Calculus

calculator dictionary graph paper graph simulator

Dedication & Special Thanks
Mark Lund & Jeff Crawford deserve most the credit for the items found on this page, from resources to links to examples worked out in detail. Having built & maintained websites for the past 5 years (2005-'10) I understand the tremendous amount of time these two individuals have spent, not only locating, but creating the awesome resources contained in these pages to help their students 'get 'it'!!! This page and many of the pages on this website would NOT be possible without the dedication of both Mark Lund & Jeff Crawford to their craft.

Unit 1 - Welcome Unit
This unit will focus on analyzing data that has a strong correlation. What linear model best fits? How do you write equations for such models? How do you use the model to answer questions?
Before we dive into Calculus we need to be ready.

Functions
Trigonometry
Algebra
.


This unit must be completed by the end of week 1
        Calculus readiness assessment

        Pre calculus tutorials resource!






Khan Academy
I believe strongly in 'math online'! Seeing different personalities present the same material in different ways. Throughout these math website pages I refer to the Khan Academy for resources, videos & practice. I hope that each math student login to the Khan Academy and use the practice problems provided & watch the videos pertaining to the particular level of math they are studying! Just email me for the 'coach' code so that you can be tracked, monitored, and helped along the way!

For Calculus students after you login and find your coach go to the practice tree and near the bottom of the tree you will see all the topics which need to be watched & practiced:
Limits1, Limits 2, Derivatives intuition, Derivatives 1, Power Rule, Special Derivatives, Quotient Rule, Product Rule, Chain Rule.





       In the drop down menu pick pick the following category:
        Finney: Calculus: graphical, numerical, algebraic, 3E

Most of the work contained in this calculus section came from the Finney & Demana Calculus books pictured to the left.
I specifically want to thank Mr. Mark Lund & Mr. Matt Green for their help and resources in becoming a more effective teacher of 'Calculus'!

If you are using the blue Finney & Demana textbook the following is the link to the solutions manual! Needless to say, this is a pdf version and may take a moment to load.

solutions manual - Finney & Demana (blue book)






















Unit 2 - Limits & Continuity
Knowing what happens as we get infinitely close opens a new world of possibilities.

Understanding limits
Finding limits
Continuity
Rates of change

This unit must be completed by the end of week 5 (week 2 for BC)

Unit 2: Learning targets

        Danger Dan Investigation


If you have not done so already make sure you watch the Khan Academy videos on Limits (just click here)!

        target 2B section 2.2 Limits involving Infinity practice:
        page 76 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 2B section 2.2 Limits involving Infinity practice:
        page 76 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 2b checkup practice

        target 2C section 2.3 Continuity:
        page 84 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        functions & limits practice

        target 2c checkup practice

        target 2D section 2.4 Rates of change 7 tangent Lines:
        page 92 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        Secant line animation #1
        Secant line animation #2
        Secant line animation #3
        Lone Rider courtesy of Mr. Crawford (Ferris High School)
        Lone Rider courtesy of Mr. Crawford w/sound(Ferris High School)


As we wrap up this unit take some time to watch & practice Derivative Intuition which will tie this unit into Unit 3!

        target 2d checkup practice

        The Definition - practice

        Unit 2 review assessment practice
















TI 89 Calculator


The TI 89 calculator is a powerful tool in calculus, unfortunately it can be confusing when first used. Mathbits.com is a fantastic website for tutorials on how to use the TI 89 series! I remember during my student teaching I had to use the following tutorials several times in order to completely understand what I was seeing on the TI89 screen!



1. introduction
2. home screen
3. graphing
4. limits
5. derivatives
6. maximums & minimums
7. integrate



Unit 3 - Derivatives Basics
Knowing what we are looking for and having the tools to find it is essential.

Definition of a derivative
Basic derivatives
Rules for derivatives
Techniques

This unit must be completed by the end of week 11 (week 3 for BC)

Learning targets
        downloadable student target checklist (self tracking)


        function matching practice

        function matching practice part 2

        more function matching practice


I think the videos in this section of the Khan Academy are especially helpful on derivatives

        function matching practice (online)

other sites that may help clear up function matching.....
        graph the derivative practice - wolfram
        how to sketch the derivative
        sketch the function, then the derivative - advanced & very detailed!!
        derivative matching game - great way to check your understanding!!

        target 3A section 3.1 Understanding Definitions for Derivatives:
        page 105 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 3A section 3.2 Understanding Definitions for Derivatives:
        page 114 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

              tutorial - Mr. Lund on tangent lines

        target 3A checkup practice

        target 3B section 3.3 Finding Basic Derivatives:
        page 124 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 3B section 3.4 Finding Basic Derivatives:
        page 135 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 3B checkup practice

        Derivative self test (online)

        Derivative self test #2 (online)


Heavy lifting portion of Calculus, there are several area of practice and videos which may help if you are having difficulty; power rule, special derivatives, quotient rule, product rule, chain rule!

        target 3C section 3.5 Unsderstanding Derivatives of Combined Functions:
        page 146 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

              tutorial - Mr. Lund on Chain Rule

              tutorial - Mr. Lund on Product Rule

              tutorial - Khan Academy on Quotient Rule

        target 3C checkup practice

        Implicit differentiation practice

        target 3D section 3.7 Apply techniques to find derivatives:
        page 162 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 3D section 3.8 Apply techniques to find derivatives:
        page 170 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

              tutorial - Mr. Lund on Logarithmic Differentiation

              tutorial - Mr. Lund on Logarithmic Differentiation part 2

              tutorial - Khan Academy on Implicit Differentiation

              tutorial - PatrickJMT on Implicit Differentiation

        target 3D checkup practice

        motion & derivatives investigation

        motion & derivatives investigation #2

        target 3E section 3.9 Interpreting derivatives:
        page 178 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 3E checkup practice
Monday
Derivatives - Product rule, Quotient rule, Trig. functions

       Entry task & exit slip

       product differentiation practice

       quotient differentiation practice

       trig function differentiation practice
Tuesday
Derivatives - chain, Implicit differentiation

       Entry task & exit slip

       chain rule differentiation practice

       implicit differentiation practice
Wednesday
Derivatives - exponential, logarithmic differentiation

       Entry task & exit slip

       exponential differentiation practice

       logarithmic differentiation practice
Thursday

        mean value theorem introduction


Khan academy videos and practice exercises on average rates are great!

        Mr. Lund Video on average rate of change!!

        average rates practice #1

        average rates practice #2
Friday

        average rates practice #3


Unit 4 - Applying Derivatives
With the derivative as a tool we can find solutions to many of life's problems.

Tangent lines
Extrema and optimizations
Related rates

This unit must be completed by the end of week 17 (week 8 for BC)

Learning targets
        downloadable student target checklist (self tracking)

        Newton's method (online)

        target 4A checkup practice

        target 4B section 4.2 Mean value theorem:
        page 202 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 4B checkup practice

        target 4C section 4.1 Extreme Values:
        page 193 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 4C section 4.3 connecting and graphing f' & f" (extremas):
        page 214 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 4C checkup practice

        Linearizations practice

        target 4D section 4.5 Linearization practice:
        page 242 #1,3,5,7 & look for linearization problems

        Extrema practice

        target 4D section 4.6 Related Rates:
        page 250 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 4D checkup practice

        target 4E section 8.2 L'Hopitals Rule:
        page 193 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 4E checkup practice


Unit 5 - Basic of Integrals
Integrals are a basic tool for solving many problems

Estimating integrals
Mean Value Theorem
Fundamental Theorem of Calculus

This unit must be completed by the end of week 21 (week 15 for BC)

Learning targets
        downloadable student target checklist (self tracking)

        motion & distance investigation

        evaluate integrals of a piecewise function practice

        target 5A section 5.1 Concept of an Integral:
        page 270 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        definite integral finite sum practice

        target 5A checkup practice

        target 5B section 5.2 Definite Integrals:
        page 282 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        definite integrals practice

        target 5B checkup practice

        target 5C section 5.3 Mean Value Theorem for Integrals:
        page 290 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        average value practice 1

        average value practice 2

        target 5C checkup practice

        area under a curver practice

        evaluate integrals & areas under curve for specific windows & discuss

        evaluate integrals & areas under curve for specific windows & discuss part 2

        target 5D section 5.4 Fundamental Theorem of Calculus:
        page 302 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        fundamental theorem of calculus practice 1

        fundamental theorem of calculus practice 2

        target 5D checkup practice

        target 5D section 5.5 Fundamental Theorem of Calculus part 2:
        page 312 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 5E checkup practice

        target 5E section 8.4 Improper Integrals:
        page 467 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        trapezoidal rule practice

        target 5F checkup practice


Unit 6 - Solving Differential equations
Challenging problems can be solved with differential equations.

Slope Fields
Integration by Substitution
Integration by Parts

This unit must be completed by the end of week 21 for BC pacing

Learning targets

        introduction to slope fields

        target 6a goals and examples

        slope fields practice

        target 6A section 6.1 Introduction to slope fields:
        page 327 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 6b goals and examples

        target 6B section 6.2 Understand slope fields:
        page 337 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        fundamental theorem example

        target 6c goals and examples

        target 6C section 6.3 Introduction to integration by parts:
        page 346 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        integration by substitution (online)

        chapter 6 section 2 - U substitution practice

        chapter 6 section 4 - integration by parts practice

        integration by parts (online)

        target 6d goals and examples

        target 6D section 6.4 Solving using integration by parts:
        these techniques and concepts can be VERY difficult, this section may take a few days to complete!
        page 357 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        Eulers method - 3 examples for practice

        exponential growth & decay practice

        target 6e goals and examples

        target 6E section 6.5 More applications:
        page 369 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        Review section:
        page 373 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        logistics practice


Unit 7 - Solving Differential equations

area between curves
volumes (area in 3D!)
length

Learning targets



        target 7a goals and examples

        target 7A section 7.1 Integrals as a Net Change:
        page 386 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        integral net change practice

        integral net change practice part 2

        target 7b goals and examples

        target 7B section 7.2 Area between curves:
        page 395 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        area between curves practice

        target 7c goals and examples

        target 7C section 7.3 Volumes (area in 3D!):
        page 406 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        visualize the 3d shape practice

        applications of integrals practice 1

        applications of integrals practice 2

        target 7d goals and examples

        target 7D section 7.4 Length of curves:
        page 416 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        Review section:
        page 431 #1,3,5,7 & 11-30 every 6th (11,17,23,29,etc)

        length of curves practice

        chapter 7 section 5 - applications to science practice


Unit 8 -

sequences
series
power series
summations
convergence

Learning targets

        target 8A section 9.1 power series:
        page 481 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 8B section 9.2 Taylor series:
        page 492 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 8B section 9.3 Taylor series continued:
        page 501 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        target 8C section 9.4 Convergence:
        page 511 #1,3,5,7 & 11-48 every 6th (11,17,23,29,etc)

        Review section:
        page 526 #1,3,5,7 & 11-30 every 6th (11,17,23,29,etc)


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