Differential Calculus through Data and Modeling
Offered By: Johns Hopkins University via Coursera
Course Description
Overview
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.
Syllabus
Course 1: Calculus through Data & Modeling: Precalculus Review
- Offered by Johns Hopkins University. This course is an applications-oriented, investigative approach to the study of the mathematical topics ... Enroll for free.
Course 2: Calculus through Data & Modeling: Limits & Derivatives
- Offered by Johns Hopkins University. This first course on concepts of single variable calculus will introduce the notions of limits of a ... Enroll for free.
Course 3: Calculus through Data & Modeling: Differentiation Rules
- Offered by Johns Hopkins University. Calculus through Data & Modeling: Differentiation Rules continues the study of differentiable calculus ... Enroll for free.
Course 4: Calculus through Data & Modeling: Applying Differentiation
- Offered by Johns Hopkins University. As rates of change, derivatives give us information about the shape of a graph. In this course, we will ... Enroll for free.
- Offered by Johns Hopkins University. This course is an applications-oriented, investigative approach to the study of the mathematical topics ... Enroll for free.
Course 2: Calculus through Data & Modeling: Limits & Derivatives
- Offered by Johns Hopkins University. This first course on concepts of single variable calculus will introduce the notions of limits of a ... Enroll for free.
Course 3: Calculus through Data & Modeling: Differentiation Rules
- Offered by Johns Hopkins University. Calculus through Data & Modeling: Differentiation Rules continues the study of differentiable calculus ... Enroll for free.
Course 4: Calculus through Data & Modeling: Applying Differentiation
- Offered by Johns Hopkins University. As rates of change, derivatives give us information about the shape of a graph. In this course, we will ... Enroll for free.
Courses
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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. These optimization techniques are important for all fields, including the natural sciences and data analysis. The topics in this course lend themselves to many real-world applications, such as machine learning, minimizing costs or maximizing profits.
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This first course on concepts of single variable calculus will introduce 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. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. This fundamental notion will be applied through the modelling and analysis of data.
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Calculus through Data & Modeling: Differentiation Rules continues the study of differentiable calculus by developing new rules for finding derivatives without having to use the limit definition directly. These differentiation rules will enable the calculation of rates of change with relative ease the derivatives of polynomials, rational functions, algebraic functions, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions. Once these rules are developed, they are then applied to solve problems involving rates of change and the approximation of functions.
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This course is an applications-oriented, investigative approach to the study of the mathematical topics needed for further coursework in single and multivariable calculus. The unifying theme is the study of functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions. An emphasis is placed on using these functions to model and analyze data. Graphing calculators and/or the computer will be used as an integral part of the course.
Taught by
Joseph W. Cutrone, PhD
Tags
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