Calculus 1 Explained
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Calculus 1 Explained

Learn Differential Calculus from scratch with easy explanations!
5.0 (11 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.
568 students enrolled
Created by Harun Omer
Last updated 7/2017
English
Curiosity Sale
Current price: $10 Original price: $50 Discount: 80% off
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Includes:
  • 3.5 hours on-demand video
  • 28 Supplemental Resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
What Will I Learn?
  • Apply Calculus and take derivatives of any function with one variable
View Curriculum
Requirements
  • Prerequisite for succeeding in calculus is a foundation in algebra
Description

This course is for you if you not only need a review of calculus but want to learn (or re-learn) calculus from scratch. Every rule of calculus is derived and explained in an easy to understand video lecture with every step explained. The focus is on quickly being able to work with calculus and be able to take the derivative of an arbitrary function of one variable -- while at the same time understanding what you are doing.

Who is the target audience?
  • Anyone who wants to learn differential calculus independently and be able to apply it
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Curriculum For This Course
35 Lectures
03:40:38
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Precalculus Review
12 Lectures 43:06

Learn how to use the vertical line test to determine whether a graph represents a function or not.

Preliminaries: Functions and the Vertical Line Test
03:00

Review the notation of functions.

Preliminaries: Notation for Functions
00:41

The domain of a function is the set of all permissible input values.

Preliminaries: The Domain of a Function
05:41

The range of a function is the set of all possible output values.

Preliminaries: Range of Functions
02:00

Understand what even and odd functions are.

Preliminaries: Even and Odd Functions
06:35

Watch some examples of even and odd functions.

Preliminaries: Even and Odd Functions Examples
06:44

Introduces you to compositions of functions with a concrete example.

Preview 03:00

The formal definition of a composition of functions.

Preliminaries: Definition of Compositions
01:06

Practice compositions of functions with exercises.

Preliminaries: Practice Compositions of Functions
06:16

Preliminaries: Decomposing Functions
02:46

A geometric explanation what tangents and secants are.

Preliminaries: Tangents and Secants
02:46
+
The Rules of Calculus
18 Lectures 02:20:38

The basic idea of differentiation.

Preview 13:08

Differentiation explained at hand of an example. Find the velocity of an object from its trajectory.

Introduction to Differentiation Part 2
06:09

Derivatives of elementary functions such as x^n, sin(x) and cos(x) are computed.

Derivatives of Elementary Functions
13:17

Multiply a function with a constant and then differentiate.

Derivative Rules: Rescaling
07:38

Build a linear combination of functions and then differentiate.
Work through the exercises!

Derivative Rules: Linear Combinations
07:45

What is the derivative of a product of functions?

Derivative Rules: Proof of Product Rule
09:48

Derivative Rules: Product Rule for Three Factors
02:04

Practice the product rule. Work through the exercises!

Derivative Rules: Application of Product Rule
07:44

What is the derivative of a quotient of functions?

Derivative Rules: Proof of Quotient Rule
06:21

Practice the quotient rule. Work through the exercises!

Derivative Rules: Application of Quotient Rule
09:34

What is the derivative of an exponential function?

Derivatives of Elementary Functions: Exponential Functions
10:03

How do you take the derivative of a composition of functions?

Derivative Rules: Proof of Chain Rule
03:29

Practice the chain rule. Work through the exercises!

Derivative Rules: Application of Chain Rule
08:22

Derivative Rules: Chain Rule with Multiple Compositions
02:34

What is the derivative of a logarithmic function?
Work through the exercises!

Derivatives of Elementary Functions: Logarithms
07:30

It is shown that the power rule is valid for any real exponent.
Work through the exercises!

Derivatives of Elementary Functions: Power Rule
09:07

Sometimes you can not solve an equation for y(x). Through implicit differentiation you may still get y'(x).

Implicit Differentiation
11:25

The big picture. Summary of what you should have learned.

Summary of Differentiation Rules
04:40
+
Applying Calculus to Optimization Problems
5 Lectures 36:54

Learn what local maxima, local minima and inflection points are.
Learn how to use the first and the second derivative test to find them.

Optimization: Finding Local Extrema
09:07

Identify local extrema (maxima and minima) using the first derivative test.

Optimization: Applying the First Derivative Test
07:39

Identify local extrema (maxima and minima) using the second derivative test.

Optimization: Applying the Second Derivative Test
08:20

Optimization with a constraint. Real world-examples.

Optimization: The Optimal Shape of a Tin Can
05:51

A typical optimization problem from business and economics.

Optimization: Company Profit
05:57
About the Instructor
Harun Omer
5.0 Average rating
11 Reviews
568 Students
1 Course
Physicist

Dr. Omer is a theoretical physicist who completed graduate studies at the University of Heidelberg in Germany and at the Massachusetts Institute of Technology (MIT). He completed his PhD work at CERN and went on to work as a researcher at Harvard University. During his career he was involved in teaching physics and mathematics to students at college or university level, including at MIT.