The course covers a range of topics, including limits and continuity, derivatives, applications of derivatives, and integrals.
Throughout the course, students will learn how to evaluate limits and understand the concepts of continuity and differentiability. They will also learn how to calculate derivatives of functions and apply them to realworld problems such as optimization and related rates.
The course also covers techniques for finding antiderivatives and evaluating definite integrals, as well as applications of integrals, including areas between curves and volumes of revolution.
Overall, this course provides a solid foundation in calculus, preparing students for more advanced topics in the subject.
Course Content:
The Calculus: Single Variable Part 1  Functions course on Coursera, created by Robert Ghrist, consists of 4 parts and a total of 13 lectures. The lectures are as follows:
Module 1: Introdution (1 video + 2 readings + 1 quiz)
Welcome to Calculus: Single Variable! below you will find the course's diagnostic exam. if you like, please take the exam. you don't need to score a minimal amount on the diagnostic in order to take the course. but if you do get a low score, you might want to readjust your expectations: this is a very hard class...
1 video
Total 8 minutes IntroductionPreview module 8 minutes
2 readings
Total 20 minutes Welcome 10 minutes
 Your Guide to Getting Started in this Course 10 minutes
1 quiz
Total 30 minutes Diagnostic Exam 30 minutes
Module 2: A Review of Functions (3 videos + 1 reading + 2 quizzes)
This module will review the basics of your (pre)calculus background and set the stage for the rest of the course by considering the question: just what <i>is</i> the exponential function?
3 videos
Total 35 minutes FunctionsPreview module 15 minutes
 Exponentials 15 minutes
 BONUS! 4 minutes
1 reading
Total 10 minutes How Grading Works 10 minutes
2 quizzes
Total 60 minutes Challenge Homework: Functions 30 minutes
 Challenge Homework: The Exponential 30 minutes
Module 3: Taylor Series (5 videos + 4quizzes)
This module gets at the heart of the entire course: the Taylor series, which provides an approximation to a function as a series, or "long polynomial". You will learn what a Taylor series is and how to compute it. Don't worry! The notation may be unfamiliar, but it's all just working with polynomials....
5 videos
Total 68 minutes Taylor SeriesPreview module 14 minutes
 Computing Taylor Series 16 minutes
 Convergence 16 minutes
 BONUS! 7 minutes
 Expansion Points 14 minutes
4 quizzes
Total 120 minutes Challenge Homework: Taylor Series 30 minutes
 Challenge Homework: Computing Taylor Series 30 minutes
 Challenge Homework: Convergence 30 minutes
 Challenge Homework: Expansion Points 30 minutes
Module 4: Limits and Asymptotics (4 videos + 1 reading + 3 quizzes)
A Taylor series may or may not converge, depending on its limiting (or "asymptotic") properties. Indeed, Taylor series are a perfect tool for understanding limits, both large and small, making sense of such methods as that of l'Hopital. To solidify these newfound skills, we introduce the language of "bigO" as a means of bounding the size of asymptotic terms. This language will be put to use in future Chapters on Calculus.
4 videos
Total 61 minutes LimitsPreview module 15 minutes
 l'Hôpital's Rule 16 minutes
 Orders of Growth 17 minutes
 BONUS! 12 minutes
1 reading
Total 10 minutes About the Chapter 1 Exam 10 minutes
3 quizzes
Total 90 minutes Challenge Homework: Limits 30 minutes
 Challenge Homework: l'Hôpital's Rule 30 minutes
 Challenge Homework: Orders of Growth 30 minutes
Reviews:
As a former student of Calculus: Single Variable Part 1  Functions by Robert Ghrist on Coursera, I found the course to be an excellent introduction to the fundamental concepts of calculus. Professor Ghrist is a highly skilled and engaging instructor who clearly has a deep understanding of the subject matter.
The course is wellstructured and provides a comprehensive overview of singlevariable calculus, with a particular focus on functions and their properties. The video lectures are clear, concise, and engaging, and the accompanying practice exercises and quizzes are helpful for reinforcing the material.
One of the things that I appreciated most about the course was the emphasis on developing intuition and understanding, rather than just memorizing formulas and procedures. Professor Ghrist does an excellent job of explaining the underlying concepts and showing how they can be applied in a variety of contexts. This approach not only makes the material more interesting and engaging, but also helps students to develop a deeper and more meaningful understanding of calculus.
Another strength of the course is the use of interactive applets and demonstrations, which allow students to explore mathematical concepts in a visual and interactive way. These resources not only make the material more accessible and engaging, but also help to deepen students' understanding and intuition.
The course also provides ample opportunities for practice and reinforcement, with a variety of quizzes, assignments, and practice exercises. These resources are welldesigned and effective, and provide students with the feedback and support they need to master the material.
Overall, I would highly recommend Calculus: Single Variable Part 1  Functions to anyone interested in learning calculus. The course is welldesigned, comprehensive, and engaging, and provides an excellent foundation for further study in calculus and related fields.
At the time, the course has an average rating of 4.7 out of 5 stars based on over 1,970 ratings.
What you'll learn:
After completing the Calculus: Single Variable Part 1  Functions course on Coursera, created by Robert Ghrist, students will have gained the following skills:

Understanding of functions and their properties, including limits, continuity, and differentiability: Students will learn about the basic concepts of functions, including their domain and range, how to graph them, and how to identify their properties such as evenness, oddness, periodicity, and symmetry. They will also learn how to determine the limits of functions, how to determine whether a function is continuous or discontinuous, and how to identify the differentiability of functions.

Ability to evaluate limits and determine the continuity and differentiability of a function: Students will learn how to evaluate limits of functions both graphically and algebraically. They will also learn about onesided limits and how to use them to determine the continuity of functions. Finally, they will learn about the differentiability of functions and how to find the derivative of a function using the definition of the derivative.

Knowledge of the derivative and its applications, including optimization and related rates problems: Students will learn about the derivative of a function and its interpretation as the rate of change of the function. They will also learn about the rules of differentiation, including the chain rule, product rule, and quotient rule. They will apply these rules to optimize functions and solve related rates problems.

Ability to calculate derivatives of functions and apply them to realworld problems: Students will gain practice in calculating derivatives of functions, including polynomial, exponential, logarithmic, and trigonometric functions. They will also learn how to apply these derivatives to solve realworld problems such as velocity and acceleration problems.

Understanding of antiderivatives and definite integrals, as well as their applications in finding areas between curves and volumes of revolution: Students will learn about the concept of antiderivatives and how they are related to the definite integral. They will learn techniques for finding antiderivatives, including substitution and integration by parts. They will also learn how to use definite integrals to find the area between two curves and the volume of revolution of a solid of revolution.

Ability to evaluate definite integrals and apply them to realworld problems: Students will gain practice in evaluating definite integrals, including improper integrals. They will also learn how to apply definite integrals to solve realworld problems such as computing work and average value.

Strong foundation in calculus, preparing students for more advanced topics in the subject: Overall, this course provides students with a strong foundation in calculus, giving them the skills and knowledge they need to continue their studies in more advanced topics such as multivariable calculus, differential equations, and mathematical modeling.
Author:
Robert Ghrist is a professor of mathematics and electrical and systems engineering at the University of Pennsylvania. He received his PhD in mathematics from the University of California, Berkeley, in 1994.
Dr. Ghrist's research interests are in the areas of applied topology, geometric analysis, and algebraic geometry. He has published numerous research papers and has received several awards and honors for his work, including the Presidential Early Career Award for Scientists and Engineers (PECASE) in 2000 and the National Science Foundation's Alan T. Waterman Award in 2007.
In addition to his research, Dr. Ghrist is also an accomplished educator. He has won several teaching awards at the University of Pennsylvania, including the Lindback Award for Distinguished Teaching and the Ira H. Abrams Memorial Award for Distinguished Teaching. He is also a coauthor of several textbooks on mathematics and engineering.
Dr. Ghrist's expertise in both mathematics and engineering makes him uniquely qualified to teach the "Calculus: Single Variable Part 1  Functions" course on Coursera. His ability to explain complex mathematical concepts in a clear and concise manner has earned him high praise from his students and colleagues.
Overall, Dr. Ghrist is a highly respected and accomplished mathematician and educator with a wealth of knowledge and experience in his field. His contributions to mathematics and engineering have had a profound impact on the field, and his teaching has inspired countless students to pursue careers in science, technology, engineering, and mathematics (STEM).
Requirements:
The requirements for the Calculus: Single Variable Part 1  Functions course by Robert Ghrist on Coursera are as follows:

Basic algebra: Students should have a good understanding of algebraic concepts, including solving linear and quadratic equations, factoring, and working with exponents and logarithms.

Trigonometry: Students should be familiar with trigonometric functions and their properties, including the unit circle, sine, cosine, and tangent.

Precalculus: Students should have a basic understanding of precalculus concepts such as functions, graphing, and inverse functions.

High school level mathematics: The course assumes a high school level of mathematics proficiency, including topics such as geometry, algebra, and calculus.

Familiarity with technology: Students should have access to a computer with internet access and be comfortable using online tools such as video lectures, quizzes, and online discussion forums.
Overall, the course is designed for students who have a strong foundation in mathematics and are comfortable with algebra and trigonometry, and who are interested in developing a deeper understanding of calculus and its applications.
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