HW1
Read Section 4.3 Derivatives and the shapes of curves. Be able to
- State the Mean Value theorem (hypothesis and conclusion)
- Draw a picture of the Mean Value theorem
- Given a differentiable function on a closed interval, find a number c guaranteed by the Mean Value theorem.
Read Section 4.8 Antiderivatives. Be able to
- Find antiderivatives of basic elementary functions (Table 2)
- State the relationships between position, velocity, acceleration
- Find a particular antiderivative given a derivative and one function value.
Hand in
4.3 #1, 6, 42
4.8 #1, 5, 10, 13, 17, 22, 27, 38, 40, 43
HW2
Read Appendix F. Sigma notation. Be able to
- Expand a sum given in Sigma notation
- Given a sum, write in sigma notation in at least two ways
- Find formulas for the summation of 1, i, i2, i3
- Learn algebra of summations
- Find the limit of a summation as n-> infinity.
Read Section 5.1 Areas and distances. Be able to
- Give lower and upper estimates of an area or distance given an equation, graph, or table of values.
- Write an algebraic representation of the left and right estimates of area.
- Use a calculator to estimate areas.
- Tell whether a given estimate is an over- or underestimate of area.
- Interpret a limit of sums as an area.
Do App F #5, 8, 13, 16, 19, 21, 33, 36, 41, 44
Do 5.1 #1, 3, 8, 11, 12, 19, 20
Extra Credit(5): Use the method of Appendix F example 5 to prove the formula of the sum of the first n cubes.
HW3
Read 5.2 The definite integral.
Be able to:
- Set up and evaluate a Riemann sum.
- Define a definite integral.
- Use the definition to evaluate a definite integral.
- Evaluate definite integrals as signed areas.
- Use the 8 properties of definite integrals for their evaluation/approximation.
Do 5.2 #2, 7, 10, 15, 17, 21, 25, 32, 35, 41, 47
HW4
Read 5.3 Evaluating Definite Integrals.
Be able to:
- State the evaluation theorem.
- Distinguish between Definite and Indefinite integrals.
- Learn basic integrals on page 358.
- Interpret the evaluation theorem as the "total change theorem".
Do 5.3 #2, 7, 12, 17, 31, 37, 42, 47, 48, 49, 52, 59, 68
HW5
Read 5.4 The Fundamental Theorem of Calculus.
Be able to:
- Evaluate Area Functions
- State the Fundamental Theorem of Calculus (FTC).
- Use the FTC part 1 to find derivatives of area functions.
- Use the FTC part 2 to evaluate integrals.
- Find the average value of a function on an interval.
Do 5.4 #2, 3, 6, 9, 12, 15, 21, 24
HW6
Read 5.5 The Substitution Rule
Be able to:
- Use a substitution to transform an integral into a simpler one
- Given an integral, pick an appropriate substitution
- Find indefinite integrals by substitution
- Evaluate definite integrals using a substitution
- Evaluate even and odd functions over symmetric limits
Do 5.5 #5, 14, 15, 17, 20, 29 35, 45, 47, 48, 52, 57, 62
HW7
Read 5.6 Integration by parts
Be able to:
- Use integration by parts to find indefinite integrals
- Use integration by parts to evaluate definite integrals
- Use the LIATE mnemonic to determine which part of an integral
to differentiate
- Use chaining to evaluate integrals requiring multiple uses of
integration by parts
- Use chaining to find recursion formulas
Do 5.6 #2, 4, 7, 10, 12, 13, 18, 24, 25, 30
HW8
Read 5.7 Additional Techniques of Integration
- Integrate powers of sine, cosine, tangent, secant
- Use Reduction formulas for integration
- Make Trig substitutions in integrals
- Choose appropriate trig substitutions to make in integrals
Do 5.7 #2, 5, 12, 15, 22, 28, 34, 38, 45, 49, 54
HW9
Read 5.8 Integration using tables and computer algebra systems
- Make an appropriate substitution so that tables can be used to integrate
- Use tables and Computer Algebra systems to integrate definite integrals
- Use tables and Computer Algebra systems to integrate indefinite integrals
Do 5.8 #2, 5, 6, 10, 19, 24, 27, 32
HW10
Read 5.9 Approximate integration
- Given the graph of a function whose first and second derivative never change sign, tell whether the left, right, midpoint, and trapezoid rules will be underestimates or overestimates
- Compute left, right, midpoint, trapezoid, and Simpson rules for approximating a definite integral.
- Find upper bounds on derivatives and make error estimates for the various rules.
- Find how large n needs to be in order to guarantee a particular error bound.
Do 5.9 #2, 4, 5, 15, 18, 20, 26, 28, 29
HW11
Read 6.1 More about areas
Do 6.1 #2, 3, 6, 15, 21, 23, 27, 29, 33, 40
HW12
Read 6.2 Volumes
Do 6.2 #1, 3, 9, 16, 20, 25, 28, 31, 39, 45, 49
HW13
Read 6.3 Volume with cylindrical shells
Read 6.4 Arc Length
Do 6.3 #5, 10, 15, 20, 22, 29, 38
Do 6.4 #2, 4, 5, 12, 17
Last Update: May 3, 2010
Ronald K. Smith
Graceland University
Lamoni, IA 50140
rsmith@graceland.edu