Department of Mathematics and Computer Science

Math 11 -- Calculus I
Dennis C. Smolarski, S.J.
Web Links

The links given below may be helpful as a supplementary source for some students to comprehend better the topics covered in class lectures. Since the pages linked were created by different individuals based on different textbooks, the presentation may not exactly correspond to that given in Thomas/Finney.

Suggestions for additional links are welcome!

Additional links may be found at the pages created by Pheng Kim Ving:
http://www.phengkimving.com/

Many of the links below are from two majors sources:
Visual Calculus with the homepage at http://archives.math.utk.edu/visual.calculus/
and Interactive Mathematics with the homepage at http://www.intmath.com/

I highly recommend the use of pages from these two interactive sources to review difficult material, and before exams. Students can look at an unsolved problem, attempt to solve it with pencil and paper, and then click on the on-line solution to verify their solution.

BACKGROUND FOR CALCULUS:
http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/CalculusTips.html "Doing Well in Calculus"

PRELIMINARY
• Web-based "Are You Ready For Calculus I?"
  Links to YouTube Videos reviewing various Calculus Concepts
  

  WEEK 1
  

• Basic Algebra
  http://archives.math.utk.edu/visual.calculus/0/ (Review of Pre-Calculus Mathematics)
• Sec 1.2 - The Slope of a Line
  
• Sec 1.3 - Equations for Lines
  

  WEEK 2
  

• Sec 1.4 - Functions and Graphs
  
• Sec 1.5 - Absolute Values
  
• Sec 1.6 - Tangent Lines and Slopes
  

  WEEK 3
  

• Sec 1.7 - The Slope of the Curve. The Derivative
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/defderdirectory/DefDer.html (Definition of Derivative Problems)
• Sec 1.8 - Velocity and Other Rates of Change
  
• Sec 1.9 - Limits
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/limcondirectory/LimitConstant.html (Limit tending toward a constant Problems)
  http://archives.math.utk.edu/visual.calculus/1/limits.18/ Visual Calculus Page with Flash Examples.
• Sec 1.10 - Infinity as a Limit
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.Html (Limit tending toward Infinity Problems)

  WEEK 4
  

• Sec 1.11 - Continuity
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/continuitydirectory/ (Continuity Problems)
• Sec 2.1 - Derivatives of Polynomials
  
• Sec 2.2 - Derivatives of Products, Powers, and Quotients
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/productruledirectory/ (Product Rule Problems)
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/quotientruledirectory/ (Quotient Rule Problems)
  On-line YouTube Video on the Product Rule
  On-line YouTube Video on the Quotient Rule
  

  WEEK 5
  

• Sec 2.3 - Implicit Differentiation and Fractional Powers
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/implicitdiffdirectory/ (Implicit Differentiation Problems) http://archives.math.utk.edu/visual.calculus/3/implicit.7/ (Implicit Differentiation Tutorial and Problems)
• Sec 2.4 - Linear Approximations and Differentials
  http://archives.math.utk.edu/visual.calculus/2/linear_app.6/ (Linear Approximation Tutorial and Problems)
  http://archives.math.utk.edu/visual.calculus/3/differentials.2/ (Differentials Tutorial and Problems)
• Sec 2.5 - The Chain Rule
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ (Chain Rule Problems)
  On-Line YouTube Video on the Chain Rule
• Sec 2.8 - Parametric Equations
  http://archives.math.utk.edu/visual.calculus/3/parametric.4/ (Tangent Line and Parametric Curve Tutorial and Problems)

  WEEK 6
  

• Sec 2.6 - Review of Trigonometry
  
• Sec 2.7 - Derivatives of Trigonmetric Functions
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/trigderivdirectory/ (Trig Derivatives Problems)
• Sec 2.9 - Newton's Method for Finding Roots
  http://archives.math.utk.edu/visual.calculus/3/newton.5/ (Newton's Method)
  
• Sec 3.1 - Graphs and First Derivatives
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/graphingdirectory/ (Graphing Problems Using Derivatives)
  Sec 3.2 - Concavity and Points of Inflection
  

  WEEK 7
  

• Sec 3.4 - Asymptotes and Symmetry
  
• Sec 3.5 - Maxima and Minima
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/ (Maximum/Minimum Problems)
  http://archives.math.utk.edu/visual.calculus/3/max.2/ (Maxima and Minima Tutorial and Problems)

  WEEK 8
  

• Sec 3.6 - Related Rates of Change
  
• Sec 3.7 - The Mean Value Theorem
  http://archives.math.utk.edu/visual.calculus/3/mvt.3/ (Mean Value Theorem)
  

  WEEK 9
  

• Sec 3.8 - Indeterminate Forms, l'Hopital's Rule
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/LHopital (Examples and problems for l'Hopital's rule.)
  http://archives.math.utk.edu/visual.calculus/3/lhospital.1/ (l'Hopital's Problems -- Finite Limits)
  http://archives.math.utk.edu/visual.calculus/3/lhospital.2/ (l'Hopital's Problems -- Infinite Limits)
  
• Sec 4.1 - Indefinite Integrals
  http://archives.math.utk.edu/visual.calculus/4/antider.1/ (Indefinite Integral [Antiderivative] Tutorial and Problems)
• Sec 4.2 - Value for the Constant of Integration
  
• Sec 4.3 - The Substitution Method of Integration
  http://archives.math.utk.edu/visual.calculus/4/substitutions.3/
  http://people.hofstra.edu/Stefan_Waner/tutorials4/unit6_2.html
  http://www.calculus.net/ci2/search/?request=category&code=1311&off=0&tag=9200438920658 (Links to various web pages about substitution)
  http://archives.math.utk.edu/visual.calculus/4/integrals.2/index.html A quiz of 50 multiple-choice problems using substitution.
  Interactive Math Video Lecture on Substitution (http://www.intmath.com/Integration/subst.wmv)
  http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/usubdirectory/ (See problems and detailed solutions at end.)
• Sec 4.4 - Integrals of Trigonometric Functions
  

This page is maintained by Dennis C. Smolarski, S.J.
Last updated 15 July 2011

Email: dsmolarski at scu.edu