 Day  Read  Use / 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 EpsilonDelta Definition 
Exercises  Tangent Lines, Velocity, and Other Rates
Exercises  The EpsilonDelta 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
USubstitution

Exercises  Antiderivatives and USubstitution 
 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 USubstitution

Exercises  More on USubstitution 
 24 
Area between Curves 
Exercises  Area Between Curves 
 25 
Volumes of Integration 

 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 
