Explanation
Precalculus 4: Exponents and logarithms You will learn: you will get a very general introduction to exponential and logarithmic functions: what they look like and what they describe; you will learn about their simplicity in some aspects, and unusual problems that you don’t necessarily think about (but you should have a general idea about them); Exponential and logarithmic functions are (next to polynomials, rational functions, power functions, trigonometric and inverse trigonometric functions that you learned in previous courses in the Precalculus series) examples. basic functions: These functions are the building blocks of all the functions we will work with in the next Calculus series. The honorable number eThe Binomial Theorem, and Pascal’s Triangle You will learn: about numbers eboth in a more intuitive way (pictures) and a more formal way.
To be able to do some formal proofs, you will need the Binomial Theorem: The theory that tells you how to raise the sum of two terms to any natural power; You’ll learn about factorization, binomial integration, and Pascal’s triangle (all of which will come back in the Discrete Mathematics course, and then you’ll get lots of practice and problem solving). combination to solve; now we only need the Binomial Theorem as a tool eyou will learn: about powers with natural exponents, filters, and logic and the calculation rules for them. nroots of numbers. We will gradually gain more understanding on the subject of preparing exponential functions. You will also find many exercises to enjoy the topic of powers of different types of exponents, and related power calculations.
What will you learn?
- How to solve problems about exponentials or logarithms (illustrated with 239 solved problems) and why these methods work.
- Applications of exponential and logarithmic functions in finance, engineering, and natural sciences (some of them in my videos, some as reading materials).
- Binomial Theorem with two proofs (additive and additive), Pascal’s Triangle, and how to apply it.
- Definitions of the Euler number e, how to estimate it, and how to prove that this number is irrational.
- Definitions and calculation rules for powers with different types of exponents (natural, integral, rational, real).
- Definition of logarithms related to exponents, with mathematical rules (even these will be related to the rules of powers).
- Exponential functions, their properties and graphs.
- Logarithmic functions, their properties and graphs.
- Power functions, their properties and graphs; interactions between power functions and exponential functions.
- Graphing transformations of exponential and logarithmic functions, and some power functions.
- Solving exponential equations and inequalities.
- Solving logarithmic equations and inequalities.
Who is this course for?
- Students planning to study Algebra, Calculus or real analysis
- High school students who are interested in university mathematics; The course is designed to be purchased by adults and students
- Anyone who wants to clear high school math and gain a deeper understanding of the subject
- College and university students studying advanced courses, who want to understand all the details (about exponents and logarithms) that they may have missed in their previous studies.
- Students who want to learn exponents and logarithms, for example in a college algebra class.
Special Precalculus 4: Exponents and logarithms
Precalculus Content 4: Exponents and logarithms
Requirements
- High school math, mostly math; solving simple equations (linear and quadratic) with unknowns; Some (but very few) differential equations will be solved during the course, but you can skip them if you want (no problem at all; it will not affect your understanding of the main subjects of the course)
- Precalculus 1: Basic concepts (mostly concept of function and related concepts; sets, logic)
- Your questions are always welcome. If something 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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