Precalculus 4: Exponentials and logarithms
Mathematics from high school to university
Created by Hania Uscka-Wehlou, Martin Wehlou | 50 hours on-demand video course
In this Precalculus 4: Exponentials and logarithms course You will learn: you will get a very general introduction to exponential and logarithmic functions: how they look and what they describe; you will learn about their simplicity in some aspects, and about some extraordinary complications you don’t necessarily have to 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 you have learned about in the previous courses in the Precalculus series) examples of elementary functions: these functions are the building blocks for all the functions we will work with in the upcoming Calculus series.
What you’ll learn
- How to solve problems concerning 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 material).
- Binomial Theorem with two proofs (a combinatorial one and one by induction), Pascal’s Triangle, and how to apply them.
- Definitions of Euler’s number e, how to approximate it, and how to prove that this number is irrational.
- Definitions and computational rules for powers with various types of exponents (natural, integer, rational, real).
- Definition of logarithms in relation to exponents, with computational rules (these will be related to the rules for 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.
- Graph transformations for exponential and logarithmic functions, and for some power functions.
- Solving exponential equations and inequalities.
- Solving logarithmic equations and inequalities.
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