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SEM3 SMS 2307 ADVANCED CALCULUS
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End of Semester Examination Sem 1, 2021/2022
CAM Examination
Quiz 1
Mid Term Examination (26 Aug 2024)
Quiz 2
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Lecture Notes
Book by Trench
Course Outline
FUNDAMENTALS OF ANALYSIS by William Chan
Interactive Real Analysis
Extra Reading
Axiom of Real Numbers
Axiom of Real Numbers
Completeness of Real Numbers (wiki)
Week 1 - Sequence
Powerpoint-Limits
Sequences of Real Numbers
Youtube: Visualise Convergent Sequence
Youtube: Visually, what is the limit of a sequence?
Youtube: Proving a Sequence Converges
Examples of Finding Limits
Common Mistake
Sequence of change in your life
Assignment 1: Sequence
Difficult Example
Do factorials really grow faster than exponential functions?
Visualise Convergent Sequence
Week 2 - Sequence: Supremum
Assignment: Tutorial 1 and 2
Class Assignment 1
Youtube: Bounded Sequence
Youtube: Monotonic Sequence
Extra Reading: Monotone Sequences
Supremum & Infimum
Video: Monotone Convergent Theorem
Extra Examples
Ambition is a Supremum
What is the supremum of an empty set?
Youtube: Supremum and Infimum with Examples
Subsequence - Week 3
Powerpoint 2 - Subequence
Powerpoint 3 - Cauchy Sequence
Example of Cauchy sequence
Completeness of the real numbers
Video: The Proof of Nested Interval Theorem
FAQ: Sequence
Week 4 - Series: Geometric Series
Powerpoint - Geometric Series
Youtube: Summation Notation - You got it right?
Youtube: Geometric Series
Series of Real Numbers
Telescoping Series
Examples and comments
More Examples
Assignment 2: Infinite Series
Week 5 - Series: Convergent Series and Their Tests
Powerpoint - Positive Series Test
Assignment: Tutorial 3 and 4
A brief History of Calculus and Analysis
Comparison Test
The Harmonic Series Diverges Again and Again
FAQ: Series
Series: Alternating Series - Week 6
Assignment: Tutorial 5 and 6
Powerpoint - Alternating Series
Youtube:How to choose a convergence test for infinite series
Youtube: Ratio Test easy explanation
Summary
Strategy for Testing Series
Example
Extra Example
Raabe's test
Mind Map: Summary of Sequence and Series
Differential Calculus - Extra Reading
Sequence and Series of Functions - Week8
Powerpoint - Pointwise convergence
Pointwise Convergence Example
Youtube: Pointwise convergence of sequences of functions.
More examples
Extra Reading/Examples
FAQ
Week 9-10 - Uniform Convergence
Assignment: Tutorial 6
Powerpoint - Uniform convergence
Uniform Convergence
Implication of Uniform Convergence
Tutorial 7
Youtube: Functional Sequence
FAQ
Week 12 - Power Series
Powerpoint - Power Series
Assignment: Tutorial 7 & 8
Power Series: other lecture note
Youtube: Power Series (not using R=1/lim an+1/an)
Power Series to solve differential Equation
Week 13 - Taylor Series
Powerpoint - Taylor Series
Tutorial 9
Youtube: Taylor Series and Maclaurin Series
FAQ
Extra Reading - Metric Space
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Session 2023/2024 Semester 1
AHMAD IBRAHIM KULLIYYAH OF LAWS
ALLIED HEALTH SCIENCE
ARCHITECTURE & ENVIRONMENTAL DESIGN
ARTS PROGRAMME
CO-CURRICULAR ACTIVITY CENTRE
DENTISTRY
ECONOMICS AND MANAGEMENT SCIENCES
EDUCATION
ENGINEERING
INFORMATION & COMMUNICATION TECHNOLOGY
INTERNATIONAL INSTITUTE FOR HALAL RESEARCH AND TRAINING
INTERNATIONAL INSTITUTE OF ISLAMIC THOUGHT AND CIVILIZATION
ISLAMIC BANKING AND FINANCE
ISLAMIC REVEALED KNOWLEDGE & HUMAN SCIENCES (KTN)
ISLAMIC REVEALED KNOWLEDGE AND HUMAN SCIENCES
LANGUAGES
LANGUAGES & PRE-UNIVERSITY ACADEMIC DEVELOPMENT
LANGUAGES & PRE-UNIVERSITY ACADEMIC DEVELOPMENT (KTN)
LANGUAGES AND MANAGEMENT
MEDICINE
NURSING
PHARMACY
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SCIENCES PROGRAMME
SEJAHTERA CENTRE FOR SUSTAINABILITY AND HUMANITY
Session 2023/2024 Semester 2
AHMAD IBRAHIM KULLIYYAH OF LAWS
ALLIED HEALTH SCIENCE
ARCHITECTURE & ENVIRONMENTAL DESIGN
ARTS PROGRAMME
CO-CURRICULAR ACTIVITY CENTRE
DENTISTRY
ECONOMICS AND MANAGEMENT SCIENCES
EDUCATION
ENGINEERING
INFORMATION & COMMUNICATION TECHNOLOGY
INTERNATIONAL INSTITUTE FOR HALAL RESEARCH AND TRAINING
INTERNATIONAL INSTITUTE OF ISLAMIC THOUGHT AND CIVILIZATION
ISLAMIC BANKING AND FINANCE
ISLAMIC REVEALED KNOWLEDGE AND HUMAN SCIENCES
LANGUAGES
LANGUAGES & PRE-UNIVERSITY ACADEMIC DEVELOPMENT
LANGUAGES AND MANAGEMENT
MEDICINE
NURSING
PHARMACY
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SCIENCES PROGRAMME
SEJAHTERA CENTRE FOR SUSTAINABILITY AND HUMANITY
Session 2023/2024 Semester 3
AHMAD IBRAHIM KULLIYYAH OF LAWS
ALLIED HEALTH SCIENCE
ARCHITECTURE & ENVIRONMENTAL DESIGN
ARTS PROGRAMME
CO-CURRICULAR ACTIVITY CENTRE
ECONOMICS AND MANAGEMENT SCIENCES
EDUCATION
ENGINEERING
INFORMATION & COMMUNICATION TECHNOLOGY
ISLAMIC BANKING AND FINANCE
ISLAMIC REVEALED KNOWLEDGE AND HUMAN SCIENCES
LANGUAGES
LANGUAGES & PRE-UNIVERSITY ACADEMIC DEVELOPMENT
LANGUAGES AND MANAGEMENT
MEDICINE
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Course info
SEM3 SMS 2307 ADVANCED CALCULUS
Instructor:
PAH CHIN HEE 5826
Skill Level
:
Beginner
