By Pheng Kim Ving, BA&Sc, MSc
- Canada



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.




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.





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

FitFlop Women s Leather Gitter Surfa Surfa Floral s Flip-Flop 7419 Svart f6754f5 -

          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
FitFlop Women s Leather Gitter Surfa Surfa Floral s Flip-Flop 7419 Svart f6754f5      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

FitFlop Women s Leather Gitter Surfa Surfa Floral s Flip-Flop 7419 Svart f6754f5


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


OLUKAI Ohana Sandaler - Menn Svart / Svart , FitFlop Women s Fino Crystal Toe-Thong Sandal Gull , Sanuk Women s Yoga Mat Wander Flip-Flop nasturtium Tidewater Women s Flip Flop Sandaler Black Buoy , Gentle Souls Women s Break My Heart 3 Gladiator Sandal rød Yellow Box Women s Jello Sandal Svart / Multi FitFlop Kvinners Lulu Thong Sandal Svart , FitFlop Kvinners Lulu Thong Sandal Svart , Kate Spade New York Women s Rhett Flip-Flop Svart , Havaianas Women s Slim Flip Flop Sand Yellow Box Women s Jello Sandal påfugl Kate Spade New York Women s Icarda Thong Sandal Pulver Hvit Glitter / Hvit Nappa , Jordens opprinnelser SARA Sedona Brown Sperry Top-Sider Abbey Sandal Svart , Skechers Cali Women s Vinyasa Flip Flop Brun perle Minnetonka Women s, Sybil Thong Sandals Rødme , Nike Womens Celso Thong Flip Flops Åpne Toe Shoes Svart Jack Rogers Women s Napa Valley Navajo Thong Sandal Cork / Gold Fleck , Havaianas Women s Slim Flip Flop Sand Grå / Lysgyllen Reef Women s Mid Sea Sandal Svart / Svart ASHVIEE Slide Sandals Cork Footbed Casual Sandals rød , FRYE Women s Ally Western Flip-Flop Svart Jack Rogers Women s Georgica Jelly Thong Sandal Svart / Svart MICHAEL Michael Kors Kvinner Plate Leather Split Toe Casual T-Strap Sandaler Tile Blue Sanuk Women s Yoga Sling 2 Flip Flop Grå , FitFlop Kvinners Lulu Thong Sandal Svart , NIKE Women s Ultra Comfort Thong Sandal Sort / Hvit-svart (004) OOFOS Unisex Overiginal Thong Flip Flop rød , FitFlop Women s Rumba Thong Sandal Metallisk 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
Crocs Women s Leigh Suede Wedge Shootie Boot Grå CLARKS Women s Caddell Hop Boot Svart LifeStride Women s Venti Ballett Flat Sort 1 , Ønsket \ Sølv , Anne Klein Women s Ovi Reptile Ballet Flat Metallic / Bronze Rollie Women s Lightweight Derby Punch Perforated Lace-Up Flat Shoe Taupe Suede , Alegria kvinners Keli profesjonell sko Glimmer Glam , 4EurSole Women s My Time Slide brun , Uterque Women Bejeweled perle sandaler 4001/351 Jessica Simpson Women s Starlite Fashion Boot Svart , Sam Edelman Women s Carter Flat Sandal Svart patent Peerage FIC Daphne Kvinner bred bredde Peep Toe Pleated Øvre Slingback med spenne (størrelse / mål Guide) Svart Ranbetty Women s Mid Chunky Block Heel Almond Toe Ekte Lær Ankel støvler For varierende anledninger Svart lær DailyShoes Women s Militær snøre seg opp Buckle Combat Boots Ankel Høy Eksklusiv Quilted Credit Card Pocket Bootie Brown Pu , JBU av Jambu Women s Wildflower To Mary Jane Flat Kull Bella Vita Women s Channing Ballet Flat Svart , Nedal Kvinner Casual Velvet Mule Slip On Loafers Blackbee , Sbicca Women s Cleveland Boot taupe Trotters Women s Anastasia Loafer Hvit , Jessica Simpson Kvinner Mandalaye Ballett Flat Navy Baby , Amalfi av Rangoni Kvinners Loredana / TES Flat Nero , BareTraps Kvinner BT Lancy Snow Boot Leire SOREL Women s After Hours Tall Wedge Boots Redwood Coach Belmont Women Round Toe Suede Brun Vinter Boot Chestnut Suede , Kamik Women s Shelly Rain Boot Svart Merrell Women s Chateau Tall Zip Polar Vanntett Snøbrett Svart CLARKS Women s Petrina Gail Platform Gull / Metallisk Lær Steve Madden Women s Carrson Dress Open Blomster , CLARKS Kvinner Lexi Marigold Q Svart lær NIKE Women s Ultra Comfort Thong Sandal Solrød / hvit-varm korall ,
     11.2 Improper Integrals
     11.3 Tests For Convergence Of Improper Integrals

FitFlop Women s Leather Gitter Surfa Surfa Floral s Flip-Flop 7419 Svart f6754f5 -


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
FitFlop Women s Leather Gitter Surfa Surfa Floral s Flip-Flop 7419 Svart f6754f5           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



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 10241569
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