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' Calculus (15th ed., Early Transcendentals).

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 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.

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
  
• Basic Algebra
  Webapp to practice factoring

  WEEK 1
  

• Sec 1.1 - Functions and Graphs
• Sec 1.2 - Combining Functions
  
• Sec 1.3 - Trigonometric Funcions
  http://www.phengkimving.com/calc_of_one_real_var/06_the_trig_func_and_their_inv/06_01_the_trig_func/06_01_01_the_trig_func.htm
  
• Sec 1.5 - Exponential Functions
  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/
• Sec 1.6 - Inverse Functions (including Inv. Trig. Funct.) and Logarithms
  http://www.phengkimving.com/calc_of_one_real_var/06_the_trig_func_and_their_inv/06_02_the_inv_trig_func/06_02_01_the_inv_trig_func.htm

  WEEK 2
  

• Sec 2.1 - Rates of Change and Tangents to Curves
• Sec 2.2 - Limit of a Function
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/limcondirectory/LimitConstant.html (Limit tending toward a constant Problems)
  Curve sculpture of a curve with a limit point (MOMA)
• Sec 2.4 - One-sided Limits
• Sec 2.5 - Continuity
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/continuitydirectory/ (Continuity Problems)

  WEEK 3
  

• Sec 2.6 - Limits involving infinity, Asymptotes
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.Html (Limit tending toward Infinity Problems)
  
• Sec 3.1 - Tangents and Derivative at a Point
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/defderdirectory/DefDer.html (Definition of Derivative Problems)

  WEEK 4
  

• Sec 3.2 - Derivative as a Function
  
• Sec 3.3 - Differentiation Rules
  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
  
  Webapp for simple derivatives
  Webapp for more challenging derivatives
  
• Sec 3.4 - Derivative as Rate of Change
  

  WEEK 5
  

• Sec 3.5 - Derivatives of Trig Functions
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/trigderivdirectory/ (Trig Derivatives Problems)
• Sec 3.6 - The Chain Rule
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ (Chain Rule Problems)
  On-Line YouTube Video on the Chain Rule

  WEEK 6
  

• Sec 3.7 - Implicit Differentiation
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/implicitdiffdirectory/ (Implicit Differentiation Problems)
  
• Sec 3.8 - Derivatives of Inverse Functions and Logs.
  http://www.intmath.com/Differentiation-transcendental/5_Derivative-logarithm.php (Derivative of Log functions)
  
• Sec 3.9 - Inverse Trig 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 7
  

• Sec 3.10 - Related Rates
  http://www.phengkimving.com/calc_of_one_real_var/08_app_of_the_der_part_2/08_02_rel_rates.htm

  WEEK 8
  

• Sec 3.11 - Linearization and Differentials
  
• Sec 4.1 - Extreme Values of Functions (Max and Min points)
• Sec 4.3 - Monotonic Functions and 1st Derivative Test
• Sec 4.4 - Concavity and curve sketching
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/graphingdirectory/ (Graphing Problems Using Derivatives)

  WEEK 9
  

• Sec 4.6 - Applied Optimization (Max/Min)
  http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/ (Maximum/Minimum Problems)
  
• Sec 4.7 - Newton's Method
  

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

Email: dsmolarski at scu.edu