1.1 Associate the proper limit symbolism with a given graphical situation.

1.2 Calculate limits of certain elementary functions.

1.3 Define the concept of limit for real-valued functions of one real variable.

1.4 Prove that a given limit statement is valid.

1.5 Define continuity.

1.6 Compute limits involving the trigonometric functions.

2.1 Define the derivative for real-valued functions of one real variable.

2.2 Calculate the derivative of certain elementary functions directly from the definition.

2.3 Calculate derivatives using the appropriate rules for sums, products, etc.

2.4 State the connection between differentiability and continuity.

2.5 Calculate higher order derivatives.

2.6 Compute derivatives by the method of implicit differentiation.

2.7 Use differentials to approximate values of a function.

3.1 Write models for real-world problems.

3.2 Set up and solve related rate problems.

3.3 Set up and solve applied min/max problems.

3.4 Use the first and second derivative to graph certain elementary functions.

3.5 State the geometrical significance of the first and second derivatives.

3.6 State the physical significance for the first and second derivatives for rectilinear motion.

3.7 State and apply the Mean Value Theorem for derivatives.

4.1 Calculate Riemann sums in simple cases.

4.2 Define the concept of the definite integral for real-valued functions of one real variable.

4.3 Calculate the definite integral in simple cases directly from the definition.

4.4 Calculate indefinite integrals for elementary functions.

4.5 State the First and Second Fundamental theorems of Calculus.

4.6 Use indefinite integrals to calculate definite integrals.

4.7 State the Mean Value Theorem for integrals.

5.1 Calculate the area between two curves.

5.2 Calculate the volume of a region given its cross sections.

5.3 Calculate the volume of a surface of revolution using the washer method.

5.4 Calculate the volume of a surface of revolution using the shell method.

5.5 Compute the arc length along a curve.

5.6 Compute the surface area of a surface of revolution.

6.1 Define the logarithm function in the natural base e.

6.2 Demonstrate the basic properties of logarithms using the definition in 6.1.

6.3 Define logarithms in bases other than e.

6.4 Calculate derivatives of the logarithmic functions.

6.5 Define the exponential function in a given base.

6.6 Calculate derivatives of the exponential functions.

6.7 Define the hyperbolic trigonometric functions.

6.8 Calculate derivatives of the hyperbolic functions.

6.9 State the geometrical interpretation of the hyperbolic functions.