Calculus: Single Variable Part 1 - Functions
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences.
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- Level Foundation
- Duration 14 hours
- Course by University of Pennsylvania
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Offered by
About
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this first part--part one of five--you will extend your understanding of Taylor series, review limits, learn the *why* behind l'Hopital's rule, and, most importantly, learn a new language for describing growth and decay of functions: the BIG O.Modules
Introduction to the Course
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1
Videos
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2
Readings
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2
Assignment
2
Assignment
- Learning Style Preference Survey
- Diagnostic Exam
1
Videos
- Introduction
2
Readings
- Welcome
- Your Guide to Getting Started in this Course
Functions
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1
Videos
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1
Readings
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2
Assignment
2
Assignment
- Core Homework: Functions
- Challenge Homework: Functions
1
Videos
- Functions
1
Readings
- How Grading Works
Exponentials
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2
Videos
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2
Assignment
2
Assignment
- Core Homework: The Exponential
- Challenge Homework: The Exponential
2
Videos
- Exponentials
- BONUS!
Taylor Series
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1
Videos
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2
Assignment
2
Assignment
- Core Homework: Taylor Series
- Challenge Homework: Taylor Series
1
Videos
- Taylor Series
Computing Taylor Series
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1
Videos
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2
Assignment
2
Assignment
- Core Homework: Computing Taylor Series
- Challenge Homework: Computing Taylor Series
1
Videos
- Computing Taylor Series
Convergence
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2
Videos
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2
Assignment
2
Assignment
- Core Homework: Convergence
- Challenge Homework: Convergence
2
Videos
- Convergence
- BONUS!
Expansion Points
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1
Videos
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2
Assignment
2
Assignment
- Core Homework: Expansion Points
- Challenge Homework: Expansion Points
1
Videos
- Expansion Points
Limits
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1
Videos
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2
Assignment
2
Assignment
- Core Homework: Limits
- Challenge Homework: Limits
1
Videos
- Limits
l'Hôpital's Rule
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1
Videos
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2
Assignment
2
Assignment
- Core Homework: l'Hôpital's Rule
- Challenge Homework: l'Hôpital's Rule
1
Videos
- l'Hôpital's Rule
Orders of Growth
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2
Videos
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2
Assignment
2
Assignment
- Core Homework: Orders of Growth
- Challenge Homework: Orders of Growth
2
Videos
- Orders of Growth
- BONUS!
Chapter 1 Review & Exam
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1
Readings
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1
Assignment
1
Assignment
- Chapter 1: Functions - Exam
1
Readings
- About the Chapter 1 Exam
Auto Summary
Explore the fascinating world of single-variable Calculus with Coursera's "Calculus: Single Variable Part 1 - Functions." This foundational course emphasizes conceptual understanding and real-world applications, making it perfect for beginners in engineering, physical, and social sciences. Highlights include an introduction to Taylor series, a blend of discrete and continuous Calculus, and a focus on growth and decay of functions using the BIG O notation. With a clear and dynamic approach, this 840-minute course, available via a Starter subscription, is designed to deepen your mathematical insights under expert guidance.
Robert Ghrist