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' Calculus (13th or 14th ed., Early Transcendentals).

Suggestions for additional links are welcome!

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

Many of the links below are from this source:
Interactive Mathematics with the homepage at http://www.intmath.com/
For additional visual examples, look at the links with Geogebra interactive graphics in the on-line Calculus book by Fr. Michael May, S.J. (St. Louis University) at this link: http://bit.ly/MikeMayCalculus.

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.

PRELIMINARY

• Web-based "Are You Ready For Calculus II?"
  Links to YouTube Videos reviewing various Calculus Concepts
  Summary sheets of Algebra, Trig, and Derivative formulas
  

  WEEK 1
  

• Sec 4.2 - Mean Value Theorem
  
• Sec 4.3-4.4 - First Deriv. Test and Concavity
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/graphingdirectory/ (Graphing Problems Using Derivatives)
  
• Sec 4.5 - Indeterminate Forms and L'Hopital's Rule
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/lhopitaldirectory/LHopital.html (Examples and problems for l'Hopital's rule.)
  

  WEEK 2

• Sec 4.8 - Antiderivatives
  Webapp for practicing antiderivative problems
• Sec 5.5 - Indefinite Integrals and the Substitution Rule
  Interactive Math Video Lecture on Substitution (http://www.intmath.com/integration/integration-mini-lecture-by-substitution.php)
  http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/usubdirectory/ (See problems and detailed solutions at end.)
  On-line YouTube Video on U-substitutions

  WEEK 3

• Sec 5.1-5.2 - Estimating area with finite sums
  Integration and Riemann Sums
  On-line YouTube Video on Approximating Definite Integrals Using Rectangles
  GeoGebra Riemann Sums example
• Sec 5.3 - Definite Integral
  On-line YouTube Video on Definite Integrals
  

  WEEK 4

• Sec 5.4 - Fundamental Th. of Calculus
  Interactive Math Video Lecture on Area under a Curve (http://www.intmath.com/integration/3-area-under-curve.php)
  http://www.intmath.com/Applications-integration/2_Area-under-curve.php
  
• Sec 5.6 - Substitution and Area between Curves
  http://www.intmath.com/Applications-integration/3_Area-between-curves.php

  WEEK 5

• Sec 6.1 - Volumes using Slices
  Volumes of Revolution -- Parabola example
  http://www.intmath.com/Applications-integration/4_Volume-solid-revolution.php
  http://old.nationalcurvebank.org/volrev/volrev.htm
  GeoGebra examples of Solids of Revolution
  
• Sec 6.2 - Volumes using Cylindrical Shells.
  GeoGebra examples of Volumes via Cylindrical Shells
  
• Sec 6.3 Length along a curve.
  

  WEEK 6

• Sec 7.1 - Log as an integral.
  http://www.intmath.com/Methods-integration/2_Integration-logarithmic-form.php (Integration with the result being a log function)
  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 7.2 - Exponential change, Separable Diff. Equations
• Sec 8.2 - Integration by Parts
  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.)
  

  WEEK 7

• Sec 8.3 - Trig Integrals
  http://www.intmath.com/Methods-integration/5_Integration-other-trigonometric-forms.php

  WEEK 8

• Sec 8.4 - Trig Substitutions
  http://www.intmath.com/Methods-integration/8_Integration-trigonometric-substitution.php
• Sec 8.5 - Partial Fractions
  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.)
  

  WEEK 9

• Sec 8.7 - Numerical Integration
  http://www.intmath.com/Integration/5_Trapezoidal-rule.php
  http://www.intmath.com/Integration/6_Simpsons-rule.php
  
• Sec 8.8 - Improper Integrals.
  
• Separable Diff Eq.
  

This page is maintained by Dennis C. Smolarski, S.J.
Last updated 21 July 2023

Email: dsmolarski at scu.edu