Precalculus 4: exponentials and logarithms
A total of 50 hours of lectures
Due to the size of precalculus, it is divided into four parts. This page describes the fourth and last of those four parts.
Prerequisites
- High-school mathematics, mainly arithmetic; solving simple equations (linear and quadratic) with one unknown; some (but very few) polynomial equations will be solved during the course, but you can skip them if you want to (no problem at all; it will not affect your understanding of the main subjects of the course)
- Precalculus 1: Basic notions (mainly the concept of function and related concepts; sets; logic)
- You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody’s advantage if you ask your questions on the forum.
Curriculum
Make sure that you check with your professor what parts of the course you will need for your exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.
Precalculus 4: exponentials and logarithms
Get the outline
A detailed list of all the lectures in part 4 of the course, including which theorems will be discussed and which problems will be solved. If you are looking for a particular kind of problem or a particular concept, this is where you should look first.
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Course Objectives & Outcomes
How to solve problems concerning exponentials or logarithms (illustrated with 239 solved problems) and why these methods work.
Binomial Theorem with two proofs (a combinatorial one and one by induction), Pascal’s Triangle, and how to apply them.
Definitions and computational rules for powers with various types of exponents (natural, integer, rational, real).
Exponential functions, their properties and graphs.
Power functions, their properties and graphs; interactions between power functions and exponential functions.
Solving exponential equations and inequalities.
Applications of exponential and logarithmic functions in finance, engineering, and natural sciences (some of them in my videos, some as reading material).
Definitions of Euler’s number e, how to approximate it, and how to prove that this number is irrational.
Definition of logarithms in relation to exponents, with computational rules (these will be related to the rules for powers).
Logarithmic functions, their properties and graphs.
Graph transformations for exponential and logarithmic functions, and for some power functions.
Solving logarithmic equations and inequalities.
Reviews (27)
I really liked the way this teacher is preparing the students step-wise for the calculus
Every topic is thoroughly explained and there aren't missing links in the reasoning. Every step is motivated and leads to the next topic. All the exercises are clearly explained step by step. Moreover, Hania always answers quickly and in-depth all the questions!
Highly recommended!