For more information, please see full course syllabus of Math Analysis

For more information, please see full course syllabus of Math Analysis

## Discussion

## Study Guides

## Download Lecture Slides

## Table of Contents

## Transcription

## Related Books

### Introduction to Math Analysis

- Depending on the school or institution providing this course, this class can go by a wide variety of different names:
- Pre-Calculus
- Math Analysis
- Trigonometry
- Algebra III
- Geometry II
- College Algebra

- Each lesson introduces the concepts, works out the ideas involved, explains how to use them, and then gives a wide variety of examples. We'll also regularly work through word problems.
- This course was designed for a wide variety of students:
- Those who are taking one of the previously mentioned classes and who want some extra help.
- People working on the material but who aren't taking a formal class at a school.
- Anyone who needs a refresher on the concepts, whether it's for science class or another math class.

- When watching the lessons, try to watch the whole lesson. While it can be tempting to skip straight to the examples, you'll gain a lot more understanding if you make sure the concepts make sense
__before__working problems. - It's very important to understand ideas that have come up in previous math classes. Very often, students have trouble not because what they're currently learning is confusing, but because they didn't fully understand past concepts. If this is true for you, use Educator.com to review the material that keeps giving you trouble. It will help a lot in the long run.
- For everyone, make sure you watch these two lessons first:
- Lesson #2:
*Sets, Elements, and Numbers* - Lesson #7:
*Idea of a Function*

- Lesson #2:
- If you find yourself struggling with word problems, check out the lesson
- Lesson #6:
*Word Problems*

- Lesson #6:
- If you've had a lot of difficulty with previous math classes, the first seven lessons after this one form a review of important concepts:
- Lesson #2:
*Sets, Elements, and Numbers* - Lesson #3:
*Variables, Equations, and Algebra* - Lesson #4:
*Coordinate Systems* - Lesson #5:
*Midpoint, Distance, the Pythagorean Theorem, and Slope* - Lesson #6:
*Word Problems* - Lesson #7:
*Idea of a Function* - Lesson #8:
*Graphs*

- Lesson #2:
- At the very end of the course is an appendix dedicated to learning how to use graphing calculators. It's got a lot of useful stuff, so check it out. We'll go over a bunch of free options as well, so it's useful even if you don't own a graphing calculator right now.

### Introduction to Math Analysis

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Title of the Course
- Different Names for the Course
- Precalculus
- Math Analysis
- Trigonometry
- Algebra III
- Geometry II
- College Algebra
- Same Concepts
- How do the Lessons Work?
- Who is this Course For?
- Those Who Need eExtra Help with Class Work
- Those Working on Material but not in Formal Class at School
- Those Who Want a Refresher
- Try to Watch the Whole Lesson
- Understanding is So Important
- What to Watch First
- What to Watch First, cont.
- Lesson #2: Sets, Elements and Numbers
- Lesson #3: Variables, Equations, and Algebra
- Lesson #4: Coordinate Systems
- Lesson #5: Midpoint, Distance, the Pythagorean Theorem and Slope
- Lesson #6: Word Problems
- Lesson #7: Idea of a Function
- Lesson #8: Graphs
- Graphing Calculator Appendix
- What to Watch Last
- Let's get Started!

- Intro 0:00
- Title of the Course 0:06
- Different Names for the Course
- Precalculus
- Math Analysis
- Trigonometry
- Algebra III
- Geometry II
- College Algebra
- Same Concepts
- How do the Lessons Work? 0:54
- Introducing Concepts
- Apply Concepts
- Go through Examples
- Who is this Course For? 1:38
- Those Who Need eExtra Help with Class Work
- Those Working on Material but not in Formal Class at School
- Those Who Want a Refresher
- Try to Watch the Whole Lesson 2:20
- Understanding is So Important 3:56
- What to Watch First 5:26
- Lesson #2: Sets, Elements, and Numbers
- Lesson #7: Idea of a Function
- Lesson #6: Word Problems
- What to Watch First, cont. 6:46
- Lesson #2: Sets, Elements and Numbers
- Lesson #3: Variables, Equations, and Algebra
- Lesson #4: Coordinate Systems
- Lesson #5: Midpoint, Distance, the Pythagorean Theorem and Slope
- Lesson #6: Word Problems
- Lesson #7: Idea of a Function
- Lesson #8: Graphs
- Graphing Calculator Appendix 7:40
- What to Watch Last 8:46
- Let's get Started! 9:48

### Math Analysis Online

### Transcription: Introduction to Math Analysis

*Hi--welcome to Educator.com?*0000

*For our first lesson, we are going to have a quick introduction to the course.*0002

*What is this course called? Depending on the school you attend, this course goes by a wide variety of different names:*0005

*Precalculus, Math Analysis...it might be called Math Analysis with Trigonometry, or simply Trigonometry...*0011

*It might be called Precalculus and Trigonometry; it could be called Algebra III; it might be called Geometry II;*0017

*it might be called Algebra III and Geometry II; it might be called College Algebra (if you are in a college course);*0022

*it might be called College Algebra with Trigonometry; and it might be called something different from all of these.*0028

*It has a lot of names, sadly; but still, all of these different names imply basically the same set of concepts.*0033

*Those that are essential for science classes, and those that form the necessary foundation for calculus, if you decide to continue in math--*0039

*those are all the concepts that this course on Educator.com will work through.*0046

*So, how do the lessons work? Each lesson starts off by introducing the concepts.*0051

*We will make sense of the ideas involved, and we will say how they connect to what we have previously learned.*0055

*After we have a sense for what we are working on, we will learn how to apply these new concepts,*0059

*whether it is through new formulas or methods for solving problems, or just a new way of thinking.*0064

*We will come to understand how to use it.*0069

*Not only will we learn how to use the concepts, though; we will also learn why they work, and why they make sense,*0071

*so we can do more than just do problems; we can also actually understand what is going on and work on later concepts with that.*0077

*Finally, we will end each lesson by working through a wide variety of examples, so we can see the concepts in action.*0084

*Plus, most lessons will contain at least one word problem to help us see how to apply math in the real world.*0091

*Who is this course for? In short, anyone who needs help with the concepts contained in this course.*0097

*This course was designed and created with many different types of students in mind.*0102

*It is for those who are taking one of those previously mentioned classes, and they just want some extra help.*0106

*It is also for people working on the material, but who aren't taking a formal class at a school,*0111

*and anyone who just needs a refresher on the concepts, whether it is for a science class or another math class that they are taking.*0116

*Because the lessons combine an understanding of the material with step-by-step working through examples,*0122

*this course is great for students with diverse needs; it can help a whole bunch of different people, because it really teaches the whole thing.*0127

*When watching lessons, some students will just skip straight to the examples and only watch enough so that they can do their homework.*0135

*I want to urge you against doing this.*0141

*While this can work for getting homework done in the short term, it quickly falls apart in the long term.*0144

*So much of math builds upon previous ideas.*0150

*If you don't really understand what is happening now, understanding later concepts will be extremely difficult.*0153

*Because so many things are built "stair-step" after another, if you don't really understand what is happening today,*0161

*you might be able to get through the homework; but getting through other work in a couple of months*0166

*is going to become really, really difficult; it might become almost impossible.*0170

*The best thing you can do for your future understanding is to focus on more than just doing homework problems.*0173

*Watch the whole lesson, and make sure that the concepts are truly clear to you.*0180

*You really want to have an understanding of everything that is going on, not just how to do problems.*0185

*This helps, not just today, but later as well: this gives you the ability to understand what is going to happen in a few months or a few years.*0190

*And of course, if you already understand the concepts, and you just want some guidance on doing the problems, by all means, skip away.*0198

*But if you don't quite understand what is going on--you don't really see how the concepts work--*0204

*try to watch the whole lesson, because that will give you a much better understanding of how those examples work.*0208

*It is like the difference between teaching someone to fish and just handing them a fish.*0213

*You can either teach them a skill for the rest of their life, that they can use as long as they need it; or you can just feed them today.*0217

*If you end up only going to the examples, you are able to eat today, but you won't necessarily be able to "eat" in the long term.*0223

*And I want to teach you as much as I can, so you can really understand, and eventually be fine without needing any outside help.*0229

*In the same way, it is so important to understand the ideas that have come up in previous math classes.*0236

*We will do a fair bit of review in this course, but occasionally that will not be quite enough sometimes.*0242

*I have taught many students who understand the material that they are currently working on,*0247

*but they keep missing problems, because they don't fully understand past concepts--things that they learned previously.*0252

*They understand the new stuff--all of the new stuff that they are working on makes sense.*0259

*They get the ideas; they can do the problems; but these old ideas, like canceling negatives,*0262

*or working with fractions--things like that--just keep coming up, and they mess them up,*0267

*and they end up not being able to get problems right, not because they don't understand the big, new, complicated idea,*0270

*but because they don't understand this old, little thing that they never quite fully worked out back then.*0276

*If you find yourself having similar problems, go back and re-learn whatever is giving you trouble.*0280

*You have access to all of Educator.com here; that is a great resource.*0285

*You have all of this material in other courses at hand, so that you can easily review whatever ends up giving you trouble now.*0289

*If you notice that you keep missing the same kinds of problems--you keep making some mistake with some specific thing--*0296

*search it on Educator.com and try to re-learn that portion.*0301

*Once you have that under your belt, you will be able to stop making mistakes on that, and you won't have to worry about those things catching you.*0304

*It is not necessarily all about not understanding what is happening today.*0310

*You might understand perfectly what is going on and the things you are learning right now.*0313

*But because of this one little thing that you didn't fully understand previously, it keeps tripping you up.*0316

*But if you go back and re-learn it, you will be in a great position.*0321

*For everyone, I highly, highly recommend starting by watching the two lessons here:*0325

*Lesson #2 (Sets, Elements, and Numbers), and Lesson #7 (Idea of a Function).*0330

*The concepts in these two show up all over math, and some teachers don't do a very good job of explaining them, sadly.*0336

*Since they are so important and so common, I want to make sure that they make sense to you as soon as possible.*0346

*So, I really want you to have a chance to watch these early on, so that the later things that build on these ideas make as much sense to you as possible.*0352

*Also, if you have difficulty with word problems, check out the fifth lesson (unsurprisingly name "Word Problems").*0361

*It is not a terribly creative title, but "Word Problems" is this lesson that will help you see how to understand word problems and how to approach them.*0367

*It will build this framework for approaching all word problems.*0374

*That is something that you can start using on anything where you are having difficulty seeing how to set it up.*0377

*If you don't have time to watch any of these right now, that is perfectly OK.*0381

*Just try to come back and watch them in the next couple of weeks.*0386

*These ideas are crucial, and it will make a lot of things easier later on, once you have a good understanding of them.*0390

*It is not something you have to get done instantly.*0396

*But by having it done as soon as you can, you will end up being able to understand later things much more easily.*0399

*If you have had difficulty in previous math classes--if math class has been a little difficult for you--*0405

*you might want to watch the first seven lessons, because they form a review of important concepts:*0409

*Lesson #2 is Sets, Elements, and Numbers; #3 is Variables, Equations, and Algebra.*0414

*4 is Coordinate Systems; 5 is Midpoint, Distance, the Pythagorean Theorem, and Slope.*0420

*6 is Word Problems (I guess that should have been the sixth lesson previously; sorry about that).*0425

*Lesson #7 is Idea of a Function; and Lesson #8 is Graphs.*0431

*The ideas in these lessons form a foundation for much of the course.*0435

*If you can make sense of them, you will be in a good position for understanding what comes later on.*0439

*So, you really want to make sure that these ideas make sense to you,*0443

*because if they don't quite make sense to you right now, later stuff is going to be really hard.*0446

*But we will do a lot of review in these beginning review pieces, so that they will give you the chance to really understand what happens later on.*0450

*At the end of this course, there is an appendix all about graphing calculators and graphing programs.*0459

*But just because it comes last, just because it comes at the end of the course, doesn't mean you should wait to watch that.*0464

*You should watch it as soon as you have the chance--as soon as you are interested in it.*0469

*By this stage in your mathematics career, you might be considering purchasing a graphing calculator, or you might already own one.*0473

*The appendix will help you get started.*0479

*It has recommendations for buying one; it goes over the basics of use; and it explores some of the more advanced abilities for graphing calculators.*0481

*And even if you don't want to buy a graphing calculator--even if you know for sure that you are not going to buy a graphing calculator*0488

*(you just don't feel like spending the money), I recommend checking out the first lesson in the appendix.*0494

*We start that lesson by looking at a bunch of free options.*0498

*And it can really help to know that these things are available, and that you can have them on any computer really, really easily.*0502

*Having access to a graphing calculator, something that you can graph with, can make a lot of problems a whole lot easier.*0507

*It helps you really quickly build up an intuition that just doing these things by hand can't get you very quickly.*0512

*So, I really recommend checking out that first lesson; see some of the free options, even if you aren't interested in buying a graphing calculator.*0517

*Finally, what do you want to watch at the very end of the course?*0524

*At the end of this course is a short section that gives a preview of calculus.*0527

*Some math classes at various schools will work through this section, but others will simply skip it.*0531

*Either way, if you eventually plan on continuing to calculus, I recommend watching it at some point.*0537

*Being exposed to the ideas of calculus before actually being in a class--*0543

*before actually making it to a calculus class--can really help things click into place later.*0549

*Plus, calculus is really cool! I think calculus is really interesting to learn about.*0554

*You will probably want to watch it once you have worked through most of the rest of the course, though,*0558

*since it builds on previous ideas (so it is useful to have that foundation already there before you watch it).*0561

*And of course, you should still feel totally free to watch this, even if you don't plan to take calculus.*0567

*I think this stuff is really interesting, and it gives you a chance to watch this stuff*0572

*and be able to understand something that you might not get exposed to otherwise.*0576

*I think calculus is really cool, so if you are a little bit interested, even if you don't think you will take calculus,*0580

*you might want to check it out, because it is really cool stuff.*0584

*All right, that finishes it for this time--we are done with our housekeeping.*0587

*Now that you have a sense of how the course works, let's dive into it!*0590

*I hope you enjoy this course and learn a lot.*0592

*I put a lot of effort into this to give you the best understanding of the concepts that I possibly could.*0594

*I am looking forward to teaching it--all right, let's go!*0598

*I will see you at Educator.com later; goodbye!*0601

1 answer

Last reply by: Professor Selhorst-Jones

Thu Jul 13, 2017 1:37 PM

Post by Mohamed E Sowaileh on July 10 at 08:40:38 AM

Hello Dr. Vincent Selhorst-Jones,

I hope you are very well,

I am a student who is extremely weak in math. In order to be very strong in math, specially for engineering field, could you provide me with sequential order of mathematical topics and textbooks. With what should I begin so that I can master big topics like calculus, statistics, probability ... etc.

Your guidance is precious to me.

Thank you so much.

4 answers

Last reply by: Firebird wang

Fri Nov 4, 2016 1:32 AM

Post by Firebird wang on November 2, 2016

Sir, I know AP Statistics is not your subject, but I just wonder if you are able to watch the two videos which called AP Statistics Practice Test 2013 an AP Statistics Practice Test 2014 in the AP Statistics content? Both videos showing network error, I dont know why. I already tried in different computers already.

1 answer

Last reply by: Professor Selhorst-Jones

Mon Jul 4, 2016 12:35 AM

Post by Rolly Rolly on July 3, 2016

Hi professor, did you use the Wacom Cintiq 22 hd to recored the lectures?

2 answers

Last reply by: Javed Ghanniaiman

Sat Jul 2, 2016 11:50 PM

Post by Javed Ghanniaiman on July 1, 2016

Hi there,

Why are the slides in jpg format? This is not appropriate for printing out properly.

They should be pdf at the very least.

0 answers

Post by Joe Gahm on January 18, 2015

YES

2 answers

Last reply by: manojh sivapathasundaram

Wed Apr 8, 2015 7:50 PM

Post by Enrique Salinas on September 2, 2014

Hi Professor selhorst-jones i am currently taking pre-calculus and am having trouble solving these two equations do you think you could help me?

the equations are 3(9+7x)-(2-x)(9+7x)and z^2(4z-z^3)+7(z^3-4z) both of these equations need to be factored

1 answer

Last reply by: Professor Selhorst-Jones

Fri Aug 29, 2014 6:15 PM

Post by John K on August 26, 2014

Professor

Is this course advisable for taking SAT Math Level 2?

1 answer

Last reply by: Professor Selhorst-Jones

Fri Jun 27, 2014 10:00 AM

Post by Jason Wilson on June 27, 2014

My android with chrome will not play the videos. Wh where Di I go for help on this?

2 answers

Last reply by: Daniel Schick

Tue Feb 18, 2014 8:05 PM

Post by Daniel Schick on February 13, 2014

Hi professor, I am taking courses on Educator because i do not have enough in my schedule to take them in school. I was wondering if this course will be able to completely take place of a high school pre-calc course or not.

1 answer

Last reply by: Professor Selhorst-Jones

Fri Dec 13, 2013 7:40 PM

Post by James Connolly on December 11, 2013

That was an awesome video and you did an excellent job explaining everything.

1 answer

Last reply by: Professor Selhorst-Jones

Thu Aug 8, 2013 3:24 PM

Post by Tribhuwan Joshi on August 3, 2013

I have a question which I need help with:

Sam and Markus are standing on level ground 100 metres apart. A large tree is due North of Markus and on a bearing 065 degrees from Sam. The top of the tree appears at an angle of elevation of 25 degrees to Sam and 15 degree to Markus. Find the hieght of the tree.

There was no diagram. Thanks in advance to anyone who helps.

The answer is 29.3m, if that helps and to check if you are correct.

If you know how to do it, then please email me to let me know: [REDACTED]@yahoo.com

Thanks again

6 answers

Last reply by: Professor Selhorst-Jones

Wed Jul 23, 2014 1:43 PM

Post by Taylor Wright on July 22, 2013

What are the differences between this course and the pre-cal course that you teach?

1 answer

Last reply by: Arshin Jain

Sun Jun 30, 2013 10:01 PM

Post by binti farah on April 21, 2013

very interesting