CHAPTER 6: At the end of CHAPTER 6 THE STUDENT WILL be able to:
Define a region between two curves in set notation.
Find the area of a region between two curves.
Find the volume of a region of known cross sections.
Find volumes of solids of revolution by using the disc method.
Find volumes of solids of revolution by using the shell method.
Determine the work done by a variable force using the definite integral.
Determine the work done by a force over a variable distance.
Use the definite integral to calculate the force exerted by a fluid against a vertical wall.
Find moments with respect to the x- and y-axes for a uniform lamina of area in a plane region.
Calculate centers of mass and centroids of plane regions.
Use the the first theorem of Pappus to find the volume of revolution using the centroid and area. CHAPTER 6: At the end of CHAPTER 6 THE STUDENT WILL be able to:
Define a region between two curves in set notation.
Find the area of a region between two curves.
Find the volume of a region of known cross sections.
Find volumes of solids of revolution by using the disc method.
Find volumes of solids of revolution by using the shell method.
Determine the work done by a variable force using the definite integral.
Determine the work done by a force over a variable distance.
Use the definite integral to calculate the force exerted by a fluid against a vertical wall.
Find moments with respect to the x- and y-axes for a uniform lamina of area in a plane region.
Calculate centers of mass and centroids of plane regions.
Use the the first theorem of Pappus to find the volume of revolution using the centroid and area. At the end of CHAPTER 6 THE STUDENT WILL be able to:
Define a region between two curves in set notation.
Find the area of a region between two curves.
Find the volume of a region of known cross sections.
Find volumes of solids of revolution by using the disc method.
Find volumes of solids of revolution by using the shell method.
Determine the work done by a variable force using the definite integral.
Determine the work done by a force over a variable distance.
Use the definite integral to calculate the force exerted by a fluid against a vertical wall.
Find moments with respect to the x- and y-axes for a uniform lamina of area in a plane region.
Calculate centers of mass and centroids of plane regions.
Use the the first theorem of Pappus to find the volume of revolution using the centroid and area.

CHAPTER 7: At the end of CHAPTER 7 THE STUDENT WILL be able to:
Integrate using the fundamental algebraic and transcendental functions integral formulas.
Integrate by substitution when appropriate.
Integrate using integration by parts.
Verify and use some reduction formulas.
Integrate powers and products of trigonometric functions.
Use trigonometric substitution to evaluate integrals involving square roots of functions:
                       a² - u², a² + u², and u² - a²        
Integrate by completing the square when appropriate.
Integrate rational functions using partial fractions when appropriate.
Integrate using integration tables.
Integrate by using substitutions to convert some rational functions of sine and cosine into
     rational functions of the variable u.
Recognize indeterminate forms and rearrange some of them as necessary.
Apply L'Hopital's Rule when appropriate.
Use limits to determine convergence or divergence of improper integrals.
Determine improper integrals with an infinite discontinuity. CHAPTER 7: At the end of CHAPTER 7 THE STUDENT WILL be able to:
Integrate using the fundamental algebraic and transcendental functions integral formulas.
Integrate by substitution when appropriate.
Integrate using integration by parts.
Verify and use some reduction formulas.
Integrate powers and products of trigonometric functions.
Use trigonometric substitution to evaluate integrals involving square roots of functions:
                       a² - u², a² + u², and u² - a²        
Integrate by completing the square when appropriate.
Integrate rational functions using partial fractions when appropriate.
Integrate using integration tables.
Integrate by using substitutions to convert some rational functions of sine and cosine into
     rational functions of the variable u.
Recognize indeterminate forms and rearrange some of them as necessary.
Apply L'Hopital's Rule when appropriate.
Use limits to determine convergence or divergence of improper integrals.
Determine improper integrals with an infinite discontinuity. At the end of CHAPTER 7 THE STUDENT WILL be able to:
Integrate using the fundamental algebraic and transcendental functions integral formulas.
Integrate by substitution when appropriate.
Integrate using integration by parts.
Verify and use some reduction formulas.
Integrate powers and products of trigonometric functions.
Use trigonometric substitution to evaluate integrals involving square roots of functions:
                       a² - u

CHAPTER : :    At the end of CHAPTER 8a THE STUDENT WILL be able to:

Define a sequence {a_n}  
Write several terms given the general term.
Define the limit of a sequence.
Use the properites of limits of sequences to determine convergence.
Use L'Hopital's Rule and the squeeze theorem to determine convergence.
Define factorial and perform algebraic operations using it.
Define the nth, or general, term of a sequence.
Define monotonic sequences and bounded sequences.
Define infinite series as a sum of terms of sequence.
Define convergent and divergent series.
Define geometric series and determine its sum if it converges.
Write a geometric series for a repeating decimal.
Know the linearity properties of infinite series.
Use the nth term test to determine convergence or divergence.
Apply the integral test to infinite series.
Define the p-series and determine convergence or divergent.
Make a list of series ass they are proved as convergent or divergent.
Define the direct comparison test and use it to determine test series against known series.
Define and use the Limit Comparison Test.
Define alternating series and apply conditions for convergence to certain test series.
Find the remainder after n-terms of an alternating series.
Approximate the sum of an alternating series.
Define absolute and conditional convergence and determine when each applies.
Know and apply the conditions of the ratio test to determine convergence or divergence of series,
      or when it fails.
Know and apply the root test to determine convergence or divergence of series and when it applies.
Use the summary of appropriate tests for convergence.

CHAPTER 8b:     At the end of CHAPTER 8 THE STUDENT WILL be able to:

Find a polynomial function P(x) to approximate a function f(x) near a point x = c where P(c) = f(c).
Know and use the Taylor/Maclaurin polynomials P_n.f(x)
Estimate the remainder R_n associated with the Taylor polynomial.
Approximate a functional value to desired accuracy.
Define Power Series centered at x = 0 and x = c.
Determine the radius of convergence for power series.
Find the interval of convergence for a power series.
Find the derivative and integral of convergent power series.
Find the interval of convergence for f(x), fN(x) and I f(x)dx.
Find a geometric power series centered at x = 0 or x = c.
Apply the linearity, power and product properties to power series.
Find power series by integration.
Approximate p with a series.
Define and use Taylor and Maclaurin Series.
Form Taylor and Maclaurin series for given functions and test for convergence.
Find a Maclaurin series for a composite function.
Use a Maclaurin expansion to find a binomial series.
Derive new power series from a given series.
Use power series to approximate a definite integral.

CHAPTER 9 :  At the end of CHAPTER 9 THE STUDENT WILL be able to:

Match standard equations for parabolas, hyperbolas, or ellipses to the given graphs. 
Sketch the graph of parabola, hyperbolas, or ellipses from the standard equation.
Find the equation of a parabola, hyperbola, or ellipse from specified data. 
Find an equation of the tangent line and normal lines to a parabola, hyperbola, or ellipse at a specified point. 
Find the arc length of a specified portion of a parabola, hyperbola, or ellipse. 
Determine where y' = 0 or y' = ¥ to locate vertices from the general equation of a conic. 
Find the area of the region bounded by the ellipse. 
Find the volume and surface area of the solid generated by revolving the region bounded by an q)  (including conics).on paper, graphing calculator and computer.
Use integration to find the area of a region bounded by polar graphs.