CALCULUS
OF ONE REAL VARIABLE

 

Lace-Up
Kina
hæl høyde er 1/2 tommer og fargen er Picket Gjerde.

A TUTORIAL

 

 

By Pheng Kim Ving, BA&Sc, MSc
Email: pheng@phengkimving.com
Toronto
- Canada

View

 

If you're using Internet Explorer and if it doesn't display the view properly, such as misplaced or (partly-)missing tables or

graphics, please try Firefox or Chrome. If the problem still doesn't go away, please let me know and I'll email you copies of
the .docx and .pdf versions of the problematic pages.

 

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.

 

 

Math Teacher/Tutor

 

If you need a math teacher/tutor and you live in (metro) Toronto then I'll be pleased to be your teacher/tutor. For more
information please click here.

 

 

 

Solutions To Problems

 

Do you need solutions to a set of problems you obtained from class or from a course? If you answer yes then please click here for more information.

 

 

Guess Who's The Guest!

 

You are the guest of this site!! If you like, please take the liberty to view or sign my guestbook. To go to the guestbook
please click here.

 

 

CONTENTS

 

Reference To A Function
Splitting Of The Topic Of The Applications Of The Derivative

Notations And Abbreviations

 

1. Limits And Continuity

 

     1.1 Limits
          1.1.1 Limits
          1.1.2 Properties Of Limits
          1.1.3 The Indeterminate Form Of Type 0/0

Vince Camuto Picket Womens D Hadia Pointed Toe D Fence Orsay Flats Picket Fence 5b2a7f5 - awesome-b12.site

          1.1.4 One-Sided Limits
          1.1.5 Limits At Infinity And Infinite Limits
         
         

     1.2 Continuity
          1.2.1 Continuity
          1.2.2 Extrema
          1.2.3 The Intermediate-Value Theorem

 

2. The Derivative

 

     2.1 Tangent Lines And Their Slopes
Vince Camuto Picket Womens D Hadia Pointed Toe D Fence Orsay Flats Picket Fence 5b2a7f5      2.2 Rates Of Change
     2.3 The Derivative
     2.4 Differentiability Vs Continuity

3. Rules Of Differentiation

 

     3.1 Differentiation Of Sums, Differences, And Polynomials
     3.2 Differentiation Of Products And Quotients
     3.3 Differentiation Of Compositions Of Functions – The Chain Rule
     3.4 Differentiation Of Inverse Functions

 

4. More On The Derivative


     4.1 Higher-Order Derivatives
     4.2 Implicit Differentiation
     4.3 The Differential

Vince Camuto Picket Womens D Hadia Pointed Toe D Fence Orsay Flats Picket Fence 5b2a7f5

 

5. Applications Of The Derivative – Part 1

 

     5.1 The Mean-Value Theorem
     5.2 Critical Points And Extrema
     5.3 The First-Derivative Test
     5.4 Concavity And Inflection
     5.5 The Second-Derivative Test
     5.6 Sketching Graphs Of Functions
     5.7 Antiderivatives And Indefinite Integrals
     5.8 Motion

6. The Trigonometric Functions And Their Inverses

 

     6.1 The Trigonometric Functions
          6.1.1 The Trigonometric Functions

          6.1.2 Trigonometric Identities
          6.1.3 Limits Of Trigonometric Functions
          6.1.4 Differentiation Of Trigonometric Functions
          6.1.5 Graphs Of Trigonometric Functions
          6.1.6 The Projectile Motion
          6.1.7 The Simple Harmonic Motion

 

     6.2 The Inverse Trigonometric Functions

          6.2.1 The Inverse Trigonometric Functions
          6.2.2 Differentiation Of The Inverse Trigonometric Functions

 

FRYE Kvinner Avery Harness Thong Flat Sandal Hvit , Women Round Toe Platform Pumps Stiletto High Heels Dress Sko rød PUMA Kvinner Vega SL Ballett Flat Rapture Rose-love Potion , Drew Shoe Women s Bloom II Taupe Nubuck Naturalizer Women s Samantha Pointed Toe Flat Hvit perle , TOMS Classic Floral Embroidery Striped Damessko Svart Suede / Rope LifeStride Women s Relay 2 Ballett Flat Blek rosa , Walking Cradles Women s Flynn Loafer Flat Navy Leather , Cole Haan Women s Tali Bow Ballet Flat Gull / Sølv Glitter 206 kollektive kvinner Madison Ballett Flat Sølv Metallisk Skinn , Allrounder av Mephisto Women s NIRO Cemento Suede / Open Mesh , Earth Women s Bay Gladiator Sandal Safir Multi Soft Leather Stuart Weitzman Women s Strapdown Ballett Flat Svart , Amalfi av Rangoni Kvinner Oslo Almond Toe Slide Flats Navy-krokodille Hot Chocolate Design Chocolaticas Sitron Kvinner Mary Jane Flat flerfarget Trotters Women s Sizzle Ballet Flat marinen , LifeStride Women s Diverse Flat Blå , Aibarbie Kvinner Galala Patent-lær Point-toe Flats Kontor Off-duty Flats Sko Grosgrain Bow Sko Sjokolade , Vionic Women s Gnist Minna Ballett Flat Berry Snake , YDN Women s Classic Pointed Toe Lace Up Ballett Flats Ankel High D Orsay Dance Shoes Svart , San Antonio sko Kvinner Avslappet Lær Åpen Tå Avslappet Slingback Sandaler Rav Hush Valper Kvinner Analyse Smart Flat Kamel SoftWalk Women s Napa Mj Mary Jane Flat Tan / Oppbevaring Bernie Fru Kvinne Zig Zag Ankel Bootie jeans , Wolky Comfort Nimes Sienna Italian Softy , LifeStride Women s Affirm Flat Svart , Aerosoles Women s Spin Class Ballett Flat Sort kombinasjon , Cobb Hill Rockport Women s Fiona Sandal taupe ALDO Kvinners Ybalelia Mule Gull

     6.3 Transcendency
          6.3.1 Transcendental Functions
          6.3.2 Transcendency Of The Trigonometric Functions

 

7. The Exponential And Logarithmic Functions

     7.1 The Natural Exponential Function
     7.2 The Natural Logarithm Function

     7.3 General Exponential And Logarithmic Functions
     7.4 Logarithmic Differentiation
     7.5 Growth And Decay
     7.6 The Hyperbolic Functions
     7.7 The Inverse Hyperbolic Functions
     7.8 Transcendency Of The Exponential And Logarithmic Functions

 

8. Applications Of The Derivative – Part 2

 

     8.1 Optimization
     8.2 Related Rates
     8.3 Tangent-Line Approximations
     8.4 Approximations Of Errors In Measurement
     8.5 Approximations Of Roots Of Functions – Newton's Method
    
     8.7 More Indeterminate Forms

 

9. The Integral

 

     9.1 Summation Notation And Formulas
     9.2 Areas And Riemann Sums
     9.3 The Definite Integral
     9.4 The Fundamental Theorem Of Calculus

 

10. Techniques Of Integration

    
10.1 Integration By Inspection
    
10.2 The Method Of Substitution
    
10.3 Integration Of Trigonometric Functions
    
10.4 Integration Of Powers Of Trigonometric Functions
    
10.5 The Inverse Trigonometric Substitution
    
10.6 Other Substitutions
    
10.7 The Method Of Partial Fractions
    
10.8 The Method Of Integration By Parts

 

11. More On The Integral


    
11.1 Approximate Numerical Integration
Mona Flying Women s Lær perforert Lace-up Oxfords Sko til kvinner Wingtip Multicolor Brougue Shoes Blå Merrell Women s Capra Bolt Mid Vanntett Fottøy Grå / Lilla , Eddie Bauer Kvinners Lukla Pro Vanntette Lettveier Cinder (Grey) Hi-Tec Women s Sierra Tarma I Vanntett-W Fottur Sko Brun / Kul Grå Eastland Women s Eden Oxford Muskat , CLARKS Kvinner Jocolin Vista Båtsko Sort perforert tekstil Meg for kvinners Halle Ballet Flat Sort Split Suede Orthofeet Plantar Fasciitis Ortopedisk Diabetic Flat Feet Bunions Walking Whitney Womens Sneakers Athletic sko Svart , Propet Women s TravelActiv Mary Jane Mote Sneaker Sølv , FitFlop Kvinner F-Sporty Elastisk Mary Jane Flat Fig , Softwalk Women s Murietta Clog Svart , Vionic Menns Orthaheel Technology White / Navy Walker Tan Bagasje MICHAEL Michael Kors Women s Ivy Bootie Boots Dark Khaki Kid Suede , J.Renee Womens Francie Svart Satin / Rhinestones , Miz Mooz Kvinners Bangkok Ankel Boot Slate Jambu Women s Bailey Maryjane Mary Jane Flat rød Kamik Women s Sharon Ankel-High Rain Boot Gul Timberland Women s Teddy Fleece Fold-Down Waterproof Boot Glassert ingefær , Soft Style Women s Angel II Pump Svart Kosmisk , Rollie Women s Lightweight Derby Lace-Up Flat Shoe Stone Leather , Bogs Womens Skylar Lace Svart LifeStride Women s Unity Harness Boot Svart Australia Luxe Collective Women s Cozy Tall Beva Laredo Womens Elaina Svart Blå av Betsey Johnson Women s SB-Jovi Heeled Sandal Sølv / Metallic , Steve Madden Women s Carrson Dress Sandal Svart Suede NIKE Women s SF AF1 Casual Shoe Svart / Svart Svart , Naturalizer Women s Cami Wedge Sandal Tan Gold , NIKE Women s Ultra Comfort Thong Sandal Klor Blå / Glacier Blå / Foto Blå , Onex Women s Nanci Wedge Sandal Hvit ,
     11.2 Improper Integrals
     11.3 Tests For Convergence Of Improper Integrals

Vince Camuto Picket Womens D Hadia Pointed Toe D Fence Orsay Flats Picket Fence 5b2a7f5 - awesome-b12.site

 

12. Applications Of The Integral

 

     12.1   The Mean-Value Theorem For Integrals
     12.2   Areas Of Plane Regions
     12.3   Finding Volumes By Slicing
     12.4   Finding Volumes By Using Cylindrical Shells
     12.5   Distance And Displacement
     12.6   Arc Length
     12.7   Areas Of Surfaces Of Revolution
     12.8   Work
     12.9   Force Exerted By A Fluid
     12.10 Net Change

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
Vince Camuto Picket Womens D Hadia Pointed Toe D Fence Orsay Flats Picket Fence 5b2a7f5           13.1.4 Vector Study Of Motion In The Plane

     13.2 The Polar Coordinate System
          13.2.1 The Polar Coordinate System
          13.2.2 Sketching Polar Curves
          13.2.3 Area By Polar Curves
          13.2.4 Arc Length And Area Of Surface Of Revolution Of Polar Curves

Flats

 

14. Infinite Series

 

     14.1 Infinite Sequences
     14.2 Infinite Series
     14.3 The Comparison Tests
     14.4 The Root And Ratio Tests
     14.5 The Integral Test
     14.6 The Alternating-Series And Absolute-Convergence Tests
     14.7. Approximations Of Sums Of Series

 

15. Representations Of Functions By Power Series

 

     15.1 Power Series
     15.2 Derivatives And Integrals Of Power Series
     15.3 Taylor Series
     15.4 Applications Of Taylor Series
     15.5 Taylor Polynomials And Taylor Theorem
     15.6 The Binomial Series

 

16. Differential Equations

 

     16.1 First-Order Equations
          16.1.1 Introduction To Differential Equations
  16.1.2 Variables-Separable Equations
          16.1.3 First-Order Linear Equations

 

     16.2 Second-Order Linear Homogeneous Equations
          16.2.1 2236654
4950576
5780921
10440837
11387027
11517526
13715769
18725310
18742516
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

          16.4.1 Approximate Graphical Solutions – Direction Fields

          16.4.2 Approximate Numerical Solutions - Euler Method

 

 

Last Updated: 14 May 2015.

 

Return To Top Of Page