Introduction to Differentiation (Differential Calculus)

A great way to start learning Calculus through video lectures and quizzes.
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  • Lectures 55
  • Length 13 hours
  • Skill Level Beginner Level
  • Languages English
  • Includes Lifetime access
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About This Course

Published 5/2015 English

Course 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!

What are the requirements?

  • Students should already be familiar with Basic Algebra
  • No prior knowledge of Calculus is required

What am I going to get from this course?

  • 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

What is the target audience?

  • Secondary and High Schools students taking Calculus 1 (Differential Calculus)
  • Students preparing for Calculus 1 (Differential Calculus) tests / exams at 'O' Level or its equivalence
  • Any adults looking for a refresher in Basic Calculus 1

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

Section 1: Introduction
About the Instructor and High Level Overview of the course.
Preview
02:38
Basic Concept of Differential Calculus
10:34
Section 2: Limits and Instantaneous Gradient of a Curve
Introduction to Limits
11:50
Introduction to Limits (cont)
08:24
Introduction to Limits (cont)
10:54
Quiz on Limits
10 questions
Answers to Quiz on Limits
19:49
Estimation of Differential using Gradient of a Chord
12:05
Estimation of Differential using Gradient of a Chord (cont)
14:22
Using Limit method to find First Derivative of Polynomials
14:44
Using Limit method to find First Derivative of Polynomials (cont)
08:56
The Derivative from First Principles
3 questions
Answers to Quiz on The Derivatives from First Principles
20:00
Section 3: Derivation of Differential Formula
Deriving the Prime Formula for Differentiation
14:03
Deriving the Prime Formula for Differentiation (cont)
12:58
12:18

Derivation of Differential formula using limit

Deriving the Prime Formula for Differentiation. Supplementary Lecture. (cont)
Preview
17:38
Section 4: Differentiation of Polynomial Functions
Determining the First Derivative using the prime Differentiation Formula
Preview
10:55
Determining the First Derivative using the prime Differentiation Formula (cont)
10:48
Differentiation using the Prime Differentiation Formula
5 questions
Answers to Quiz on Differentiation using the Prime Differentiation Formula
13:52
Product Rule
19:22
Differentiation with Product Rule
5 questions
Answers to Quiz on Differentiation with Product Rule
16:33
Quotient Rule
19:35
Differentiation with Quotient Rule
5 questions
Answers to Quiz on Differentiation with Quotient Rule
15:49
Chain Rule
09:59
Differentiation with Chain Rule
5 questions
Answers to Quiz on Differentiation with Chain Rule
14:56
Differentiation of Implicit Functions
15:07
Differentiation of Implicit Functions (cont)
08:52
Differentiation of Implicit Functions
3 questions
Answers to Quiz on Differentiation of Implicit Functions
13:55
Higher Order Differentiation
Preview
07:26
Differentiation of Polynomial Functions
4 questions
Answers to Quiz on Differentiation of Polynomial Functions (1 of 2)
13:05
Answers to Quiz on Differentiation of Polynomial Functions (2 of 2)
12:52
Section 5: Tangent and Normal Lines
Finding Equation of Tangent and Normal Lines to a curve
17:38
Finding Equation of Tangent and Normal Lines to a curve (cont)
12:01
Tangent and Normal Lines to a Polynomial Curve
4 questions
Answers to Quiz on Tangent and Normal Lines to a Polynomial Curve
14:48
Section 6: Characterization of Polynomial Curves
Turning & Stationary Points, Maximum & Minimum Point & Point of Inflection
07:31
Examining Maximum and Minimum Points
19:44
Examining Maximum and Minimum Points (cont)
13:48
Minimum and Maximum Points
3 questions
Answers to Quiz on Maximum and Minimum Points (Part 1 of 2)
11:12
Answers to Quiz on Maximum and Minimum Points (Part 2 of 2)
13:16
Determining Maximum & Minimum Points using the Second Derivative of the Curves
18:05
Determining Max & Min Points using the Second Derivative of the Curves (cont)
19:13
Finding Minimum and Maximum Points using the Second Derivative
3 questions
Answers to Quiz on Maximum & Minimum Points using the Second Derivatives
Preview
14:45
Determining Points of Inflection using the Second Derivative of the Curves
18:55
Points of Inflection
3 questions
Answers to Quiz on Points of Inflection (part 1 of 2)
19:58
Answers to Quiz on Points of Inflection (part 2 of 2)
14:57
Section 7: Problem Solving using Maximum & Minimum Values
Solving Geometrical problems using Maximum and Minimum Values
13:46
Solving Geometrical problems using Maximum and Minimum Values (cont)
18:26
Problem Solving using Maximum & Minimum Values
3 questions
Answers to Quiz on Problem Solving using Max & Min Values (Part 1 of 2)
19:57
Answers to Quiz on Problem Solving using Max & Min Values (Part 2 of 2)
19:57
Section 8: Differential as Rate of Change
Finding Rates of Change in problems involving Geometry
12:21
Finding Rates of Change in problems involving Geometry (cont)
11:05
Finding Rates of Change in problems involving Geometry (cont)
14:51
Rates of Change
3 questions
Answers to Quiz on Rates of Change
19:26
Using Derivative to Approximate results of Small Changes to the input
13:09
Approximation of Change
4 questions
Answers to Quiz on Approximation of Change
14:25
Section 9: Conclusion
Conclusion
00:49

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Instructor Biography

Mr Mohd Fikri Abdul Aziz, (BEng Electronics Engineering)

A Penang based Engineer cum Tutor, a father of four, with a passion to teach and help students excel in Math. He is also known as MrMaths by his students.

He was graduated with Bachelors Degree in Electronics Engineering from the University of Sheffield in England. He has fourteen years of working experience in electronics industry with Intel Corp and Dell Corp and years of Mathematics teaching and home tutoring experience. In the past he has also taught Physics. Today he is a full time Math tutor Since January 2012, he started tutoring outside of Penang and outside of Malaysia using Video Conferencing on the internet. Teaching in both Bahasa Melayu (Malay) and in English.

He is friendly and always treat his students as if they are his own children.

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