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Secret Revealed: How to Study (and Get an A!) in Calculus (Watch This First!)
 
Precalculus Review
         Did you notice that calculus itself is pretty easy? It is the algebra and trig manipulation that kills you. Check out this video for a review.
                    Essential Topics from Precalculus that you need to be successful in calculus
                    Graphing for Calculus 101: How to make a quick and useful plot of a function without connecting any dots (excerpt from above)
                    Essential Things You Need to Remember from Trigonometry (excerpt from full video above)
         Domain and Range of a Function
                    Domain and Range: Everything You Always Wanted to Know (but were afraid to ask!)
 
Limits
          Definition of a Limit
                    Limits: Formal definition and proof using epsilon - delta syntax
          Calculate Limits
                    Explanation of pi using limit of ratio of circumference to radius
          Indeterminate Forms - L'Hopital Rule
                    Limit of indeterminate form using L'hopital's rule with both x and y variables
Derivatives
          Related Rates
                    Everything You Ever Wanted to Know About Related Rate Problems (but were afraid to ask)
                    Word problem revenue rate changing using related rates and chain rule
                    Word problem involving sand dumped using derivatives and rates
                    1991 AP: Tightrope walker - find speed of shadow on ground and on side wall of building -- related rates
                    Related rate problem man walking away from light what is speed of shadow
                    Related rate problem bucket on pulley man walking with rope find speed of bucket
                    Great word problem - minimize cost given variable labor and ops costs and fuel efficiency as fcn of speed
                    Word problem funnel water being added find dh/dt given dV/dt -- a related rates problem in effect
          Newton's Method (Newton Raphson Method)
                    Newton's Method Overview
Integrals
          How to Calculate Integrals
                    Integration Jungle Guide
          Difficult Integrals
                    Integral of 1/(x * sqrt(4x+1))
                    Integral of 1 over sqrt of a polynomial: Is it a real problem or is it BS just to torture calculus students?
                    Gnarly integral of (2x + 1) / sqrt(2 -3x - 2x^2) using inverse trig and complete the square
                    Integral with sin and cos terms in denom using algebraic tricks and trig identities
                    Integral using partial fractions and other tricks
          Fundamental Theorem Of Calculus
                    Fundamental Theorem Part 1: Is it a remnant from the last UFO to visit earth?
                    Fundamental Theorem Part II Proof
                    d/dx of integral from 0 to x of a function of f(t)dt
                    d/dx of integral from -x to x of e^-t^2 dt
                    Contrived AP calculus problem 12 + integral from a to x of f(t)/t^3 = 4 * sqrt(x) solve for f(x) and a
                    d/dx of integral from 1 to 2x of sqrt(1+t^2) dt
                    d/dx of the integral from 0 to x^3-1 of f(t) dt
          Riemann Sums
                    Tutorial: Riemann sums, finite sums, integrals part 1
                    Tutorial: Riemann sums, finite sums, integrals part 2
                    Classic AP Calculus Riemann Sum problems explained "soup to nuts"
                    Riemann sum of ln(x-2) using the average of left and right for each interval
          Area Under Curve
                    Integral to find the area of a triangle
                    Polar coordinate function r = 1 - 2sin(theta) used to calculate area using integral
                    Find area bounded by sqrt(x) + sqrt(y) = 1, y=0, x=0 Substitution in definite integral
          Volume of Revolution
                    Volume of revolution between x^2 and x^3 around y axis
                    Area and volume free response problem from the 2002 AP exam
          Surface Area of Revolution
                    Surface area of a doughnut using volume of revolution
          Curve Length
          Substitution
                    Integral of tan^n(x) sec^2(x) dx
                    Integral of 1/(x * sqrt(4x+1)) --Shrewd Manipulation Required to find Inverse Trig Solution
                    Find area bounded by sqrt(x) + sqrt(y) = 1, y=0, x=0 Substitution in definite integral
                    Integral involving sqrt(a^2 - x^2) -- trigonometric substitution
                    Integral of [ln(x-2)]
                    Integral involving substitution of lnx
                    Integral of (sinx)^3cosxdx
          Integration by Parts
                    Integration to find reduction formula for integral of tan^n(x) dx -- interesting problem
                    Integral of x^2 * sinx dx using multiple rounds of integration by parts
                    Integral of e^5x sin(3x) dx -- Integration by parts used successively
                    Integral of [ln(x-2)]
          Inverse Trig - Complete the Square First
                    Gnarly integral of (2x + 1) / sqrt(2 -3x - 2x^2) using inverse trig and complete the square
                    Integral involving sqrt(a^2 - x^2) -- trigonometric substitution
          Partial Fractions
                    Integral using partial fractions and other tricks
                    Partial Fractions: Soup to Nuts Part 4 of 4
                    Partial Fractions: Soup to Nuts Part 3 of 4
                    Partial Fractions: Soup to Nuts Part 2 of 4
                    Partial Fractions: Soup to Nuts Part 1 of 4
          Trig Functions
                    Integral of (sinx)^3cosxdx
                    Integral of tan^n(x) sec^2(x) dx
                    Integration to find reduction formula for integral of tan^n(x) dx -- interesting problem
                    Integral of e^5x sin(3x) dx -- Integration by parts used successively
          Exponential and Logarithmic Functions
                    Exponential decay problem using carbon 14 dating
                    Word problem: percentage of households with cable TV
Slope Fields and Differential Equations
                    Slope fields and differential equations: explained "soup to nuts"
                    Differential Equation solved using separation of variables -- excellent Partial Fractions Tutorial
                    Differential Equation x' - xcos(t) = cos(t) solution using separation of variables
                    Integral of 1 over sqrt of a polynomial: Is it a real problem or is it BS just to torture calculus students?
Series
                    Find total distance traveled by bouncing ball
Word Problems
          How to Analyze and Solve Word Problems
                    How to solve calculus word problems
          Word Problems involving Rates of Change
                    Classic algebra 1 word problem - Dan and Ken both mowing the lawn -- how long does it take?
          Related Rates
                    Everything You Ever Wanted to Know About Related Rate Problems (but were afraid to ask)
                    Word problem revenue rate changing using related rates and chain rule
                    Word problem involving sand dumped using derivatives and rates
          Word Problems involving Summation or Accumulation of Change
                    Word problem - calculate ice thickness as function of time given rate information
                    Exponential decay problem using carbon 14 dating
                    Word problem: percentage of households with cable TV
          Position, Velocity, and Acceleration
                    Classic AP Calculus test free response problem almost guaranteed to be on the test
                    Vector Velocity and Position -- Calculate if/when skaters intersect
          Word Problems involving Distance
                    1991 AP: Tightrope walker - find speed of shadow on ground and on side wall of building -- related rates
                    Related rate problem bucket on pulley man walking with rope find speed of bucket
                    Related rate problem man walking away from light what is speed of shadow
          Word Problems involving Cones
                    Word problem funnel water being added find dh/dt given dV/dt -- a related rates problem in effect
                    Word problem involving sand dumped using derivatives and rates
          Word Problems involving Ladders and Shadows
                    1991 AP: Tightrope walker - find speed of shadow on ground and on side wall of building -- related rates
                    Related rate problem man walking away from light what is speed of shadow
          Word Problems involving Economics, Profit, Revenue, Costs
                    Everything You Ever Wanted to Know About Cost, Revenue, Profit Problems (but were afraid to ask)
                    Great word problem - minimize cost given variable labor and ops costs and fuel efficiency as fcn of speed
                    Word problem revenue rate changing using related rates and chain rule
AP Calculus Test Classic Problems
                    d/dx of integral from -x to x of e^-t^2 dt
                    2005 AP Calculus AB Free Response - Rod heated from one end, find a number of attributes
                    Contrived AP calculus problem 12 + integral from a to x of f(t)/t^3 = 4 * sqrt(x) solve for f(x) and a
                    Area and volume free response problem from the 2002 AP exam
                    Classic AP Calculus test free response problem almost guaranteed to be on the test
                    1991 AP: Tightrope walker - find speed of shadow on ground and on side wall of building -- related rates
Polar Coordinates
                    Polar coordinate function r = 1 - 2sin(theta) used to calculate area using integral
Multi-variable Calculus
                    My favorite calculus problem ever - Maximize Utility as function of buying several goods
Lagrange Multipliers
                    Lagrange Multiplier Solution to Multi-variable Utility Maximization Problem
Gradient and Partial Derivatives
                    My favorite calculus problem ever - Maximize Utility as function of buying several goods
                   Great Problem Involving Directional Derivative and Gradient -- Do YOU know the true meaning??
 
Complex Variables
                    Euler's Formula e^(i theta) = sin(theta) + i cos(theta) -- Where did it come from? What is the Beauty in this Equation?
 
Chemistry Videos
Nomenclature (Naming of Molecules)
          How to Memorize all of the Element Names and Functional Group Names, Formulas, and Valences
                    How to Memorize in 30 minutes or Less and Have a Nomenclature Error-free year!
 
Equations and Reactions
          How to Calculate Limiting Reagent, Yield, and Percent Yield
                    Calculate Limiting Reagent, Yield, and Percent Yield from a Chemical Equation
 
Dimensional Analysis
          Using Dimensional Analysis to Solve Any Kind of Unit Conversion Problem
                    Dimensional Analysis Soup to Nuts
 
Rocket Science Videos
Rocket Science 301: Space Shuttle Challenger: The Untold Story, Fundamental Design Considerations
Rocket Science 201: Futuristic Space Transportation: Space Elevator, Natl Aerospace Plane, Scramjet
Rocket Science 201: Launch Operations, Early Orbit Operations, Footage of Apollo 11 Launch
Rocket Science 201: Types of Orbits: Low Earth, Geostationary, Sun synchronous, Hohmann, Ground tracks
Rocket Science 201: Orbital Mechanics -- What does it mean to be in orbit and how do you move around
Rocket Science 101: Engineering Part 2: Max Q, How to Get to Orbit, Weightlessness
Rocket Science 101: Engineering and Design of a Rocket
Rocket Science 101: Rocket Fuels, Proper Use of Physical Terms and Units
Rocket Science 101: Physics of Rocketry: Newton's Laws, Propulsion
Rocket Science 101: History of Rocketry Part 2: Goddard, Von Braun, Space Race
Rocket Science 101: History of Rocketry Part 1: Greeks, Chinese, Froissart, Spencer, Tsiolkovsky
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