Explanation
In Calculus 1, part 1 of 2: Limits and Continuity, you will learn: about this course, and about Calculus in general and its topics. You will learn: you will get a brief review of the Precalculus material that you think you need to master to be able to follow Calculus, but you will also get words of encouragement and motivation, I promise. You will learn: how to generalize some formulas with or without the help of math input. You will learn: the concept of sequence of numbers, with many examples and examples; sequential, monotone series, finite series; defining the limits (both appropriate and inappropriate) of numerical sequences, with many examples and examples; arithmetic operations on sequences and Limitation Rules for sequences; collection points for the series; the concept of continuity of functions in mathematics, and how the Laws of Limits of Series will serve later in Calculus to calculate limits of functions and proof of continuity of functions in elementary school; Squeeze Theorem for sequences; Weierstrass theorem on monotone integrals and finite series; extended facts and figures; non-decisional forms and their importance; some of the first ideas of comparing infinities (Standard Limits in Infinity); a word about sequence limits in metric spaces; Cauchy series (fundamental series) and graph construction of real numbers using equivalence relations on all Cauchy series with rational elements.
What will you learn?
- How to solve problems involving limits and continuity of real-valued functions in 1 variable (illustrated with 491 solved problems) and why these methods work.
- The structure and properties of the real numbers as an ordered field with the Axiom of Completeness, and the consequences of this definition.
- Extended real calculations, and a variety of unspecified forms.
- Advanced, weak, and reformed Axiom of Completion of these requirements.
- Sequence numbers and combinations or variations thereof; epsilon-definition of the series limit, with illustrations and examples; capital points.
- Finding new limits from previous limits: the limits of the sum, difference, product, quantity, etc., of two series, with illustrations, formal proofs, and examples.
- Squeeze Theorem for sequences
- Squeeze Theorem of functions
- The concept of the limit of a real-valued function of one real variable at a point: Cauchy’s definition, Heine’s definition; corresponding evidence.
- Limits and infinity of functions: Definition of Cauchy (epsilon-delta) and definition of Heine (sequence) of these parameters; equivalent.
Who is this course for?
- University and college students who want to learn Univariate Calculus (or Real Analysis)
- High school students interested in college math; The course is designed to be purchased by adults and students
Specificatoin of Calculus 1, part 1 of 2: Limits and continuity
- Publisher: Udemy
- Teacher: Hania Uscka-Wehlou, Martin Wehlou
- Language : English
- Level : All Levels
- Number of courses: 226
- Duration: 59 hours and 58 minutes
Mathematics Content 1, part 1 of 2: Limits and continuity
Requirements
- “Precalculus 1: Basic Concepts” (or equivalent): Mathematical text, logic, plagiarism, proof
- “Precalculus 2: Differentiation and Rational Functions” (or equivalent)
- “Precalculus 3: Trigonometry” (or equivalent)
- “Precalculus 4: Exponential and Logarithms” (or equivalent)
- Your questions are always welcome. If anything in the lectures is not clear, please, ask. It is better to use QA, so that all other students can see the additional explanation about the unclear topics. Remember: you are never alone in your doubts, and everyone benefits if you ask your questions in the forum.
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Quality: 720p
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file size
42.11 GB