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MAC2312  -  Calculus II
Handouts & Worksheets


 

 

 

 

Review, Handouts, and Worksheets

 

Algebra Study Guide - Courtesy of AIMS Community College - Worksheet
Analyze Functions Review - Worksheet
College Algebra web site - Link
Calculus I - Handouts Web Page - Link

Trigonometry and Derivative Formulas
Trig Identities & Formulas - Everything  ,  Identities
Differentiation Formulas and Corresponding Integrals:  Formulas1 - LargeFormulas2
Derivatives of the Transcendental Functions - Summary
Expressing Inverse Hyperbolic Functions as Logarithms - formulas

Symbolic Algebra - Online Programs
Integral Calculator - SolveMyMath.com
Wolfram Mathematica Online Integrator  - 
Mathematica
Best Graphing Program! - GRAPH (for free download)
Online JAVA Dynamic Calc Plotter -  Link

   
REVIEW   Integration
Chapter 5   Chapter Notes  -  Chapter 5

Uses of Differential Calculus & Integral Calculus  -  Notes

Geometry Formulas -  Formulas
Differentiation / Integral Formulas:  Formulas3 (2 pages)

Transcendental Functions & Derivatives - Summary

The Definite Integral -  Vocabulary
The Fundamental Theorem of Calculus -  Notes
Estimate the Area Under a Curve - NotesC , NotesBW
Estimate the Area Between Two Curves - Notes  ,  Notes
Find the Area Between 2 Curves - Worksheet

Area under a Curve -  Summation  ,  Infinite Sum
Average Value of a Function - Notes
Mean Value Theorem for Integrals - Notes
2nd Fundamental Theorem of Calculus -  Worksheet
     
Chapter 6
  Applications of the Definite Integral
    Chapter Notes  -  Chapter 6

Formulas
Geometry Formulas -  Formulas
Differentiation / Integral Formulas:  Formulas3
(2 pages)
Summary of Integral Applications - Formulas

Position & Velocity
Position vs Time (vertical) -  avi
Position vs Time (horizontal) -  avipdf GRAPH Animation  (Calc, then Animate)
Position vs Velocity - Worksheet & Notes  (4 pages)
Horizontal Motion - notes
Motion along a straight line - Worksheet

Applications of the Definite Integral - Formulas

AREA

Estimate the Area Under a Curve - NotesC , NotesBW
Estimate the Area Between Two Curves - Notes  ,  Notes
Find the Area Between 2 Curves - Worksheet


VOLUME

Finding the Volume of a Shed - by Cross-Sections  -  Worksheet
Finding Volumes by Cross-Sectional Area  -  PowerPoint
Volume of a Bullet (Paraboloid) by Disk Method - PDF slides
(10 pages)
Find the Volume of coffee in a mug by Disk Method - Outline animation
Volume of a Sphere by Disk Method -  Notes
Volume of a Cone by Disk Method - numerical
Washer Method -  animation
Cylinder/Shell Method - animation
Graph of a Torus
Some Really Awesome Animations!!!   Topic Catalog


LOGARITHMIC AND EXPONENTIAL FUNCTIONS
Exponential and Logarithmic Functions Summary - Notes: Summary
Logarithmic Functions - Notes2

What is  e ? -  NotesCalculus Proof
Exponential Functions  -  Notes2 , Notes3
Population Growth -
formula Differential Equation
     
Chapter 7   Techniques of Integration
    Chapter Notes  -  Chapter 8
Integration by Parts - Proof
Trigonometric Integrals - Formulas
Integrate  sin6(x) cos4(x)  - 3 techniques
Integrals involving x2 and a2 Formulas
Partial Fraction Decomposition - SummaryAdvanced Homework
Numerical Integration - NotesWorksheet1 Worksheet2
Errors in Numerical Integration -  Notes
Improper Integrals Notation -  Outline Graphs
Solving Systems of Linear Equations - TI-84 - Notes
Test 2 - Chapter 7 - Review
     
Chapter 8 Sequences and Infinite Series
    Convergence / Divergence of Series Tests - Outline
Power Series Expansions of Functions - Functions Functions with Summations
Absolute Convergence Tests - Notes
Test 3 - Chapter 8 - Review
     
Chapter 9    Power Series 
    Chapter Notes  -  Notes
Taylor Polynomial - P3(x)
Taylor Polynomial approximations of f(x) = e^x  -  notesgrf
Taylor Series Expansions of Functions
     Definitions
     Functions
     More functions
     Functions with Summations
 
      Functions with Summations & Taylor Formula
     
Chapter 10   Conic Sections and Polar Coordinates
    Conic Sections
The Conic Sections
       Diagram - 2 nappes of a cone
       Summary of graphs and equations
The Parabola
       4 Cases
       Rotation of Axes - Animation (grf)
The Circle
       Diagram
       Worksheet , Key
The Ellipse
       Diagram: 1 Ellipse
       Diagram: 2 Ellipses
       Rotation of Axes - Algebra  ,  Animation (grf)
The Hyperbola
       Diagram: 1 Hyperbola
       Diagram: 2 Hyperbolas
       Rotation of Axes - Algebra Animation (grf)
       Box-Asymptotes-Foci  -  Video  ,  Applet

Find an Equation of the Graphs (Conic Sections)
      
Worksheet , Large
       Homework

3-D Graphs
Intersection of a 3-D graph with a plane (level surfaces)   [ Requires  DPGraph Viewer ]
A)  Scrollbar:  A variable
B)  Scrollbar:  Z slice for level surfaces
       Cone - Intersections are the conic sections
       Sphere - Level Surfaces are circles
       Paraboloid - Level Surfaces are ellipses
       Hyperboloid - Level Surfaces are hyperbolas

YouTube Videos of CT Scans - Level Surfaces
       CT Scan: Overview - Linkmp4

       Whole Body cross-sectional images - Linkmp4
       CT Scan with Contrast, multiple scans - Linkmp4
       Head CT Scan - Linkmp4

Polar Graphs
All kinds of Polar Grids:  pdf  ,  Word
Polar Graphing
       Table of Values & graph for r = sin(Ө) -  notesAnimationgrf
       Table of Values & graph for r = sin(2Ө) -  notesAnimationgrf
Polar Forms of Lines - notes
Polar Form of the Conics - grf
Graph of a Butterfly -
grf

Test 4 - Chapters 9 & 10 - Review

   

Final Exam - Review




Misc.   History of Logarithms - Notes
Hyperbolic Functions - graphs
Hanging Cables - the Catenary Curve - Notes
Expressing Inverse Hyperbolic Functions as Logarithms - formulas