Calculus 1, part 1 of 2: Limits and continuity

🚀 Course Title: Calculus 1, Part 1 of 2: Limits and Continuity 📚

🎓 Course Overview:

"Single variable calculus with elements of Real Analysis: from axioms and proofs to illustrations and computations."

📝 Week 1-3: Introduction to the Course You're about to embark on a mathematical adventure through the world of limits, continuity, and beyond. This course is designed to give you a deep understanding of Calculus, its applications, and the underlying principles that make it work. 🔍

📘 Preliminaries: Basic Notions and Elementary Functions (S2) We'll start with a refresher on Precalculus concepts to ensure you're ready for Calculus. Don't worry if some topics feel daunting; we're here to guide you through every step. 🤫✨

🌍 The Nature of the Set of Real Numbers (S4) Explore the intriguing properties of the real numbers, including the Axiom of Completeness and its profound implications for limits and beyond. 🌍

🔁 Sequences and Their Limits (S5) Dive into sequences with a focus on finding and understanding their limits. We'll cover everything from basic concepts to advanced topics like extended reals, and even touch upon the convergence of sequences using Cauchy's criterion. 🎬

🏜 Limit of a Function in a Point (S6) Understand the precise definition of a function's limit at a point and the concept of continuity, accompanied by practical examples and computational rules for limits. 📈

🚀 Infinite Limits and Limits in the Infinities (S7) Learn to handle limits involving rational functions as they approach zero or infinity, and how these relate to asymptotes. 🚀

✍️ Continuity Properties and Graphing Functions (S8-S9) Explore the properties of continuous functions and start graphing real-valued functions by identifying domains, discontinuities, and asymptotes. This sets the stage for our next course segment on derivatives. 📈

🔍 Extras (S11) Beyond this course, we offer a variety of courses that build upon each other. Keep an eye out for our future offerings and what might be on the horizon! 🧠✨

🚀 Additional Resources (S11) For those looking to dive deeper or prepare for exams, make sure to check out the comprehensive list of all videos and solved problems in "001 List_of_all_Videos_and_Problems_Calculus_1_p1.pdf" linked in video 1. This resource will accompany your learning journey throughout the course. 📄

Why Take This Course?

• Understand the Fundamentals: Master the core concepts of limits and continuity that are essential for advanced calculus topics.
• Real-World Applications: Learn how calculus is applied in various fields such as physics, engineering, economics, and more.
• Step-by-Step Guidance: With detailed video lectures and problem-solving examples, you'll have a clear path to learning.
• Flexible Learning: Study at your own pace, with resources available 24/7 for review and practice.

Join us on this journey through the heart of mathematics. With expert instruction, engaging content, and a supportive community, you'll be well-equipped to conquer the world of calculus. Enroll now and let's discover the wonders of limits and continuity together! 🌟🚀

Important Notes:

• Course Adaptation: The content of this course may vary depending on your institution or country's standards. Always confirm with your professor which parts of the course are required for your exam.
• Comprehensive Course Material: A detailed description of all videos and problems is provided in the resource file linked at the beginning of the course. Make sure to utilize these materials for a deeper understanding of the subjects covered. 📚👍