This specialization in Integral Calculus through Data and Modeling builds on foundational calculus concepts to develop the theory and applications of integral calculus. The focus is on using calculus to address questions in natural and social sciences, enabling students to process, analyze, and interpret data through scientific computing and mathematical modeling.
Topics covered include functions as models of data, differential and integral calculus of functions of one and several variables, differential equations, and optimization and estimation techniques.
Through projects and real-world applications, students will gain practical experience in applying calculus to analyze and model data, providing valuable insights for policy critiques and problem-solving across various disciplines.
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This course comprises four modules, covering series and integration, techniques of integration for single and multivariable functions, integration applications, and vector calculus, providing a comprehensive understanding of calculus through practical applications.
This module introduces the notions of series, sequences, and integration, providing a foundational understanding of the integral and its applications. Students will learn to analyze and model real-world data and critique policies based on their findings.
Building on the integral of a single-variable function, this module extends the understanding of integrals to work with functions of more than one variable. Students will gain expertise in approximating definite integrals and apply these techniques to real-world problems through a peer-reviewed project.
This module focuses on the applications of integration, allowing students to compute quantities by evaluating definite integrals. It expands the notion of average value, develops formulas for velocity, acceleration, and areas between curves, and applies the tools of calculus to analyze and model real-world data.
Continuing the study of calculus, this module delves into the applications of integration to vector-valued functions and vector fields. Students will learn about line integrals, Green's Theorem, and their applications to real-world problems, providing a solid foundation for advanced mathematics, computer science, or data science.
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