Precalculus 4: Exponentials and logarithms

🎉 Precalculus 4: Exponentials and Logarithms 📚

Course Headline:

Master the Algebra 2 topics of exponential, logarithmic, and power functions with our Precalculus 4 course, as you prepare to dive into the world of Calculus!

Introduction to the Course 🔍

In this course, you'll embark on a mathematical journey through the realm of exponential and logarithmic functions. These fundamental concepts are not only beautiful in their simplicity but also serve as the building blocks for more complex functions you'll encounter in Calculus. You'll get a general introduction to these functions, understanding their elegance and the complexities that make them indispensable in higher mathematics. 🎓

S1. The Noble Number e & The Binomial Theorem 🌿

• e: Discover the mysterious and fascinating number e, its properties, and why it's central to calculus and natural growth models.
• The Binomial Theorem: Learn how this theorem simplifies expansions of powers and binomials, preparing you for algebraic manipulations in Calculus.

S2. Exponential Functions & Their Graphs 📈

• Understand the definition and properties of exponential functions.
• Learn how to sketch their graphs by hand or using graphing software/tools.

S3. Logarithmic Functions as Inverses to Exponential Functions 🔄

• Dive into logarithms with various bases and learn why they are inverses of exponential functions.
• Explore the properties and graphs of logarithmic functions, and see how transformations can alter their appearance.

S4. Solving Exponential Equations & Inequalities 🔍

• Gain expertise in solving linear, quadratic, and exponential equations and inequalities.
• Learn to interpret the solutions in real-world contexts like growth rates, compound interest, and radioactive decay.

S5. Solving Logarithmic Equations & Inequalities 🧮

• Master the techniques for solving logarithmic equations and inequalities.
• Understand how to rewrite expressions involving powers and roots to solve for unknown exponents and bases.

S6. Applications of Exponential & Logarithmic Functions 🌍

• Apply your knowledge to real-world problems such as understanding percent change, growth models, and calculating compound interest.
• Explore various applications in different fields like science, finance, and technology.

S7. Advanced Topics 🌟

• Dive deeper with more advanced examples from Calculus, including hyperbolic functions and the use of derivatives to understand growth models.
• Solve mixed equations and inequalities involving radicals, exponentials, and logarithms.

S8. Extras & Beyond 🔄

• Get a preview of all the courses we offer to complement your learning journey.
• Catch a glimpse into our future course plans and potential release dates.

Course Notes & Resources 📚

• Detailed Description: A comprehensive list of all videos and problems solved in this course, along with their titles, is available in the resource file "001 List_of_all_Videos_and_Problems_Precalculus_4.pdf", which can be found under video 1 ("Introduction to the Course").
• Problem Solving: Watch and learn from 239 carefully chosen problems, each with a detailed solution approach.
• Stay Updated: Remember to check with your professor what topics are essential for your final exam, as requirements may vary by institution or year.

Join us on this enlightening adventure into the world of exponentials and logarithms, where you'll not only understand these fundamental concepts but also how they apply to real-life scenarios. 🚀✨