review

This applications-oriented course studies mathematical topics needed for calculus. It emphasizes using functions to model and analyze data. Graphing calculators or computers are integral to the course.

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Calculus through Data & Modeling: Limits & Derivatives

This first course on single variable calculus concepts introduces the notions of limits of a function to define the derivative of a function. In mathematics, the derivative measures the sensitivity to change of the function. This fundamental notion will be applied through the modelling and analysis of data.

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Calculus through Data & Modeling: Differentiation Rules

Calculus through Data & Modeling: Differentiation Rules introduces new rules for finding derivatives, enabling the calculation of rates of change for various functions, including polynomials, rational functions, algebraic functions, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions. These rules are then applied to solve problems involving rates of change and function approximation.

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Calculus through Data & Modeling: Applying Differentiation

As rates of change, derivatives give us information about the shape of a graph. In this course, we will apply the derivative to find linear approximations for single-variable and multi-variable functions. This gives us a straightforward way to estimate functions that may be complicated or difficult to evaluate. We will also use the derivative to locate the maximum and minimum values of a function.

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Learning objectives

Model data with both single and multivariable functions
Find maximum and minimum values of both single and multivariable functions, with and without constraints, to find optimal solutions to problems.

Understand properties of different types of functions to apply them accordingly to model different situations.
Perform operations of differential calculus, such as finding velocity, acceleration, rates of change, and slopes of tangent lines.

Model data with both single and multivariable functions
Find maximum and minimum values of both single and multivariable functions, with and without constraints, to find optimal solutions to problems.
Understand properties of different types of functions to apply them accordingly to model different situations.
Perform operations of differential calculus, such as finding velocity, acceleration, rates of change, and slopes of tangent lines.

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Time

0 hours

Level

Intermediate

Via

Coursera

Institution

Johns Hopkins University

Instructor

Joseph W. Cutrone, PhD

Level

Intermediate

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