Master the Fundamentals of Calculus

Focused View

Dr Ling Meng Kay Daniel, PhD

3:03:01

199 View

1. Introduction to Differentiation

1.1 Lecture 1 - Introduction to Differentiation.pdf

1. Introduction to Differentiation.mp4

02:36

2.1 Differentiation from First Principle - Student.pdf

2. Differentiation from First Principle.mp4

04:14

2. Basic Differentiation Properties and Techniques

1.1 Basic Differentiation Properties and Techniques - Student.pdf

1. Basic Differentiation Properties and Techniques.mp4

06:42

2.1 Chain Rule - Student.pdf

2. Chain Rule.mp4

03:48

3.1 Product Rule - Student.pdf

3. Product Rule.mp4

03:48

4.1 Quotient Rule - Student.pdf

4. Quotient Rule.mp4

03:59

5.1 Differentiation of Trigonometric Functions - Student.pdf

5. Differentiation of Trigonometric Functions.mp4

06:39

6.1 Differentiation of Inverse Trigonometric Functions - Student.pdf

6.2 Proof of the Inverse Trigonometric Functions Derivatives.pdf

6. Differentiation of Inverse Trigonometric Functions.mp4

04:48

7.1 Differentiation of Exponential Functions (Student).pdf

7. Differentiation of Exponential Functions.mp4

03:32

8.1 Differentiation of Logarithmic Functions (Student).pdf

8. Differentiation of Logarithmic Functions.mp4

03:48

9.1 Implicit Differentiation - Student.pdf

9. Implicit Differentiation.mp4

04:02

10.1 Parametric Differentiation - Student.pdf

10. Parametric Differentiation.mp4

02:40

11.1 Differentiation Techniques Practices (Student).pdf

11. Differentiation Techniques Practices.mp4

03:30

3. Applications of Differentiation

1.1 Applications of Differentiation (Increasing & Decreasing Functions) - Student.pdf

1. Applications of Differentiation (Increasing & Decreasing Functions).mp4

02:18

2.1 Applications of Differentiation (Concavity of Functions) - Student.pdf

2. Applications of Differentiation (Concavity of Functions).mp4

02:31

3.1 Applications of Differentiation (Stationary Points) - Student.pdf

3. Applications of Differentiation (Stationary Points).mp4

06:43

4.1 Applications of Differentiation (Maxima & Minima Problems) - Student.pdf

4. Applications of Differentiation (Maxima and Minima).mp4

04:18

5.1 Maxima and Minima Problem-Solving - Student.pdf

5. Maxima and Minima Problem-Solving.mp4

04:55

6.1 Applications of Differentiation (Connected Rate of Change) - Student.pdf

6. Applications of Differentiation (Connected Rates of Change).mp4

04:48

7.1 Lecture 20 - Connected Rate of Change Problem-Solving (Student).pdf

7. Connected Rates of Change Problem-Solving.mp4

03:21

8.1 Lecture 21 - Applications of Differentiation (Gradient, Tangent and Normal) - Student.pdf

8. Applications of Differentiation (Gradient, Tangent and Normal).mp4

05:20

9.1 Gradient, Tangent and N ormal Problem-Solving (Student).pdf

9. Gradient, Tangent and Normal Problem-Solving.mp4

03:48

10.1 Applications of Differentiation - Kinematics (Student).pdf

10. Applications of Differentiation (Kinematics).mp4

03:52

11.1 Lecture 24 - Kinematics Problem-Solving (Student).pdf

11. Kinematics Problem-Solving.mp4

03:09

4. Quiz 1

1. Quiz 1.html

5. Introduction to Integration

1.1 Lecture 25 - Introduction to Integration notes.pdf

1. Introduction to Integration.mp4

03:15

6. Basic Integration Properties and Techniques

1.1 Lecture 26 - Basic Integration Properties and Techniques (Student).pdf

1. Basic Integration Properties and Techniques.mp4

05:59

2.1 Lecture 27 - Integration of Trigonometric Functions (Student).pdf

2.2 Notes on Basic Trigonometric Integration.pdf

2. Integration of Trigonometric Functions.mp4

04:46

3.1 Lecture 28 - Integration of Functions to obtain Inverse Trigonometric Functions (Student).pdf

3. Integration of Functions to obtain Inverse Trigonometric Functions.mp4

03:18

4.1 Lecture 29 - Integration of Exponential and Logarithmic Functions (Student).pdf

4. Integration of Exponential and Logarithmic Functions.mp4

03:45

5.1 Lecture 30 - Integration of f(x) over [a^2-f(x)^2] or f(x) over [f(x)^2-a^2] - Student.pdf

5. Integration of f(x) over [a^2-f(x)^2] or f(x) over [f(x)^2-a^2].mp4

03:15

6.1 Lecture 31 - Additional Trigonometric Integrals using Factor Formula (Self-Read).pdf

6.2 Lecture 31 - Miscellaneous Trigonometric Integrals (Student).pdf

6. Miscellaneous Trigonometric Integrals.mp4

03:41

7.1 Lecture 32 - Definite Integration by Substitution (extra self-study notes).pdf

7.2 Lecture 32 - Integration by Substitution (Student).pdf

7. Integration by Substitution.mp4

03:47

8.1 Lecture 33 - Integration by Parts (Proof).pdf

8.2 Lecture 33 - Integration by Parts (Student).pdf

8. Integration by Parts.mp4

03:51

9.1 Lecture 34 - Extension of Integration of Fractional Polynomials (Self-Read).pdf

9.2 Lecture 34 - Integration of Fractional Polynomials (Student).pdf

9. Integration of Fractional Polynomials.mp4

03:44

7. Applications of Integration

1.1 Lecture 35 - Applications of Integration notes (Limiting Sum and Definite Integrals) notes.pdf

1. Applications of Integration (Limiting Sums and Definite Integrals).mp4

04:36

2.1 Lecture 36 - Applications of Integration (Area under Curve) Student.pdf

2. Applications of Integration (Area under a Curve).mp4

03:52

3.1 Lecture 37 - Area under a Curve Problem.pdf

3. Area under a Curve Problem-Solving.mp4

04:14

4.1 Lecture 38 - Applications of Integration (Area between two curves) Student.pdf

4. Applications of Integration (Area between two Curves).mp4

03:28

5.1 LECTUR~1.PDF

5. Applications of Integration (Evaluating Areas of Parametric Equations).mp4

03:56

6.1 Lecture 40 - Volume of Revolution with x-axis (Student).pdf

6. Applications of Integration (Volume of Revolution with x-axis).mp4

04:16

7.1 Lecture 41 - Volume of Revolution with y-axis (Student).pdf

7. Applications of Integration (Voume of Revolution with y-axis).mp4

04:44

8.1 Lecture 42 - Volume of Revolution Problem-Solving (Student).pdf

8. Volume of Revolution Problem-Solving.mp4

03:25

9.1 Lecture 43 - Further Volume of Revolution Problem-Solving (Solutions).pdf

9.2 Lecture 43 - Further Volume of Revolution Problem-Solving (Student).pdf

9. Further Volume of Revolution Problem-Solving.html

8. Quiz 2

1. Quiz 2.html

9. Further Calculus Concepts, Problems and Quiz Solutions

1.1 Quiz 1 Solutions.pdf

1.2 Quiz 2 Solutions.pdf

1. Solutions for Quiz 1 and 2.html

2.1 Lecture 45 - Optimization with Constraints (Student).pdf

2. Optimization with Constraints.mp4

03:30

3.1 Further Practice Problem 1 - Student.pdf

3. Further Practice Problem 1.mp4

05:01

4.1 Further Practice Problem 2 - (iii) Exact Volume.pdf

4.2 Further Practice Problem 2 - Student.pdf

4. Lecture 47 Further Practice Problem 2.mp4

03:29

Description

Master the fundamentals of Calculus for GCE/IGCSE/IB Mathematics students.

What You'll Learn?

Limits
Basic Techniques of Differentiation
Chain Rule, Product Rule and Quotient Rule
Differentiation of Algebraic Expressions
Differentiation of Trigonometric Functions
Differentiation of Exponential Functions
Differentiation of Logarithmic Functions
Concept of Stationary Points
Applications of Differentiation
Integration and its Relationship with Differentiation
Basic Techniques of Integration
Definite Integration
Applications of Integration

Who is this for?

Students who are taking the GCE/IGCSE 'A' level Mathematics

Students who are taking the IB Diploma SL/HL Mathematics

Students who are going to study Engineering or any Mathematics-intensive courses at universities and need a good Calculus foundation

Students who are taking the GCE/IGCSE 'O' level Pure Mathematics

Any learner who has a keen interest to recap or learn Calculus for FUN!

What You Need to Know?

Basic understanding of Trigonometry, Algebra, Indices, Exponential Functions, Logarithms, Graphing, Coordinate Geometry

More details

Description
Dear students,
Welcome to this course "Master the Fundamentals of Calculus"!
This course is designed specially for students who are: doing college-level mathematics, taking their IGCSE/GCE A levels or the IB SL/HL Mathematics examinations. Students who are taking the IGCSE/GCE O levels pure mathematics are also welcome to read this course for advanced enrichment.
What you will learn:
At the end of the course, and depending on which exams you are taking, you will learn most/all of the following
Concept of limits
Chain rule, Product rule and Quotient rule
Differentiation of Algebraic functions, Trigonometric functions, Exponential functions, Logatihmic functions etc
Concept of Stationary Points
Applications of Differentiation - Maxima/Minima, Connected Rates of Change, Gradient/Tangents/Normal, Kinematics
Integration techniques
Finite and Infinite Integration
Applications of Integration - Area under Graph, Volume of Revolution, Kinematics
Along the way, there will be quizzes and practice questions for you to get familiarized with Calculus. There are also further practices which willÂ enhance your understanding of the topic. More practice questions will be added in the near future to provide ample opportunities for students to improve on their Calculus fundamentals.
If you encounter any problems, please do not hesitate to contact me for more clarifications.
I hope that you will find this course useful in your academic pursuit. Enjoy the course! Cheers! ;-)
Dr. Ling M K Daniel, PhD
Who this course is for:
Students who are taking the GCE/IGCSE 'A' level Mathematics
Students who are taking the IB Diploma SL/HL Mathematics
Students who are going to study Engineering or any Mathematics-intensive courses at universities and need a good Calculus foundation
Students who are taking the GCE/IGCSE 'O' level Pure Mathematics
Any learner who has a keen interest to recap or learn Calculus for FUN!

User Reviews

Rating

average 0

Total votes0

Focused display

Hi everyone! I am Dr Daniel Ling and I am a lecturer in Singapore with more than 16 years of experience teaching and tutoring Math and Physics. I have taught students from various top schools in Singapore such as the Raffles Girls’ School, Dunman High School, Catholic High School (CHS), Nanyang Girls’ High School, Nanhua High School, ACS(Independent), SJI, School of the Arts, Xinmin Sec School, Holy Innocents’ High School, Raffles Institution (formerly Raffles JC), National JC, St Andrew JC, Serangoon JC, Nanyang JC, Jurong JC, Tampines JC etc.Currently, I am an associate lecturer at a private school where I teach Physics and Mathematics to both local and international students under the school’s GCE O/A Levels preparatory courses.I possesses a bachelor degree in Electrical Engineering (2nd Upper Hons) from NUS, a Post-Graduate Diploma in Education (Credit) from NIE, a MBA from Australian Institute of Business and a Master of Education (M.Ed) from Aspen University, United States, specializing in curriculum development and outcome assessment. I also hold a PhD in Education from Asia e University.I am passionate about mathematics and physics and I hope to share my passion with all my students!

Udemy

View courses Udemy

Students take courses primarily to improve job-related skills.Some courses generate credit toward technical certification. Udemy has made a special effort to attract corporate trainers seeking to create coursework for employees of their company.