Introduction to Differentiation (Differential Calculus)

A great way to start learning Calculus through video lectures and quizzes.

4.25 (62 reviews)
Udemy
platform
English
language
Math
category
8,383
students
13 hours
content
Apr 2016
last update
$19.99
regular price

What you will learn

Perform raw Differentiation using Limit method

Perform Differentiation using the Prime Formula, Product Rule, Quotient Rule and Chain Rule

Perform Differentiation on Explicit and Implicit Functions

Find the equations of Tangent and Normal Lines to a curve

Perform Higher Order Differentiation

Identify and determine Turning Points, Stationary Points, Maximum Points, Minimum Points and Points of Inflection on a curve using Second Order Derivative

Solve Geometrical problems using Maximum and Minimum values

Find Rates of Change in problems involving Geometry

Approximate results of small changes to the input

Description

This is an introductory course on Differential Calculus. It comprises of a total of close to 13 hours worth of videos and quizzes. This is perfect for secondary school students seeking a good primer on Calculus. It is also great as a refresher for everyone else.

The course is arranged from the very basic introduction and progresses swiftly with increasing depth and complexity on the subject. It is recommended that the students do not skip any part of the lectures, or jump back and forth, because good understanding of the fundamental is important as you progress.

Quizzes are included on 15 subtopics to strengthen your understanding and fluency on this topic. So it is advisable that you attempt all the questions.

The course is delivered by an experienced teacher with five years of experience teaching students on a one to one basis. The instructor understands the difficulties that students normally face to become competent in mathematics. So words and examples were carefully chosen to ensure that everybody gets the most out of this series of lectures. This is a MUST course for all secondary school students.

Have fun learning!

Content

Introduction

About the Instructor and High Level Overview of the course.
Basic Concept of Differential Calculus

Limits and Instantaneous Gradient of a Curve

Introduction to Limits
Introduction to Limits (cont)
Introduction to Limits (cont)
Quiz on Limits
Answers to Quiz on Limits
Estimation of Differential using Gradient of a Chord
Estimation of Differential using Gradient of a Chord (cont)
Using Limit method to find First Derivative of Polynomials
Using Limit method to find First Derivative of Polynomials (cont)
The Derivative from First Principles
Answers to Quiz on The Derivatives from First Principles

Derivation of Differential Formula

Deriving the Prime Formula for Differentiation
Deriving the Prime Formula for Differentiation (cont)
Deriving the Prime Formula for Differentiation. Supplementary Lecture.
Deriving the Prime Formula for Differentiation. Supplementary Lecture. (cont)

Differentiation of Polynomial Functions

Determining the First Derivative using the prime Differentiation Formula
Determining the First Derivative using the prime Differentiation Formula (cont)
Differentiation using the Prime Differentiation Formula
Answers to Quiz on Differentiation using the Prime Differentiation Formula
Product Rule
Differentiation with Product Rule
Answers to Quiz on Differentiation with Product Rule
Quotient Rule
Differentiation with Quotient Rule
Answers to Quiz on Differentiation with Quotient Rule
Chain Rule
Differentiation with Chain Rule
Answers to Quiz on Differentiation with Chain Rule
Differentiation of Implicit Functions
Differentiation of Implicit Functions (cont)
Differentiation of Implicit Functions
Answers to Quiz on Differentiation of Implicit Functions
Higher Order Differentiation
Differentiation of Polynomial Functions
Answers to Quiz on Differentiation of Polynomial Functions (1 of 2)
Answers to Quiz on Differentiation of Polynomial Functions (2 of 2)

Tangent and Normal Lines

Finding Equation of Tangent and Normal Lines to a curve
Finding Equation of Tangent and Normal Lines to a curve (cont)
Tangent and Normal Lines to a Polynomial Curve
Answers to Quiz on Tangent and Normal Lines to a Polynomial Curve

Characterization of Polynomial Curves

Turning & Stationary Points, Maximum & Minimum Point & Point of Inflection
Examining Maximum and Minimum Points
Examining Maximum and Minimum Points (cont)
Minimum and Maximum Points
Answers to Quiz on Maximum and Minimum Points (Part 1 of 2)
Answers to Quiz on Maximum and Minimum Points (Part 2 of 2)
Determining Maximum & Minimum Points using the Second Derivative of the Curves
Determining Max & Min Points using the Second Derivative of the Curves (cont)
Finding Minimum and Maximum Points using the Second Derivative
Answers to Quiz on Maximum & Minimum Points using the Second Derivatives
Determining Points of Inflection using the Second Derivative of the Curves
Points of Inflection
Answers to Quiz on Points of Inflection (part 1 of 2)
Answers to Quiz on Points of Inflection (part 2 of 2)

Problem Solving using Maximum & Minimum Values

Solving Geometrical problems using Maximum and Minimum Values
Solving Geometrical problems using Maximum and Minimum Values (cont)
Problem Solving using Maximum & Minimum Values
Answers to Quiz on Problem Solving using Max & Min Values (Part 1 of 2)
Answers to Quiz on Problem Solving using Max & Min Values (Part 2 of 2)

Differential as Rate of Change

Finding Rates of Change in problems involving Geometry
Finding Rates of Change in problems involving Geometry (cont)
Finding Rates of Change in problems involving Geometry (cont)
Rates of Change
Answers to Quiz on Rates of Change
Using Derivative to Approximate results of Small Changes to the input
Approximation of Change
Answers to Quiz on Approximation of Change

Conclusion

Conclusion

Screenshots

Introduction to Differentiation (Differential Calculus) - Screenshot_01Introduction to Differentiation (Differential Calculus) - Screenshot_02Introduction to Differentiation (Differential Calculus) - Screenshot_03Introduction to Differentiation (Differential Calculus) - Screenshot_04

Reviews

Andrew
December 1, 2017
It was good. I was able to acquire some new knowledge as I never took calculus before so that's what i'm happy about. If I had to compare difficulty with my previous math class which was advanced trigonometry, I would say calculus is harder because it's much different and something entirely new. Especially the transition from pre-calculus to calculus 1. I will now move onto integral calculus and then multi variable calculus. Integral calculus and multi-variable calculus looks very fun. My goal is to understand Quantum physics on a mathematical perspective because i'm interested in the natural world and how it functions in the reality in which we live in. Thank you for this course.
Daniel
November 6, 2017
Had some diffuculty following every word from the instructor. The instructor went straight into the lesson with calculus calculations without an explanation of why and how calculus used. Just adding a "d" in front of a simple algebra formular which, to the beginner, it appears to do nothing to the outcome or result of that particulr
Kevin
May 27, 2017
I will give this 5 star because it is very beginner friendly like me. I can understand the topics deeply because before this guy start, he will explain the foundation first. at the moment as i am writing this, i am stuck in the "Please tell us more about this course" section, there is a question stating "Is the course delivering on your expectation?" I answered "No" because I didn't expect how this instructor teach. Not your typical instructor that leave you hanging; he will engraved to your brain how this thing works.
Lida
October 28, 2016
Awesome course! Thanks for the great explanations about key concepts. The course has helped me understand better about Calculus. The instructor explains it much better than the way my teacher teaches.
William
March 16, 2016
He didn't really "prove" the formula for differentiation; he just demonstrated that it does indeed hold for x to the one through x to the five. How do we know the formula doesn't break down at, say, x to the 17th? (It doesn't, but that was never proved.)
Muhammad
May 14, 2015
The instructor knows the subject really well and he imparted his knowledge in the easiest language possible. My understanding of Calculus has improved by attending this course. Good job.

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udemy ID
3/17/2015
course created date
1/21/2021
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