
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^31 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(x2) 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(x2)] 
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(x2)] 
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 
Multivariable
Calculus 
My
favorite calculus problem
ever  Maximize Utility as
function of buying several
goods 
Lagrange
Multipliers 
Lagrange
Multiplier Solution to Multivariable
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
Errorfree 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 
