Exam 1:

1.  Types of mathematical objects. 
    Intervals of real numbers and interval notation. 
    Numbers, sets, functions, domains, ranges, graphs, 
    the vertical line test, piecewise defined functions, 
    increasing and decreasing functions.  [Sec. 1.1]
2.  Linear functions, polynomials, power functions, rational
    functions, algebraic functions, trigonometric functions.  
    [Sec. 1.2]
3.  Graphs of functions. Manipulation of graphs 
    by translation, reflection, and stretching.  
    The four arithmetic operations between two functions.  
    Composition of functions.  [Sec. 1.3]
4.  Tangent lines, calculating the slope of a tangent line 
    using a limit.  Velocity as a limit.  [Sec. 1.4]
5.  Limits, intuitively. Evaluation of finite 
    and infinite limits.  One-sided limits.  
    Vertical asymptotes.  [Sec. 1.5]
6.  Calculating limits using the limit laws.  
    The squeeze theorem.  [Sec. 1.6]
7.  Continuity, the Intermediate Value Theorem.  [Sec. 1.8]


Exam 2:

1.  Geometric meaning of the derivative. Its definitions 
    using limits.  Average and instantaneous rates of change.  [Sec. 2.1]
2.  The derivative as a function.  Different notations for
    derivatives.  How can a function fail to be differentiable?  
    Differentiability implies continuity.  
    Higher derivatives.  [Sec. 2.2]
3.  Derivative of a power function.  Computation of derivatives 
    using the Constant Multiple Rule, the Sum Rule, 
    the Product Rule, the Quotient Rule.  [Sec. 2.3]  
4.  Derivatives of trigonometric functions.  [Sec. 2.4]
5.  The Chain Rule.  (Very important!) [Sec. 2.5]
6.  Implicit differentiation.  [Sec. 2.6]

Exam 3:

1.  Rates of change and related rates problems.  Examples 
    of rates of change.  Expect a rates of change 
    or a related rates word problem. [Sec. 2.7-2.8]
2.  Linear approximation and differentials.  
    Know the approximation formula and be able to use it.  
    Know the definition of differential and be able 
    to compute the differential of a function.  [Sec. 2.9]
3.  Absolute and local maxima and minima.  
    The Extreme Value Theorem.  Fermat's Theorem.  
    Critical number of a function.  
    The Closed Interval Method for computing the global 
    min or global max values of a continuous function.  [Sec. 3.1]
4.  Rolle's Theorem, and the Mean Value Theorem - statement, 
    geometric meaning, applications.  [Sec. 3.2]
5.  Effect of the first and second derivative on the graph 
    of a function.  Using them to find local maxima and minima 
    of functions.  Concavity of a function and relation with 
    the second derivative.  Critical numbers, inflection points.  
    [Sec. 3.3]
6.  Limits at infinity.  Know the basic idea and 
    the geometric meaning, and be able to calculate 
    easy examples.  Horizontal asymptotes.  
    Infinite limits at infinity.  [Sec. 3.4]
7.  Sketching the graph of a function by using calculus.
    Slant asymptotes.  [Sec. 3.5]
    
Material covered after Exam 3 (which will be on the final exam):

1.  Optimization problems.  [Sec. 3.7]
2.  Newton's method.  [Sec. 3.8]
3.  Antiderivatives.  [Sec. 3.9]