Pre-Calculus Mathematics - Fundamentals of Functions
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Pre-Calculus Mathematics - Fundamentals of Functions

How to represent all fundamental math functions graphically
4.6 (6 ratings)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
632 students enrolled
Created by Dániel Csíkos
Last updated 7/2017
English
Current price: $12 Original price: $20 Discount: 40% off
4 days left at this price!
30-Day Money-Back Guarantee
Includes:
  • 1.5 hours on-demand video
  • 1 Article
  • 1 Supplemental Resource
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion

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What Will I Learn?
  • How to draw any of the functions
  • What the main properties of functions are
  • How the graphs and operations are connected
  • How to solve graphical problems with functions easily
  • Linear functions
  • Absolute value functions
  • Quadratic functions
  • Square root functions
  • Rational functions
  • Exponential functions
  • Logarithmic functions
  • Trigonometric functions
View Curriculum
Requirements
  • Very basic elementary school level mathematical knowledge
  • A desire to get better in mathematics
Description

Welcome!

This course offers a quick overview of the fundamentals of mathematical functions. By taking and finishing this course you are going to understand what the basic functions mean and how you can represent them graphically. Therefore you are going to know how you can draw functions which are connected to the basic functions.

I dedicate a section to every important function. First I introduce the function and its main properties to you, and then I show you numerical examples. These sample problems are going to help you to get the essence of each function. There are several checkpoints where you can check your knowledge through solving quizes.

I believe in learning through examples so the course is highly practical. If you want to practice, you can stop the videos and make an effort of solving the numerical examples by yourself!

You don't need much of a prior knowledge to take this course. If you know how to add, subtract, multiply and divide numbers, you are basically good to go! I'm going to clear the necessary details during the lectures.

This course is primarily designed for secondary school students who are learning about these function in school but who are struggling with the understanding of the functions. However if you passed secondary school but you feel like you need to practice the basics, you are also welcome in this course!

I hope I can help you with this course just like I've already helped more than 600 students! I can't wait to see you inside! Have fun and learn a lot!

Who is the target audience?
  • Secondary school students (appr. between age 14-19)
  • Anyone who wants to revise basics before learning higher level mathemarics (Calculus, etc.)
Compare to Other Pre-Calculus Courses
Curriculum For This Course
31 Lectures
01:15:52
+
Introduction
1 Lecture 01:33

Introduction to the content of the course

Preview 01:33
+
Linear function
5 Lectures 15:30

What a linear function is, what the parameters of the linear function mean

Preview 02:52

How to find the x-intercept of a linear function

Preview 02:39

Practice example about the main properties of a linear function

Preview 03:03

How to determine the equation of a linear function if you know its diagram

3. Example – Graphical representation
03:43

How to plot a linear function if you know its equation

4. Example – Graphical representation
03:13

Let's see whether you have learnt everything in this section or not!

Checkpoint - Linear function
7 questions
+
Absolute value function
4 Lectures 10:15

What an absolute value function is, how to the absolute value x function looks like

Absolute value function
01:23

How to apply basic transformations to functions, translation along x and y

Transformation of functions
02:53

How to determine the parameters of the transformation if the diagram of the transformed function is known

1. Example – Transformations
02:23

How to plot an absolute value function with basic function transformations

2. Example – Transformations
03:36

Let's see whether you have learnt everything in this section or not!

Checkpoint - Absolute value function
6 questions
+
Quadratic function
3 Lectures 09:31

What a quadratic function means, how the diagram of the x squared function looks like

Quadratic function
01:19

How to analyze a quadratic function by drawing its diagram

1. Example – Extreme value of the quadratic function
03:10

How to analyze a general second order term by reformulating and drawing its diagram

2. Example – Range, roots
05:02

Let's see whether you have learnt everything in this section or not!

Checkpoint - Quadratic function
2 questions
+
Square root function
3 Lectures 05:43

What a square root function means, how the diagram of the square root x function looks like

Square root function
02:59

How to determine the domain of a square root function

1. Example – Domain of the function
00:54

How to plot an arbitrary square root function

2. Example – Graphical representation
01:50

Let's see whether you have learnt everything in this section or not!

Checkpoint - Square root function
2 questions
+
Rational function
2 Lectures 03:15

What a rational function means, how the diagram of the (1 per x) function looks like

Rational function
01:32

How to plot an arbitrary (1 per x) like function

1. Example – Graphical representation
01:43
+
Exponential function
3 Lectures 07:42

What an exponential function means, how the diagram of the general exponential function looks like

Exponential function
03:21

How to plot a given exponential function

1. Example – Graphical representation
02:21

How to find the base of the exponential function from its diagram

2. Example – Base of the exponential function
02:00

Let's see whether you have learnt everything in this section or not!

Checkpoint - Exponential function
3 questions
+
Logarithmic function
2 Lectures 07:11

What a logarithmic function means, how the diagram of the general logarithmic function looks like

Logarithmic function
04:28

How to plot a given logarithmic function

1. Example - Graphical representation
02:43

Let's see whether you have learnt everything in this section or not!

Checkpoint - Logarithmic function
3 questions
+
Trigonometric functions
6 Lectures 14:39

What the trigonometric functions (sine, cosine, tangent, cotangent) are, what are the main properties of the trigonometric functions

Trigonometric functions
04:08

What the most important function values of trigonometric functions (sine, cosine, tangent) are

Important function values
01:30

How to solve a basic trigonometric equation considering the basic properties of the trigonometric functions

1. Example – Solving a basic trigonometric equation
02:51

Practice example about the main properties of the trigonometric functions

2. Example – Domain
01:33

How the transformations of the trigonometric functions affect the range of the sine or cosine function

3. Example – Range
01:53

How the transformations of the trigonometric functions affect the periodicity of the sine or cosine function

4. Example – Periodicity
02:44

Let's see whether you have learnt everything in this section or not!

Checkpoint - Trigonometric functions
6 questions
+
Useful formulas
1 Lecture 00:03

The useful formulas that you need to know about the functions that you've just learnt about

Useful formulas
00:03
1 More Section
About the Instructor
Dániel Csíkos
4.7 Average rating
72 Reviews
2,392 Students
10 Courses
Mechanical engineer

* GÖRGESS LE A MAGYAR VERZIÓÉRT *

Welcome to my page! :)

I'm a mechanical engineer and an online entrepreneur. I'm already teaching more than 2300 students worldwide and I look forward to see you as my student, too.

Besides my engineering and mathematical profile, I'm committed to honor my Hungarian heritage by introducing Budapest and Hungary to everyone around the world. I'd love to bump into you in Budapest so I designed my Budapest courses with my engineering preciseness to give you the ultimate experience!

I've got my MSc level degree in mechanical engineering at Budapest University of Technology and Economics and I'm enthusiastic about sharing my knowledge and my love of engineering sciences.

I've been teaching and helping mechanical engineering students as a private tutor in various subjects for 3 years. Therefore I not only know how to understand a topic as a student but also how to make it understandable for others. I passed most of my subjects with an excellent mark and I hope I can help you to reach the desired mark or objective for yourself by ease, too. I offer guidance to understanding either if you are a student or if you want to refresh and widen your knowledge as an engineer in practice.

If you can trust me and follow my courses, I can take you from beginner level to be an expert of mechanics enginnering related topics. I came far on this road and I wish you great success, too!

I'm looking forward to welcome you in any of my courses! It would be so much fun and honor to me to help you worldwide :)

Daniel


Üdvözöllek!

Én egy frissen végzett gépészmérnök vagyok, aki tudja, hogy miből tart elvégezni egy nehéz képzést vagy túlesni egy lehetetlennek tűnő vizsgán, ezért szeretném továbbadni neked is a tudásom! Legyen szó egyetemi szintű gépész tárgyakról vagy az érettségiről, én már megszereztem a magam ötösét és itt az ideje, hogy te is megszerezd azt a jegyet, amitől boldog leszel.

Már évek óta segítek másoknak felkészülni, ezért tudom, hogy hogy értessek meg bármilyen tananyagot is. Ezt tapasztald meg nyugodtan, minden kurzusomhoz van elérhető ingyenes bemutató rész, bátran nézd végig őket és az alapján hozz döntést!

Én nagyon remélem, hogy a sikeres diákjaim között köszönthetlek majd és együtt készülhetünk fel!

Dani