Calculus: Single Variable Part 2 - Differentiation

About this course: 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 second part--part two of five--we cover derivatives, differentiation rules, linearization, higher derivatives, optimization, differentials, and differentiation operators.

Created by:  University of Pennsylvania

• Taught by:  Robert Ghrist, Professor

  Mathematics and Electrical & Systems Engineering

Commitment 6-8 hours/week Language English, Subtitles: Chinese (Simplified) How To Pass Pass all graded assignments to complete the course. 课程作业

每门课程都像是一本互动的教科书，具有预先录制的视频、测验和项目。

来自同学的帮助

与其他成千上万的学生相联系，对想法进行辩论，讨论课程材料，并寻求帮助来掌握概念。

University of Pennsylvania The University of Pennsylvania (commonly referred to as Penn) is a private university, located in Philadelphia, Pennsylvania, United States. A member of the Ivy League, Penn is the fourth-oldest institution of higher education in the United States, and considers itself to be the first university in the United States with both undergraduate and graduate studies.

Syllabus


WEEK 1


A New Look at Differentiation



Think derivatives mean "slopes"? Not anymore... In this module, we will reconsider what a derivative is and means in terms of the asymptotic (or big-O) notation from the previous chapter. This will give us a new language for describing and understanding rates of change and the rules that govern them.


3 videos, 2 readings, 2 practice quizzes expand

1. 阅读: How Grading Works
2. 阅读: Your Guide to Getting Started in this Course
3. Video: Derivatives
4. 练习测验: Challenge Homework: Derivatives
5. Video: Differentiation Rules
6. Video: BONUS!
7. 练习测验: Challenge Homework: Differentiation Rules

Graded: Core Homework: Derivatives
Graded: Core Homework: Differentiation Rules

WEEK 2


Putting Derivatives to Work



Why exactly are derivatives so central to calculus? In part, it is because they are so ubiquitously useful! In this module, we will recall a few core applications of derivatives. In so doing, we'll see exactly how having an understanding of the asymptotics assists in building applications of the derivative.


5 videos, 3 practice quizzes expand

1. Video: Linearization
2. 练习测验: Challenge Homework: Linearization
3. Video: Higher Derivatives
4. Video: BONUS!
5. 练习测验: Challenge Homework: Higher Derivatives
6. Video: Optimization
7. Video: BONUS!
8. 练习测验: Challenge Homework: Optimization

Graded: Core Homework: Linearization
Graded: Core Homework: Higher Derivatives
Graded: Core Homework: Optimization

WEEK 3


Differentials and Operators



There is much more to derivatives than simply their computation and applications. So much of how they arise is calculus is in the mysterious guise of *differentials*. These arise from implicit differentiation, which in turn reveals a deeper level of understanding of what differentiation means.


3 videos, 1 reading, 2 practice quizzes expand

1. Video: Differentials
2. 练习测验: Challenge Homework: Differentials
3. Video: Differentiation Operator
4. Video: BONUS!
5. 练习测验: Challenge Homework: Differentiation Operator
6. 阅读: About the Chapter 2 Exam

Graded: Core Homework: Differentials
Graded: Core Homework: Differentiation Operator
Graded: Chapter 2: Differentiation - Exam