CALCULUS OF ONE REAL VARIABLE   A TUTORIAL

By Pheng Kim Ving, BA&Sc, MSc
Email:
Toronto

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Welcome To CALCULUS OF ONE REAL VARIABLE!!

This website posts a tutorial on the introductory calculus of one real variable, free!! It provides a complete treatment of the
introductory calculus of functions of one real variable. It's organized to accompany two one-semester first and second calculus
courses or one two-semester first calculus course.

Each chapter is divided into sections. Each section discusses the topics that are the subject of the section and provides
examples each followed by its complete solution. The presentation of each section is fairly comprehensive and detailed, almost
the same as in textbooks, not just a summary of the topics. Each section includes a set of problems with complete solutions.

The examples and problems supply drills on the basic techniques for the topics discussed in the section, and some are
theoretical and/or difficult.

If you have thoughts or comments about the site and you like to make them public, please don't hesitate to sign my guestbook.
The link to the guestbook is accessible under the heading “ Guess Who's The Guest!”, below.

## Guess Who's The Guest!

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 CONTENTS

1. Limits And Continuity

2. The Derivative

2.1 Tangent Lines And Their Slopes
2.2 Rates Of Change
2.3 The Derivative
2.4 Differentiability Vs Continuity

3. Rules Of Differentiation

4. More On The Derivative

5. Applications Of The Derivative – Part 1

6. The Trigonometric Functions And Their Inverses

6.1 The Trigonometric Functions
6.1.1 The Trigonometric Functions

6.2 The Inverse Trigonometric Functions

7. The Exponential And Logarithmic Functions

8. Applications Of The Derivative – Part 2

9. The Integral

11. More On The Integral

12. Applications Of The Integral

13. Plane Curves

13.1 Parametric Curves
13.1.1 Parametric Curves
13.1.2 Tangent And Sketching Of Parametric Curves
13.1.3 Arc Length And Area Of Surface Of Revolution Of Parametric Curves
13.1.4 Vector Study Of Motion In The Plane

14. Infinite Series

15. Representations Of Functions By Power Series

16. Differential Equations

16.2 Second-Order Linear Homogeneous Equations
16.2.1 Equations With Constant Coefficients – Characteristic Equation
16.2.2 Equations With Variable Coefficients – Reduction Of Order

16.3 Second-Order Linear Non-Homogeneous Equations
16.3.1 Equations With Constant Coefficients – Undetermined Coefficients
16.3.2 Equations With Variable Coefficients – Variation Of Parameters

16.4 Approximate Solutions

Last Updated: 14 May 2015.