Department of Mathematics and Computer Science

Math 12 -- Calculus II
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 following page, at the American University in Cairo:
http://www1.aucegypt.edu/faculty/werner/MW132.htm, or
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.

NOTE: The "Table of Elementary Integrals" often referred to in "Visual Calculus" modules below can be accessed at http://archives.math.utk.edu/visual.calculus/4/antider.2/index.html

PRELIMINARY

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

  WEEK 1
  

• Sec 4.3 - 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.)
  On-line Google Video on U-substitutions
  On-line YouTube Video on U-substitutions
• Sec 4.5 - Definite Integrals: Area under a Curve
  On-line YouTube Video on Definite Integrals
  Sec 4.6 - Calculating Definite Integrals by Summation
  Integration and Riemann Sums
  Riemann Sum applet (adjustable function)
  On-line YouTube Video on Approximating Definite Integrals Using Rectangles
  
• Sec 4.7 - The Fundamental Theorems of Integral Calculus
  http://archives.math.utk.edu/visual.calculus/4/ftc.10/index.html
  Interactive Math Video Lecture on Area under a Curve (http://www.intmath.com/Integration/area.wmv)
  http://www.intmath.com/Applications-integration/2_Area-under-curve.php
  http://www.intmath.com/Integration/3_Area-under-curve.php

  WEEK 2
  

• Sec 4.8 - Substitution in Definite Integrals
  http://archives.math.utk.edu/visual.calculus/4/substitutions.3/ (See last two problems for examples on definite integrals.)
  Sec 4.9 - Rules for Approximating Definite Integrals
  http://archives.math.utk.edu/visual.calculus/4/approx.1/index.html
  http://www.intmath.com/Integration/5_Trapezoidal-rule.php
  http://www.intmath.com/Integration/6_Simpsons-rule.php
  http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/techniques/numerical.html
  
• Sec 5.1 - Net Change in Position and Distance
  Sec 5.2 - Areas between Curves
  http://archives.math.utk.edu/visual.calculus/5/area2curves.3/index.html
  http://www.intmath.com/Applications-integration/3_Area-between-curves.php
• Sec 5.3 - Calculating Volumes by Slicing. Volumes of Revolution
  Volumes of Revolution -- Parabola example
  Volumes of Revolution (Needs LiveMath Plug-In/ActiveX [and NOT LiveMath "Maker" or LiveMath "Viewer"] -- works with Firefox and Netscape but not with Explorer)
  http://www.intmath.com/Applications-integration/4_Volume-solid-revolution.php
  http://curvebank.calstatela.edu/volrev/volrev.htm
  On-line Google Video on Volumes Via Disks/Washers
  

  WEEK 3
  

• Sec 5.4 - Volumes Modeled with Washers and Cylindrical Shells
  http://archives.math.utk.edu/visual.calculus/5/volumes.5/index.html (Volumes of Revolution)
  http://archives.math.utk.edu/visual.calculus/5/volumes.6/index.html (Volumes of Revolution -- Cylindrical Shells)
  Volumes of Revolution -- Washers (Needs LiveMath Plug-In/ActiveX [and NOT LiveMath "Maker" or LiveMath "Viewer"] -- works with Firefox and Netscape but not with Explorer)
  Volumes of Revolution -- Cylindrical Shells (Needs LiveMath Plug-In/ActiveX [and NOT LiveMath "Maker" or LiveMath "Viewer"] -- works with Firefox and Netscape but not with Explorer)
  http://library.thinkquest.org/3616/Calc/S3/VoSoR.html
  On-line Google Video on Volumes Via Cylindrical Shells
  

  WEEK 4
  

• Sec 5.5 - Lengths of Plane Curves
  http://archives.math.utk.edu/visual.calculus/5/arclength.1/index.html
• Sec 6.1 - Inverse Functions
  Sec 6.2 - The Inverse Trigonometric Functions
• Sec 6.3 - The Derivatives of the Inverse Trigonometric Functions
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/invtrigderivdirectory/InvTrigDeriv.html
  http://www.intmath.com/Differentiation-transcendental/3_Derivative-arcsin-arccos-arctan.php
  http://www.intmath.com/Methods-integration/6_Integration-inverse-trigonometric-forms.php

  WEEK 5
  

• Sec 6.4 - The Natural Logarithm and Its Derivative
  http://www.intmath.com/Differentiation-transcendental/5_Derivative-logarithm.php (Derivative of Log functions)
  http://www.intmath.com/Methods-integration/2_Integration-logarithmic-form.php (Integration with the result being a log function)
  Sec 6.5 - Properties of Natural Logarithms
  http://archives.math.utk.edu/visual.calculus/3/logdiff.1/index.html (Using logarithms to simplify derivatives.)
• Sec 6.6 - The Exponential Function e^x
  http://www.intmath.com/Methods-integration/3_Integration-exponential-form.php
  http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/expondirectory/ (See problems and detailed solutions at end.)
  Sec 6.7 - The Functions a^x and a^u
  http://www.phengkimving.com/calc_of_one_real_var/07_the_exp_and_log_func/07_03_gen_exp_and_log_func.htm
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/logdiffdirectory/ (Logarithmic Differentiation Problems) Sec 7.1 - Basic Integration Formulas
  http://www.jtaylor1142001.net/calcjat/Contents/CLogExp.htm Problems and detailed solutions for Logarithm and Exponential derivatives and integrals.

  WEEK 6
  

• Sec 7.2 - Integration by Parts
  http://archives.math.utk.edu/visual.calculus/4/int_by_parts.3/index.html
  http://www.intmath.com/Methods-integration/7_Integration-by-parts.php
  http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/intbypartsdirectory/ (See problems and detailed solutions at end.)
  On-line Google Video on Integration by Parts
  
• Sec 7.3 - Products and Powers of Trigonometric Functions
  http://www.intmath.com/Methods-integration/5_Integration-other-trigonometric-forms.php

  WEEK 7
  

• Sec 7.4 - Even Powers of Sines and Cosines
• Sec 7.5 - Trig Substitutions for sums or differences of squares
  http://archives.math.utk.edu/visual.calculus/4/substitutions.2/index.html
  http://www.intmath.com/Methods-integration/8_Integration-trigonometric-substitution.php

  WEEK 8
  

• Sec 7.6 - Integrals involving quadratics and completing the square
• Sec 7.7 - Partial Fractions
  http://archives.math.utk.edu/visual.calculus/4/partial_fractions.2/index.html
  http://www.intmath.com/Methods-integration/11_Integration-partial-fractions.php
  http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/partialfracdirectory/ (See problems and detailed solutions at end.)
  On-Line Google Video on Partial Fractions

  WEEK 9
  

• Sec 7.8 - Improper Integrals
  http://archives.math.utk.edu/visual.calculus/4/improper.2/index.html
• Sec 9.1 - Hyperbolic functions
  http://www.phengkimving.com/calc_of_one_real_var/07_the_exp_and_log_func/07_06_the_hyp_func.htm
• Sec 9.4 - Inverse Hyperbolic functions
  http://www.phengkimving.com/calc_of_one_real_var/07_the_exp_and_log_func/07_07_the_inv_hyp_func.htm

This page is maintained by Dennis C. Smolarski, S.J.
Last updated 12 September 2010

Email: dsmolarski at scu.edu