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 Tutorials and some notes are in Adobe Acrobat (PDF) format.  Download the free Adobe Acrobat reader for viewing and printing these files.

 

This web site is dedicated to mathematics enthusiasts, beginners, those who love to learn, to seek the truth in beauty or in form or just simply thirsting for answers and/or knowledge.

 

General Information		Substitution in Integral and Differentials
Objectives		Do we need Mean Value Theorem?
Syllabus		Extreme Value Theorem
References		Intermediate Value Theorem
Notes on Derive		Boundedness Theorem
General Advice and Learning Guide		Monotone Function and Continuity
Problem-Solving Process		Injective Function and Monotone Function
Tutorials		Riemann Integral and Bounded Function
Guide and Comment for Tutorial Assignment		Riemann Integral and Infinite Series
Example Sessions		Derived functions and Derivative
Online Quizzes		Continuity, Differentiability, Weierstrass' Function
Precalculus Online Quiz		Intermediate Value Theorem for Derived Function
A Formula of Euler and Appreciating Calculus  PDF version		Monotone Function, Bounded Variation, Fundamental Theorem of Calculus
Tests and Past Exam Papers		Heine-Borel, Bolzano Weierstrass Theorems, Uniform Continuity and Riemann Integrability
Letter to Students		Composition and Riemann Integrability
Letter to and from a fellow teacher		Composition and Lebesgue Integrability
Link to other Calculus Web sites		Change of Variable in Riemann and Lebesgue Integration
Comment and Errata to Calculus, an introduction Calculus, an introduction available from NUS Coop		The Cantor Set
Download a Trial Version of Derive		Darboux's Fundamental Theorem of Calculus
Review of 1999-2000 1st Semester Exam    Download and install the following 3 math fonts to view the review:Click to install  font a  font b font c		L Hopital's Rule - And a Generalized Version    Concavity - Definitions and Equivalence
Book on web: Real Numbers?  New		Integration By Parts
Mathematical Analysis, An Introduction    New Now ALL fourteen chapters come with exercise problems Comments welcomed The real  numbers, Sequences, Continuous functions, Differenmtiable functions, Integration,  Series,  Series of functions and Power Series, Uniform Convergence and differentiation, Uniform Convergence, Integration and Power Series.  Weierstrass Approximation Theorem The Elementary Functions Arithmetic of Power Series Special Test for Convergence - Kummer, Raabe, Gauss and Bertrand's Tests Improper and Lebesgue Integral		Application of integration - arc length, volume of solid of revolution, area of surface of revolution        Sequences and Series     Arc Length, Function of Bounded Variation and Total Variation     Kestelman's Change of Variable Theorem    Change of Variables Theorems in Integration   - a follow up of  "change of Var  in Riemann and Lebesgue Integration" shorter proof. Functions Having Finite Derivatives, Bounded Variation, Absolute Continuity, the Banach Zarecki Theorem and de La Vallee Poussin Theorem   New Elementary Proof of de la Vallee Poussin Theorem Function of Bounded Variation and Johnson Indicatrix   New   When is a function absolutely continuous? The answer and application to generalized change of variable for Lebesgue integral. New
Followed Up readings: Advanced Calculus		Partial Fraction Expansion -- Its proof, a simple application of complex analysis  New
Mathematics Diagnostic Testing		On the primitive of product of two functions  New
Basic Skills help:  Algebra refresher  Inequalities		Convergence of å sin(sqrt(n)x)/n and other problems  New

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If you have any comment or suggestion regarding this website (for example, you feel that you like something (other than lecture notes!!) to be put on the web. Or if you have found some interesting websites. Or, you particularly like something we have put here.)   I shall be glad to hear from you. You may e-mail A/P Ng Tze Beng at  MATV23@nus.edu.sg

Calculus Web Statistics          

This page was last updated on 09/07/2011

By Ng Tze Beng