Department of Mathematics and Computer Science

Math 13 -- Calculus III
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 (15th 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 two major sources:
Interactive Mathematics with the homepage at http://www.intmath.com/
http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx Paul's Online Math Notes for Calculus II (Single Variable Calculus, including Series and Sequences and introduction to 3 D) NOTE: each topic page has a link to "practice problems" for the topic at the bottom.
http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx Paul's Online Math Notes for Calculus III (Multivariable Calculus) NOTE: each topic page has a link to "practice problems" for the topic at the bottom.
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 the 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 III?"
  Links to YouTube Videos reviewing various Calculus Concepts
  

  WEEK 1
  

• Sec 7.3 - Hyperbolic Functions
  http://www.phengkimving.com/calc_of_one_real_var/07_the_exp_and_log_func/07_06_the_hyp_func.htm (Hyperbolic Functions)
  http://www.phengkimving.com/calc_of_one_real_var/07_the_exp_and_log_func/07_07_the_inv_hyp_func.htm (Inverse Hyperbolic Functions)
  
• Sec 10.1 - Sequences
  http://www.phengkimving.com/calc_of_one_real_var/14_infinite_series/14_01_infinite_sequences.htm (Infinite Sequences)
  http://tutorial.math.lamar.edu/Classes/CalcII/Sequences.aspx (Paul's Online Math Notes - Sequences)

  WEEK 2

• Sec 10.2 - Infinite Series
  http://www.phengkimving.com/calc_of_one_real_var/14_infinite_series/14_02_infinite_series.htm (Infinite Series)
  
• Sec 10.8 - Taylor and Maclaurin Series
  http://www.intmath.com/series-expansion/1-taylor-series.php (Interactive Mathematics - Taylor Series)
  http://www.intmath.com/series-expansion/2-maclaurin-series.php (Interactive Mathematics - Maclaurin Series)
  http://www.phengkimving.com/calc_of_one_real_var/15_rep_of_func_by_pow_series/15_03_taylor_series.htm (Taylor Series)
  http://tutorial.math.lamar.edu/Classes/CalcII/Series_Basics.aspx (Paul's Online Math Notes - Series)
  http://tutorial.math.lamar.edu/Classes/CalcII/TaylorSeries.aspx (Paul's Online Math Notes - Taylor Series)

  WEEK 3

• Sec 10.9 - Convergence of Taylor Series
  https://www.geogebra.org/m/JDxzvGxD#material/Wv4gg9GT (Geogebra demo of Taylor Polynomial)
  http://www.phengkimving.com/calc_of_one_real_var/15_rep_of_func_by_pow_series/15_05_taylor_polyn_and_taylor_thrm.htm (Taylor Polynomials and Taylor Theorem)
  
• Sec 10.10 - Binomial Series
  http://www.phengkimving.com/calc_of_one_real_var/15_rep_of_func_by_pow_series/15_06_the_binomial_series.htm (Binomial Series)
  http://tutorial.math.lamar.edu/Classes/CalcII/BinomialSeries.aspx (Paul's Online Notes - Binomial Series)

  WEEK 4

• Sec 11.1 - Parameterizations of Plane Curves
  
• Appendix A.3 and Sec 11.6 - Conic Sections
  http://www.intmath.com/plane-analytic-geometry/intro.php (Interactive Math -- Analytic Geom and Conic Sections)
  Parabola Interactive visualization
  Ellipse Interactive visualization
  Hyperbola Interactive visualization
  

  WEEK 5

• Secs 12.1-12.2 - Three-D Coordinate Systems. Vectors
  http://www.intmath.com/vectors/6-3-dimensional-space.php (Interactive Math -- 3-D Coordinate System)
  http://www.intmath.com/vectors/7-vectors-in-3d-space.php (Interactive Math -- Vectors in 3-D)
  http://tutorial.math.lamar.edu/Classes/CalcIII/3DCoords.aspx (Paul's Online Math Notes - 3 D Coordinates)
• Sec 12.3 - Dot Product.
  http://www.intmath.com/vectors/5-dot-product-vectors-2-dimensions.php (Interactive Math - Dot Product)
  http://tutorial.math.lamar.edu/Classes/CalcII/DotProduct.aspx (Paul's Online Math Notes - Dot Product)

  WEEK 6

• Sec 12.4 - Cross Product.
  http://www.mathsisfun.com/algebra/matrix-determinant.html (Determinant of a Matrix)
  http://www.intmath.com/vectors/8-cross-product-vectors.php (Interactive Math - Cross Product)
  http://mathinsight.org/cross_product (Math Insight - Cross Product)
  http://tutorial.math.lamar.edu/Classes/CalcII/CrossProduct.aspx (Paul's Online Math Notes - Cross Product)
• Sec 12.5 - Lines and Planes in Space
  http://mathinsight.org/line_parametrization (Math Insight - Parameterization of a Line)
  http://mathinsight.org/forming_planes (Math Insight - Forming Planes)
  http://mathinsight.org/plane_parametrization (Math Insight - Parameterization of a Plane)
  http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfLines.aspx (Paul's Online Math Notes - Equations of Lines)
  http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfPlanes.aspx (Paul's Online Math Notes - Equations of Planes)
• Sec 12.6 - Cylinders and Quadric Surfaces
  http://tutorial.math.lamar.edu/Classes/CalcIII/QuadricSurfaces.aspx (Paul's Online Math Notes - Quadric Surfaces)
  https://nmd.web.illinois.edu/quadrics/index.html (Univ. Illinois -- Interactive Gallery of Quadric Surfaces)

  WEEK 7

• Secs 14.1-14.2 - Functions of Several Variables, Limits and Continuity in Higher Dimensions
  http://mathinsight.org/level_sets (Math Insight - Level Curves)
  http://tutorial.math.lamar.edu/Classes/CalcIII/Limits.aspx (Paul's Online Math Notes - Limits in 3-D)
• Sec 14.3 - Partial Derivatives
  http://demonstrations.wolfram.com/PartialDerivativesIn3D/ (Wolfram Demo -- Partial Derivatives in 3D)
  http://tutorial.math.lamar.edu/Classes/CalcIII/PartialDerivatives.aspx (Paul's Online Math Notes - Partial Derivatives)
  

  WEEK 8

• Sec 14.4 - The Chain Rule
  http://tutorial.math.lamar.edu/Classes/CalcIII/ChainRule.aspx (Paul's Online Math Notes - Multi-variable Chain Rule Rule)
• Sec 14.5 - Directional Derivatives and Gradient Vectors
  http://mathinsight.org/directional_derivative_gradient_introduction (Math Insight - Directional Derivatives and Gradients)
  http://tutorial.math.lamar.edu/Classes/CalcIII/DirectionalDeriv.aspx (Paul's Online Math Notes - Directional Derivatives)
  http://tutorial.math.lamar.edu/Classes/CalcIII/GradientVectorTangentPlane.aspx (Paul's Online Math Notes - Gradient Vector, Tangent Planes and Normal Lines)
• Sec 14.6 - Tangent Planes and Differentials
  http://tutorial.math.lamar.edu/Classes/CalcIII/Differentials.aspx (Paul's Online Math Notes - Differentials)
  http://tutorial.math.lamar.edu/Classes/CalcIII/TangentPlanes.aspx (Paul's Online Math Notes - Tangent Planes)

  WEEK 9

• Sec 14.7 - Extreme Values and Saddle Points
  http://tutorial.math.lamar.edu/Classes/CalcIII/RelativeExtrema.aspx (Paul's Online Math Notes - Relative Min/Max)
  http://tutorial.math.lamar.edu/Classes/CalcIII/AbsoluteExtrema.aspx (Paul's Online Math Notes - Absolute Min/Max)
  
• Sec 14.8 - Lagrange Multipliers.
  http://tutorial.math.lamar.edu/Classes/CalcIII/LagrangeMultipliers.aspx (Paul's Online Math Notes - Lagrange Multipliers)

This page is maintained by Dennis C. Smolarski, S.J.
Last updated 7 January 2024

Email: dsmolarski at scu.edu