Calculus 2, part 1 of 2: Integrals with applications

🚀 Calculus 2, Part 1 of 2: Integrals with Applications 📚

Course Introduction 🎓

Dive into the world of Integral Calculus, where we'll explore the theory and practical applications that allow us to compute areas between curves, curve lengths, and volumetric measurements. This course is a pivotal step in your journey through advanced calculus.

🔹 What You'll Learn

• The scope of this course and the significance of Integral Calculus.
• The basics of differentiation in reverse to understand integrals as a process of reversing the differentiation process.

Integration by Parts: Product Rule in Reverse 🍏⫫📈

• ⭐️ Master Integration by Parts: Learn this fundamental technique and see it applied to various functions, from basic to mind-bending examples.

Change of Variables: Chain Rule in Reverse 🌍

• ⭐️ Solve Complex Integrals: Discover how variable substitution can simplify multistep problems within integrals.

Integrating Rational Functions: Partial Fraction Decomposition 🎢

• ⭐️ Break Down Rational Functions: Learn the art of breaking down rational functions into simpler parts for easier integration.

Trigonometric Integrals ⚫️

• ⭐️ Conquer Trigonometric Functions: Learn different methods to compute integrals with trigonometric functions, including some exotic ones!

The Fundamental Theorem of Calculus & Beyond 🧭

• ⭐️ Understand The Fundamental Theorem: Explore its applications in evaluating areas, computing limits, and finding derivatives.

Area, Arc Length, Rotational Volume & More 📏✨

• ⭐️ Calculate Geometric Properties: Compute the area between curves, arc length of functions, rotational volume, and even more.

Improper Integrals: Exploring the Infinite ⚡

• ⭐️ Tackle Improper Integrals: Learn about improper integrals over infinite intervals and at endpoint discontinuities.

Comparison Criteria for Convergence 🔍

• ⭐️ Evaluate Convergence: Use comparison criteria to determine the convergence of improper integrals by comparing them to well-known cases.

Extras & What's Next? 👀

• ⭐️ Explore More: Get a sneak peek into additional courses we offer and catch a glimpse of our future course plans.

Course Resources 📚

• A comprehensive list of all videos and problems for this course is available in the resource file "001 List_of_all_Videos_and_Problems_Calculus_2_p1.pdf", located under video 1, "Introduction to the Course."

Make sure to align your studies with your professor's expectations for the final exam. The content of this course can vary by region and institution, and even from year to year.

Embark on a calculus odyssey that will transform the way you see geometry, analysis, and problem-solving. With Integral Calculus as your compass, navigate through the intricate landscape of advanced mathematics! 🌟