What you'll learn
- Limits of sequences
- Sandwich principle
- Completeness of the real numbers
- Limit of a function at a point
- Continuity of functions
- Intermediate value theorem
- Extremum theorem
- Bolzano-Weierstrass theorem
Requirements
- Know what integers, rational number, irrational numbers, and real numbers are
Description
This course is the first course of my "Understanding Calculus" course series. In this course, students will be introduced with
(1) Sequences and their limits
(2) Completeness of the real numbers
(3) Limit of a function at a point
(4) Continuity of functions
(5) Intermediate value theorem (IVT)
(6) Extremum theorem.
This course is very mathematically rigorous in the sense that we do manipulate the epsilon-N arguments for limit of a sequence and the epsilon-delta argument for limit of functions. These kinds of arguments are the gems of calculus and settle down the foundation for differentiation and integration that is to come in the next two courses in the series.
Who this course is for:
- Math/science/engineering undergraduates/early graduates
- Engineers who want to get a solid background in analysis through calculus
- People who want to understand/review calculus mathematically
Course content
- 00:19Slides used in this lecture.
- Preview01:46
Instructor
![Min Wu](data:image/svg+xml,%3Csvg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 64 64"%3E%3C/svg%3E){kind=avatar}
- 4.8 Instructor Rating
- 13 Reviews
- 31 Students
- 2 Courses
Hi, everyone. My name is Min Wu. I am a Math PhD candidate. During my journey of math, I have been teaching advanced math courses for 8+ years. Courses I have taught include
Calculus,
Linear Algebra,
Advanced Calculus,
Abstract Algebra,
Probability Theory,
Mathematical Statistics,
Differential Geometry,
Topology,
Algebraic Topology,
Measure Theory (aka Real Analysis), just to name a few.
In my past teaching experience, I often found student having difficulty understanding math topics mainly because they do not understand math in the right way. Mathematics is the playground of sufficiently rigorous logic and people should understand math subjects using logic. With sufficient familiarity with logic, everyone should be able to understand math. As Albert Einstein says, "Any fool can know. The point is to understand," I truly believe that people who are willing to spend some time getting themselves familiar with logic would be able to understand math very well.