DayReadUse / Do
1
Precalculus Review
   Are You Ready for Calculus?

   Notes on Transcendental Functions
   Graphs of Functions You Should Know

   Exercises - Review of Some Ideas from Precalculus
2
Introduction to Calculus
   Tangent Lines, Velocity, and Other Rates
   An Intuitive Way to Think About Limits
   The Epsilon Delta Definition of a Limit
   Examples of Using the Epsilon-Delta Definition
   Exercises - Tangent Lines, Velocity, and Other Rates
   Exercises - The Epsilon-Delta Def. of a Limit (and Review)
3
Limits
   Proof of the Limit of a Sum Law
   The Limit Laws

   Infinite Limits
   Limits at Infinity
   Exercises - Limits

4
More Limits
   Comparisons of Functions
   Limits of Compositions
   Exercises - Comparisons of Functions (and Review)
   Exercises - Limits of Compositions (and Review)

   More Practice - Limit Laws
   More Practice - Infinite Limits and Limits at Infinity
   More Practice - Limits
5
Continuity
   Continuous Functions and Discontinuities
   Exercises - Continuous Functions (and Review)

   More Practice - Continuity
6
The Intermediate Value Theorem
   The Intermediate Value Theorem (IVT)
   Proof of the IVT (for the curious)
   Exercises - Intermediate Value Theorem (and Review)

   More Practice - Intermediate Value Theorem
7
Derivatives and Differentiability
   The Definition of the Derivative
   Differentiability
   Acceleration, Velocity, and Speed
   Exercises - Definition of Derivative (and Review)
   Exercises - Differentiability

   More Practice - Definition of Derivative
   More Practice - Differentiability and Continuity
8
Induction
   Summations and Sigma Notation
   Two Important Properties of Sums (Linearity)
   Induction
   More Exercises - Induction and Sums
9
Basic Rules of Differentiation
   Basic Derivative Rules
   Proof Derivatives of Constant Functions are Zero
   The Binomial Theorem
   Proof of the Power Rule (for positive integer powers)
   Proof of the Derivative of the Sine Function
   Proof of the Sum and Difference Rules
   Proof of the Constant Multiple Rule
   Proof of the Product Rule
   Proof of the Quotient Rule
   Exercises - Basic Derivative Rules (and Review)
   Exercises - Derivatives Involving Trig (and Review)
10
Chain Rule
   Proof of the Chain Rule (for Compositions)
   Exercises - The Chain Rule (and Review)

   More Practice: The Chain Rule
12
Implicit Differentiation
   Implicit Differentiation
   The Power Rule for Derivatives (for rational powers)
   Exercises - Implicit Differentiation (and Review)

   More Practice - Implicit Differentiation
11
More Derivative Rules
   Inverse Trigonometric Functions
   Derivatives of Inverse Trigonometric Functions

   
A Natural Question
   Logarithmic Differentiation
   Exercises - More Derivative Rules

   Exercises - Higher Order Derivatives
   Exercises - Logarithmic Differentiation
   Exercises - Finding Derivatives (Mixed Techniques)
12
Related Rates    Exercises - Related Rates

   More Practice - Related Rates
13
Differentials and Approximation    Exercises - Differentials and Approximation
14
Extrema
   Extrema of Functions
   Proof of the Boundedness Theorem (for the curious)
   Proof of the Extreme Value Theorem (for the curious)
   Proof of Fermat's Theorem
   Exercises - Extrema of Functions
15
Mean Value Theorem
   Proof of Rolle's Theorem
   Proof of the Mean Value Theorem
   Proof that Functions with Zero Derivatives are Constant
   Exercises - The Mean Value Theorem

   More Practice - The Mean Value Theorem
16
Graphing
   The First Derivative Test
   The Second Derivative Test
   Concavity
   The Graphing Handout

   Exercises - Graphing Functions
       (Note, this set of exercises duplicates many of the problems
         in the Graphing Handout - it's a work in progress)
17
Optimization    Exercises - Optimization
19
Antiderivatives
U-Substitution
   Exercises - Antiderivatives and U-Substitution
20
Separable Differential Equations    Exercises - Separable Differential Equations
21
Riemann Sums and the Definite Integral
   Summation Techniques
   Approximating the Area Under a Function
   Riemann Sums and the Definite Integral
   Finding Definite Integrals Directly from Riemann Sums
   Exercises - Summation Techniques
   Exercises - Riemann Sums
21
The Average Value of a Function
The Mean Value Theorem for Integrals
   Exercises - Mean Value Theorem for Integrals
22
The Fundamental Theorem of Calculus
   Evaluating Definite Integrals with Antiderivatives
   Properties of the Definite Integral
   The Derivative of a Definite Integral Function
   Exercises - The Fundamental Theorem of Calculus (Part I)
   Exercises - Fundamental Theorem of Calculus (Part II)
23
More on U-Substitution    Exercises - More on U-Substitution
26
The below sections are "in progress" or coming sooon    
24
Area between Curves    Exercises - Area Between Curves
25
Finding Volumes with Definite Integrals    
26
Integration by Parts    
27
Approximate Integration    
28
Improper Integrals    
29
Application: Probability Distributions & Functions of Random Variables    
30
Taylor Polynomials    
31
Sequences & Series    
32
Power Series    
33
Taylor Series    
34
3D & Higher Dimensional Spaces    
35
Multivariable Functions    
36
Partial Derivatives    
37
Linearizations    
38
Vectors    
39
The Dot Product    
40
The Normal Equation of a Plane    
41
The Gradient Vector    
42
The Chain Rule    
43
Optimization    
44
Lagrange Multipliers    
45
Integrals over General Regions    
46
Application: Joint Density Functions    
47
Triple Integrals