Udemy – Calculus 1, part 1 of 2: Limits and continuity 2024-10

Udemy – Calculus 1, part 1 of 2: Limits and continuity 2024-10 Downloadly IRSpace

Apr 17, 2025 - 12:47 Updated: Apr 21, 2025 - 04:53

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Udemy – Calculus 1, part 1 of 2: Limits and continuity 2024-10

Calculus 1, part 1 of 2: Limits and continuity, You will learn: about the content of this course, and generally about Calculus and its topics. You will learn: you will get a brief recap of the Precalculus stuff you are supposed to master in order to be able to follow Calculus, but you will also get some words of consolation and encouragement, I promise. You will learn: how to generalise some formulas with or without help of mathematical induction. You will learn: the concept of a number sequence, with many examples and illustrations; subsequences, monotone sequences, bounded sequences; the definition of a limit (both proper and improper) of a number sequence, with many examples and illustrations; arithmetic operations on sequences and The Limit Laws for Sequences; accumulation points of sequences; the concept of continuity of arithmetic operations, and how The Limit Laws for Sequences will serve later in Calculus for computing limits of functions and for proving continuity of elementary functions; Squeeze Theorem for Sequences; Weierstrass’ Theorem about convergence of monotone and bounded sequences; extended reals and their arithmetic; determinate and indeterminate forms and their importance; some first insights into comparing infinities (Standard Limits in the Infinity); a word about limits of sequences in metric spaces; Cauchy sequences (fundamental sequences) and a sketch of the construction of the set of real numbers using an equivalence relation on the set of all Cauchy sequences with rational elements.

What you’ll learn

How to solve problems concerning limits and continuity of real-valued functions of 1 variable (illustrated with 491 solved problems) and why these methods work.
The structure and properties of the set of real numbers as an ordered field with the Axiom of Completeness, and consequences of this definition.
Arithmetic on the extended reals, and various types of indeterminate forms.
Supremum, infimum, and a reformulation of the Axiom of Completeness in these terms.
Number sequences and their convergence or divergence; the epsilon-definition of limits of sequences, with illustrations and examples; accumulation points.
Getting new limits from old limits: limit of the sum, difference, product, quotient, etc, of two sequences, with illustrations, formal proofs, and examples.
Squeeze Theorem for sequences
Squeeze Theorem for functions
The concept of a finite limit of a real-valued function of one real variable in a point: Cauchy’s definition, Heine’s definition; proof of their equivalence.
Limits at infinity and infinite limits of functions: Cauchy’s definition (epsilon-delta) and Heine’s definition (sequential) of such limits; their equivalence.

Who this course is for

University and college students wanting to learn Single Variable Calculus (or Real Analysis)
High school students curious about university mathematics; the course is intended for purchase by adults for these 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 Course : 226
Duration : 60 hours and 0 minutes

Content of Calculus 1, part 1 of 2: Limits and continuity

Calculus 1, part 1 of 2 Limits and continuity

Requirements

“Precalculus 1: Basic notions” (or equivalent): mathematical notation, logic, sets, proofs
“Precalculus 2: Polynomials and rational functions” (or equivalent)
“Precalculus 3: Trigonometry” (or equivalent)
“Precalculus 4: Exponentials and logarithms” (or equivalent)
You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody’s advantage if you ask your questions on the forum.

Pictures

Calculus 1, part 1 of 2 Limits and continuity

Sample Clip

Installation Guide

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Subtitle : English

Quality: 720p

The 2024/10 version has increased the duration by 2 minutes compared to the 2023/9 version.

Udemy – Calculus 1, part 1 of 2: Limits and continuity 2024-10