Course Summary
Learn the basics of discrete calculus, an essential tool for analyzing and modeling systems with discrete features. This course covers topics such as difference equations, generating functions, and combinatorial analysis.Key Learning Points
- Understand the fundamentals of difference equations and recurrence relations
- Learn how to use generating functions to solve combinatorial problems
- Gain the ability to model and analyze systems with discrete features
Related Topics for further study
Learning Outcomes
- Develop a strong understanding of difference equations and their applications
- Learn how to use generating functions to solve complex combinatorial problems
- Gain the ability to model and analyze systems with discrete features
Prerequisites or good to have knowledge before taking this course
- Familiarity with basic algebra and calculus
- A basic understanding of combinatorics
Course Difficulty Level
IntermediateCourse Format
- Online Self-Paced Course
Similar Courses
- Discrete Mathematics
- Combinatorics and Probability
- Mathematical Thinking in Computer Science
Related Education Paths
Notable People in This Field
- Dr. Arthur Benjamin
- Terence Tao
Related Books
Description
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.
Outline
- A Calculus for Sequences
- Sequences
- BONUS!
- Differences
- Discrete Calculus
- Your Guide to Getting Started in this Course
- How Grading Works
- Core Homework: Sequences
- Core Homework: Differences
- Challenge Homework: Differences
- Core Homework: Discrete Calculus
- Challenge Homework: Discrete Calculus
- Introduction to Numerical Methods
- Numerical O.D.E.s
- Numerical Integration
- Core Homework: Numerical O.D.E.s
- Series and Convergence Tests
- Infinite Series
- Convergence Tests I
- Convergence Tests II
- Absolute & Conditional
- Core Homework: Infinite Series
- Challenge Homework: Infinite Series
- Core Homework: Convergence Tests I
- Challenge Homework: Convergence Tests I
- Core Homework: Convergence Tests II
- Core Homework: Absolute & Conditional
- Power and Taylor Series
- Power Series
- Taylor Series Redux
- Approximation and Error
- BONUS!
- Core Homework: Power Series
- Challenge Homework: Power Series
- Core Homework: Taylor Series Redux
- Challenge Homework: Taylor Series Redux
- Core Homework: Approximation and Error
- Concluding Single Variable Calculus
- Calculus Redux
- BONUS!
- Foreshadowing
- Credits
- About the Chapter 5 Exam
- About the 5-CHAPTER GREAT BIG FINAL EXAM!
- Chapter 5: Discretization - Exam
- 5-CHAPTER GREAT BIG FINAL EXAM!
Summary of User Reviews
Learn Discrete Calculus with Coursera! This course has received high praise from many users for its comprehensive coverage of the topic and engaging teaching style. Students have found the course to be informative and highly engaging, making it a great choice for anyone looking to learn more about discrete calculus.Key Aspect Users Liked About This Course
Many users have found the course to be highly engaging.Pros from User Reviews
- Comprehensive coverage of the topic
- Engaging teaching style
- Informative and helpful content
- Great for beginners and more advanced learners
Cons from User Reviews
- Some users found the course to be too basic
- Not suitable for those looking for a highly technical course
- Limited interaction with instructors and other students
Robert Ghrist
4.6 Raiting
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