Learn integral calculus through modeling. Master integration techniques for single-variable and multivariable functions.
Suggested by: Coursera (What is Coursera?)
No prior knowledge required
No unnecessary risks
This specialization builds on topics introduced in single and multiple variable differential calculus to develop the theory and applications of integral calculus. The specialization focuses on using calculus to solve questions in the natural and social sciences. Students will learn to use the techniques presented in class to process, analyze, and interpret data, and communicate meaningful results using scientific calculations and mathematical models.
In each module, learners will be given sample problems with solutions to help them develop their skills and confidence, followed by graded tests to showcase what they have learned.
Through a culminating project, students will use their skills to:
This course continues your calculus studies by introducing the concepts of series, sequences, and integration. These basic tools allow us to develop the theory and applications of the second central tool in calculus: the integral. Rather than measuring rates of change, the integral provides a way to measure the accumulation of a quantity over a range of input values. This concept of accumulation can be applied to various quantities, including money, populations, weight, area, volume, and air pollution. The concepts in this course are relevant to many other fields beyond classical mathematics. Through projects, we will apply the tools of this course to analyze and measure real-world data, and from this analysis we will provide policy critiques. Similar to the derivative, several important methods have been developed for calculating accumulation. Our course begins by studying the deep and meaningful corollary of the fundamental theorem of calculus, which develops the relationship between derivative and integration operations. If you are interested in studying more advanced mathematics, this course is for you.
In this course description, we will build on the concepts of the integral of a one-dimensional function over a range. Now, we will extend our understanding of integrals to work with functions with more than one variable. First, we will learn how to differentiate a multivariate function over different regions of the plane. Next, we will introduce vector functions, which assign a point to a vector. This will prepare us for the final course in the specialization on vector calculus. Finally, we will introduce techniques for evaluating absolute integrals when working with discrete data, and during a collaborative project, we will apply these techniques to real-world problems.
This course continues your calculus studies by focusing on applications of integration. The applications in this section share many common themes. First, each is an example of a quantity that is considered by evaluating an absolute integral. Second, the formula for that application follows from Riemann sums. Instead of measuring rates of change as we did with differential calculus, the absolute integral allows us to measure the accumulation of a quantity over a range of input values. The concept of accumulation can be applied to a variety of quantities, including money, populations, weight, area, volume, and pollution as well as chemicals. The concepts in this course are relevant in many fields outside of classical mathematics.
We will extend the concept of the average value of a data set to allow for infinite values, develop the formula along an arc and a curve, and derive formulas for velocity, acceleration, and fields between curves. Through examples and projects, we will apply the tools of this course to analyze and study real-world data.
This course continues your calculus studies by focusing on applications of integration to vector-valued functions, or vector fields. These are functions that assign vectors to points in space, allowing us to develop advanced theories to apply to real-world problems. We define line integrals, which can be used to find the work done by a vector field. We conclude this course with Green’s Theorem, which describes the relationship between certain types of line integrals on closed paths and double integrals. In the discrete case, this theorem is known as the string theorem and allows us to measure areas of polygons. We use this version of the theorem to develop more tools for data analysis through a collaborative project.
Upon successful completion of this course, you will have all the tools required to master any advanced mathematics, computer science, or data science that builds on the foundations of one-dimensional or multidimensional computation.
