*Adapted from http://www.maa.org/features/readbook.html

When students read the text before class, the fundamental nature of class meetings is changed. The students arrive familiar with basic concepts and definitions, providing more class time to address the major ideas and subtleties of the mathematics. In addition, the instructor is no longer viewed as the sole source of content for the course, and this encourages greater independence, and more lively interactions, among students.  One of the challenges to learning mathematics is that understanding is often built in stages, and one's perspective deepens upon revisiting concepts a second, third, nth time. If class time may be spent on students' second exposure to basic terminology and elementary examples, then the class is able to get to deeper mathematics more quickly and in more detail. Indeed, this moves a class session from simply introductory lectures to a time when elementary ideas are clarified (as necessary) and expanded upon.

The Details of the Assignments

The reading assignments for the entire year are below. This frees class time from announcing or distributing the assignments and makes the assignments conveniently available to students outside of class. Each posting lists the specific section(s) to read, which parts should be emphasized, and which can be skipped, if any. There are also several basic questions that the student should be able to answer after completing the reading. The questions serve to focus the students' reading and give them feedback on their level of comprehension; students email their responses to me (submit@smithmath.com) before the following class meeting*. This gives me feedback on the level of the students' understanding before class and allows me to make adjustments as necessary.  These responses are graded.

Suggested Method for Completing Assignments

  1. Read the calendar to establish what reading needs to be done for the next class
  2. Read the questions that correspond to the section(s) (do not try to answer)
  3. Do assigned reading
  4. Re-read and answer questions

 

*The subject line for emails should be “section ______” only.  If your email is not configured with your real name, please include it at the beginning of the body.

Section P.1 – Graphs and Models

To read:  All.  Question 3 is IMPORTANT!

Reading Questions:

  1. Without graphing, what kind of symmetry does the graph of y=2x3 + 3x2 + x have, how do you know?
  2. How is a point that lies on the graph of a function referred to (what is it called)? Why? What is the set of all of these?
  3. What two branches of mathematics are joined in calculus?  What multiple perspectives are mentioned in increasing understanding of core concepts?  How are the previous two questions related?
  4. In your own words, what is a mathematical model and how can it be used?

Section P.2 – Linear Models and Rates of Change

To read: All.  Be sure to understand the various views of slope.

Reading Questions:

  1. What is the definition of slope?  For what type of line does the definition not hold true?
  2. What symbol means “change” and how is it read?
  3. What are the names of the 3 different forms of equations of lines?  What are the forms, be sure to define all variables?
  4. After example 2, it is mentioned that an average rate of change is always calculated over an interval, explain why.

Section P.3 – Functions and Their Graphs

To read: All

Reading Questions: Let f(x)=x2

  1. What is f(7)? What is f(x-1)?
  2. How is the graph of y=f(x)+3 =x2+3 related to the graph of y=f(x)? Why?
  3. How is the graph of y=f(x+3) =(x+3)2 related to the graph of y=f(x)? Why?
  4. In your own word explain the difference between implicit and explicit forms.

Section P.4 – Fitting Models to Data

To read: All

Reading Questions:

  1. Using a TI-8x calculator, what is the algorithm (step-by-step method) to find a mathematical model using data (you may need to do outside reading, i.e. user’s manual)?
  2. Using the model in example 3, predict the amount of daylight on February 10.
  3. What part of the model in example 1 supports the conclusion given?  Explain.

Section 1.1 – A Preview of Calculus

To read: All

Reading Questions:

  1. What is calculus?  How is it different from precalculus?
  2. Compare and contrast a tangent line and a secant line (be thorough) 

Section 1.2 – Finding Limits Graphically and Numerically

To read: All

Reading Questions:

  1. Explain in your own words how one can use a table of values to find a limit.
  2. Explain in your own words how one can use a graph to find a limit.
  3. Why is using a table of values to find a limit referred to as finding the limit numerically?
  4. In what 3 cases do limits fail to exist? Explain the cases.
  5. Explain the ε-δ definition of limit in your own words (keep it simple).  How does it related to finding limits graphically and/or numerically?

Section 1.3 – Evaluating Limits Analytically

To read: All; be sure to understand example 8

Reading Questions:

  1. Many limits can be found with direct substitution, in general, when do “problems” occur (what type functions cause these “problems,” what are the “problems” called)?
  2. What is the limit as x approaches zero of the ratio of sine of x to x?
  3. Give an example of two functions that agree at all but one point.
  4. In your own words, explain the Squeeze Theorem.

Section 1.4 – Continuity and One-Sided Limits

To read: All.  Be sure to understand the Intermediate Value Theorem

Reading Questions:

  1. In your own words, compare and contrast removable discontinuities and non-removable discontinuities.
  2. The definition of continuity discusses open intervals, how can one extend the definition of continuity to closed intervals?
  3. Explain the Intermediate Value Theorem in your own words.
  4. If the functions f and g are continuous for all real x, is f+g always continuous for all real x.  Is f/g always continuous for all real x? If either is not continuous, give an example to verify your conclusion.

Section 1.5 – Infinite Limits

To read:  All

Reading Questions:

  1. What is an infinite limit, how is it related to an asymptote of a graph?
  2. Does the graph of every rational function have a vertical asymptote?  Explain.

Section 2.1 – The Derivative and the Tangent Line Problem

To read: All.

Reading Questions:

  1. Why is finding the slope of a tangent line trickier than finding the slope of a secant line?  
  2. What is the process of finding the derivative of a function called?
  3. What are the four common notations used to denote the derivative of y=f(x) mentioned in the text?
  4. For a function f, what does the difference quotient (f(a+h) - f(a))/ h measure?
  5. How are differentiability and continuity related?

Section 2.2 – Basic Differentiation Rules and Rates of Change

To read: All.

Reading Questions:

  1. What is the derivative of f(x)=x3?
  2. Let f(x)=x1/3 (the cube root of x). Use the derivative of y=f(x) to explain why f'(x) does not exist at x=0.
  3. What is said in the text to be the first step in many differentiation problems?
  4. Using Theorem 2.6 and the constant multiple rule (remember -1 is a constant), find the derivative of –sin x, then find the derivative of that function.  What do you notice?

Section 2.3 – Product and Quotient Rules and Higher-Order Derivatives

To read: All.  Know the two rules, as well as the notations on p.125, COLD.

Reading Questions:

  1. What is the product rule? Create (not copy) and work one problem using the product rule.
  2. Regarding example 7, explain the math that allows one to go from the quotient in step 3 to –kx^(-k-1) in step 4
  3. When, according to the text, can a quotient be differentiated with the constant multiple rule as opposed to the quotient rule?
  4. The text alludes that one is not necessarily “done” after differentiating.  What comes next?  What characterizes a “final” answer?  

Section 2.4 – The Chain Rule

To read: All.

Reading Questions:

  1. Explain in your own words what the chain rule is.
  2. When dos one need the chain rule?

Section 2.5 – Implicit Differentiation

To read: All.

Reading Questions:

  1. In your own words, state the guidelines or implicit differentiation.
  2. Explain the connection between the chain rule and implicit differentiation.
  3. What mode in your calculator can prove useful in graphing the functions in this section?

Section 2.6 – Related Rates

To read: All.

Reading Questions:

  1. In your own words, what is meant by “related rates”
  2. In your own words, state the guidelines for solving related-rate problems
  3. Explain the connection of the chain rule, implicit differentiation and related-rate problems

Section 3.1 – Extrema on an Interval

To read: All.

Reading Questions:

  1. What are extrema?
  2. What is the extreme value theorem, why does it make sense?
  3. What is the value of the derivative of a function at that functions extrema?  

Section 3.2 – Rolle’s Theorem and the Mean Value Theorem

To read: All.

Reading Questions:

  1. Explain Rolle’s Theorem in your own words.
  2. Explain the Mean Value Theorem in your own words.
  3. Can you find a function f such that f(-2) = -2, f(2) = 6 and f’(x)<1 or all x?  Why or why not?

Section 3.3 – Increasing and Decreasing Functions and the First Derivative Test

To read: All.

Reading Questions:

  1. What, in your own words, is the First Derivative Test?  How does one interpret the results of the test?
  2. A differentiable function f has one critical number at x=5.  Identify the relative extrema of f at the critical number if f’(4) = -2.5 and f’(6) = 3 (is it a MAX or MIN).  Explain how you know.

Section 3.4 – Concavity and the Second Derivative Test

To read: All.

Reading Questions:

  1. What is concavity?
  2. What is the second derivative test and how should one interpret the results?
  3. Compare and contrast points of inflection with extrema

Section 3.5 – Limits at Infinity

To read: All.

Reading Questions:

  1. What, in your own words, is a limit at infinity? How does it compare/contrast to an infinite limit (section 1.5)?
  2. Explain the connection between horizontal asymptotes and limits at infinity.
  3. How did you find horizontal asymptotes in precalculus and how does it compare to this method?

Section 3.6 – A Summary of Curve Sketching

To read: All.

Reading Questions:

  1. When sketching a graph by hand, how many concepts does the text state should be considered?  What are they?
  2. Suppose f(0) = 3 and 2 ≤ f’(x) ≤ 4 for all x in the interval [-5, 5].  Determine the greatest and least possible value of f(2).  How do you know?

Section 3.7 – Optimization Problems

To read: All.

Reading Questions:

  1. What is a primary equation?  What are secondary equations?  How are they used to find optimal values?
  2. A shampoo bottle is a right circular cylinder.  Because the surface are of the bottle does not change when it is squeezed, is it true that the volume remains the same?  Explain.

Section 3.9 – Differentials

To read: All.  Pay close attention to example 7.

Reading Questions:

  1. Often differentiable functions are described as “locally linear.”  What do you think that means (its okay to look it up)?  How could it be related to the text’s concept of the linear approximation of a function?
  2. Why would a tangent line approximation, as opposed to an exact value, be useful?
  3. Compare and contrast the derivative of a function and the differential (keep it simple).
  4. When using differentials, what is meant by the terms propagated error, relative error, and percent error?

Section 4.1 – Antiderivatives and Indefinite Integration

To read: All.  Study the Basic Integration Rules on p.250.

Reading Questions:

  1. How are the terms ‘indefinite integral’ and ‘antiderivative’ related?
  2. How many antiderivatives does 2x have? Why?
  3. How are integration and differentiation related?
  4. What does the text (correctly) say is one of the most important steps in integration?

Section 4.2 – Area

To read: All.  Know the summation formulas in Theorem 4.2

Reading Questions:

  1. In your own words, how is approximating the area of a plane region using rectangles related to Archimedes’ method of exhaustion?
  2. In your own words, how is the Squeeze Theorem related to the definition of the area of a region in the plane.

Section 4.3 – Riemann Sums and Definite Integrals

To read: All.

Reading Questions:

  1. Compare and contrast the ‘Definition of the Area of Region in the Plane’ (p.265) with the ‘Definition of a Riemann Sum’. Be careful, notice what is ‘missing’ from the Riemann Sum.  What impact does that element have?
  2. Compare and contrast the ‘Definition of the Area of Region in the Plane’ (p.265) with the ‘Definition of a Definite Integral’.
  3. Explain the idea of a Riemann sum in your own words.   

Section 4.4 – The Fundamental Theorem of Calculus

To read: All, but you can skip the proof of the FTC in the section. We'll look at a different approach in class.

Reading Questions:

Find the area between the x-axis and the graph of f(x)=x3 + 4 from x=0 to x=3.

Does every continuous function have an antiderivative? Why or why not?

Explain the Mean Value Theorem for Integrals in your own words.

Section 4.5 – Integration by Substitution

To read:

Reading Questions:

  1. Explain the difference between a definite integral and an indefinite integral.
  2. What are the five steps in the process of substitution?
  3. Substitution attempts to undo one of the techniques of differentiation. Which one is it?

Section 4.6 – Numerical Integration

To read: Explanation of the Trapezoidal Rule, example 1, ‘technology’ note and comparison notes of Midpoint and Trapezoidal Rules.  Omit Simpson’s Rule and Error Analysis.

Reading Questions:

Why would we want to approximate an integral using the Trapezoidal Rule?

 A function f exists such that f” < 0 on the interval [a, b].  Is an approximation using the Trapezoidal Rule grater than or less than the definite integral of f on the interval [a, b]?  Explain your reasoning.

Section 5.1 – The Natural Logarithmic Function: Differentiation

To read: All.

Reading Questions:

1.      Define the base for the natural logarithmic functions.

2.      Why is the derivative of y = ln u the same as the derivative of y = ln |u|?

3.      Explain how the logarithmic properties in Theorem 5.2 are related to exponential properties

Section 5.2 – The Natural Logarithmic Function: Integration

To read: All.

Reading Questions:

Generally describe, in your own words, the functions that can be integrated using the natural logarithmic integration rule.

Explain why we now can find integration formulas for the four “other” trigonometric functions.  Why didn’t we need the natural logarithmic integration rule for sin x and cos x?

Section 5.3 – Inverse Functions

To read: All.

Reading Questions:

1.      Why do you think we are studying inverse functions now?

2.      Explain, in your own words, the meanings of “one-to-one” and “strictly monotonic”.

3.      Describe the relationship between the graph of a function and the graph of its inverse function. How does that impact the relationship of their derivatives?

Section 5.4 – Exponential Functions: Differentiation and Integration

To read: All.

Reading Questions:

1.      Describe the relationship between the graphs of f(x)= ln x and g(x) = ex.

2.      What is so fascinating about y = ex in regard to calculus?  In your own words explain that property.

3.      Why does the answer to #2 (above) make integration of y = ex easier?

Section 5.5 – Bases Other Than e and Applications

To read: All.

Reading Questions:

  1. When considering derivatives, why does y = 2x not “work” the same way as y = ex, or does it? Explain.
  2. Explain how limits can be used to relate the compound interest formula with the continuous compounding interest formula

Section 5.6 – Inverse Trigonometric Functions: Differentiation

To read: All.

Reading Questions:

  1. What is the domain of the function arccos(x)? Why?
  2. Why do you think we are studying the inverse trig functions now? Be clear!
  3. Explain how to graph y = arccot (x) on a graphing utility that does not have the arccotangent function.

Section 5.7 – Inverse Trigonometric Functions: Integration

To read:  All.

Reading Questions:

  1. How is this integration similar to integration involving logarithms?  How is it different?
  2. One might claim that the key to this section is merely recognition and application of the appropriate formula. In your own words, what tricks for recognition might one use to discern which formula to apply?  Use problems from the section as examples.

Section 6.1 – Slope Fields and Euler’s Method

To read: All.

Be sure to understand:  Example 2

Reading Questions:

1.      In your own words, explain the difference between a general solution and a particular solution of a differential equation.

2.      Describe how to use Euler’s method to approximate the particular solution of a differential equation.

3.      In your own words, what is a slope field?

Section 6.2 – Differential Equations: Growth and Decay

To read: All

Be sure to understand: Example 1.  

Reading Questions:

  1. In your own words, explain what the C and k represent in the exponential growth and decay model.
  2. Give the differential equation that models exponential growth and decay and translate it into words.

Section 6.3 – Separation of Variables and the Logistic Equation

To read:  All except section about orthogonal trajectories (example 8).

Be sure to understand: What the logistic equation is.

Reading Questions:

  1. In your own words, describe how to recognize and solve differential equations that can be solved by separation of variables.
  2. State the test for determining if a differential equation is homogenous.  Give and example and include a definition of homogenous is this context.

Section 7.1 – Area of a Region Between Two Curves

To read: All

Be sure to understand: The section “Integration as an Accumulation Process”

Reading Questions:

  1. Let f(x)=sin(x)+10 and g(x)=2x-5. Set up the integral that determines the area of the region bounded by y=f(x) and y=g(x) between x=-1 and x=3.
  2. The area of the region bounded by the graphs of y = x3 and y = x cannot be found by the single integral .  Explain why this is so.  Use symmetry to write a single integral that does represent the area.

Section 7.2 – Volume: The Disk Method

To read: All

Be sure to understand: What solids of revolution are and the formula used to find their volume.

Reading Questions:

  1. Let R be the rectangle formed by the x-axis, the y-axis, and the lines y=1 and x=3. What is the shape of the solid formed when R is rotated about the x-axis?
  2. Let T be the triangle formed by the lines y=x, x=1 and the x-axis. What is the shape of the solid formed when T is rotated about the x-axis?
  3. What is the difference between the disk method and the washer method?
  4. Compare and contrast the processes of finding the volume of solids of revolution and solids with know cross sections.

Section 7.4 – Arc Length and Surfaces of Revolution

To read: All

Be sure to understand:

Reading Questions:

  1. What precalculus formula and representative element are used to develop the integration formula for arc length?
  2. How are arc length and surface area related?
  3. What is a frustum and what does it have to do with surface area?

Section 8.1 – Basic Integration Rules

To read: All

Be sure to understand: Gray box entitled “Procedures for Fitting Integrands to Basic Rules”

Reading Questions:

  1. Explain why the antiderivative y1 = sec2 (x) + C1 is equivalent to the antiderivative y2 = tan2 (x) + C
  2. Consider the integrals ,, and.  Which of these cannot be evaluated using the 20 basic integration rules? Explain why not.

Section 8.2 – Integration by Parts

To read: All

Be sure to understand: Theorem 8.1

Reading Questions:

  1. Integration by parts attempts to undo one of the techniques of differentiation. Which one is it?
  2. Each integral can be evaluated using u-substitution or integration by parts. Which technique would you use in each case? Do not evaluate the integral, but explain your choice.
    2.  
  1. In your own words, state the guidelines for integration by parts.

Section 8.3 – Trigonometric Integrals

To read: All

Be sure to understand:  Grey boxes and Wallis’s formulas.  Example 8 is tricky; be careful.

Reading Questions:

1.      In your own words, describe how you would integrate  for each condition.

a.     m is positive and odd

b.     n is positive and odd

c.     m and n are both positive and even

2.      In your own words, describe how you would integrate  for each condition.

a.     m is positive and even

b.     n is positive and odd

c.     n is positive and even, and there are no secant factors.

d.     m is positive and even, and there are no tangent factors.

Section 8.5 – Partial Fractions

To read: All

Be sure to understand: The blue box and the gray box.

Reading Questions:

  1. Describe the decomposition of the proper rational function N(x)/D(x) if D(x) = (px + q)m.  Explain why you chose that method.
  2. Describe the decomposition of the proper rational function N(x)/D(x) if D(x) = (ax2 + bx + c)n.  Where ax2 + bx + c is irreducible.  Explain why you chose that method.
  3. Why is partial fraction decomposition useful?

Section 8.7 – Indeterminate Forms and L'Hôpital's Rule

To read: All

Be sure to understand: Theorem 8.4.

Reading Questions:

  1. List six different indeterminate forms.
  2. State L'Hôpital's Rule.
  3. Find the differential functions f and g such that  and.  Explain how you obtained your answers.

Section 8.8 – Improper Integrals

To read: All

Be sure to understand: Bold vocabulary terms, blue boxes and example 9.

Reading Questions:

  1. How many different types of improper integrals exist?  Describe the different types.
  2. Define the terms converges and diverges when working with improper integrals.
  3. Consider the integral.  To determine the convergence or divergence of the integral, how many improper integrals must be analyzed?  What must be true of each of these integrals if the given integral converges?

Section 9.1 – Sequences

To read: All

Be sure to understand: All blue boxes.

Reading Questions:

  1. In your own words, state the squeeze theorem.
  2. In your own words, what is a sequence?
  3. Give an example of a monotonically increasing bounded sequence that does not converge
  4. Give an example of an unbounded sequence that converges to 100

Section 9.2 – Series and Convergence

To read: All

Be sure to understand: Definitions of various types of series, nth-Term Test for Divergence

Reading Questions:

  1. What is the difference between a series and a sequence?
  2. Describe the difference between and .
  3. State, in your own words, the nth-Term Test for Divergence.
  4. There are two sequences associated with every series. What are they?

Section 9.3 – The Integral Test and p-Series

To read: All

Be sure to understand: The definition and properties of a p-series, how to use the Integral Test

Reading Questions:

  1. Define a p-series and state the requirements for its convergence.
  2. In your own words, state the Integral Test and give an original example of its use.

Section 9.4 – Comparisons of Series

To read: All

Be sure to understand: Blue boxes.

Reading Questions:

  1. State the Direct Comparison Test and give an original example of its use.
  2. State the Limit Comparison Test and give an original example of its use.
  3. Why would one want to compare series with each other?

Section 9.5 – Alternating Series

To read: All

Be sure to understand: The alternating series test.

Reading Questions:

  1. What, in our own words, is an alternating series?  Give an example.
  2. Compare and contrast absolute convergence and conditional convergence.  Give examples of each.

Section 9.6 – The Ratio and Root Tests

To read: All

Be sure to understand: Ratio Test (!!!), Root Test, the gray box titled “Guidelines for Testing a Series…” and summary of tests chart

Reading Questions:

  1. What is the first test that should be applied to a series to determine convergence or divergence?
  2. State, in your own words, the Root Test.  Give an example of when it could not be used to determine convergence or divergence.
  3. State, in your own words, the Ratio Test. Give an example of when it could not be used to determine convergence or divergence.

Section 9.7 – Taylor Polynomials and Approximations

To read: All,

Be sure to understand: the definition of the Taylor polynomial.

Reading Question :

  1. Explain the basic pattern of the Taylor polynomial for a function f(x) at x=c in your own words.
  2. Why would you want to find the Taylor polynomial of a function?
  3. In your own words, briefly explain the idea and process (how, why, etc.) of building the Taylor polynomial for a function f(x).
  4. What is a Maclaurin Polynomial?

9.8 – Power Series

To read: All

Be sure to understand: Why the Ratio Test is used.

Reading Questions:

  1. Define a power series for a precalculus student.
  2. How do power series differ from the series we have looked at up to this point?
  3. Describe the radius of convergence for a power series.  Describe the interval of convergence for a power series.  If two power series have the same radius of convergence, do they necessarily have the same interval of convergence?  Elaborate.
  4. Describe how to differentiate and integrate a power series with a radius R.  Will the series resulting from the operations of differentiation and integration have a different radius of convergence? Explain.

Section 9.9 – Representation of Functions by Power Series

To read: All

Be sure to understand: Long division in margin, blue box and example 4.

Reading Questions:

  1. Give two good reasons for writing a known function (such as cos(x)) as a power series.
  2. The radius of convergence of a power series is 3.  What is the radius of convergence of the series? Explain.
  3. Explain, in your own words, the process of using long division to find a power series.

Section 9.10 – Taylor and Maclaurin Series

To read: All

Be sure to understand: Blue boxes and gray “guidelines” box

Reading Questions:

  1. State the guideline for finding a Taylor Series.
  2. Briefly compare and contrast Taylor and Maclaurin Polynomials with Taylor and Maclaurin Series.
  3. If f is an even function, what must be true about the coefficients an in the Maclaurin series f(x) = ?
  4. Define the binomial series. What is its radius of convergence?

Section 10.1 – Conics and Calculus

To read: All

Be sure to understand: How to find the equations of conic sections

Reading Questions:

  1. Give the definition of a parabola and give an example equation in standard form.  Then solve that equation for y.
  2. Give the definition of a hyperbola and give an example equation in standard form.  Then solve that equation for y.
  3. Give the definition of an ellipse and give an example equation in standard form.  Then solve that equation for y.

Section 10.2 – Plane Curves and Parametric Equations

To read: All

Be sure to understand: “Eliminating the Parameter” and “Finding Parametric Equations”

Reading Questions:

  1. What, in your own words, is a plane curve?
  2. Explain the process of sketching  plane curve given by parametric equations. What is meant by the orientation of the curve?

Section 10.3 – Parametric Equations and Calculus

To read: All

Be sure to understand: The blue boxes (theorems)

Reading Questions:

  1. Give the integral formulas for the areas of the surfaces of revolution formed when a smooth curve C is revolved about (a) the y-axis and (b) the x-axis.
  2. How does using the parametric form of the derivative compare to related rates problems?
  3. Give the integral formula for arc length in parametric form.
  4. Why not just convert all parametric equations to two variable equations and use the “old” formulas for the derivative, etc?

Section 10.4 – Polar Coordinates and Polar Graphs

To read: All

Be sure to understand: Blue boxes

Reading Questions:

1.      Describe the patterns of the equations of the various special polar graphs.

2.      Why did we cover parametric equations before now (how is this similar)?

Section 10.5 – Area and Arc Length in Polar Coordinates

To read: All

Be sure to understand: Examples 3 and 4

Reading Questions:

  1. Compare and contrast Theorem 10.15 to the Definition of the Area of a Surface of Revolution in Section 7.4.  Which one seems easier to use.  Why?
  2. Explain why finding points of intersection of polar graphs may require further analysis beyond solving two equations simultaneously.

Section 11.1 – Vectors in the Plane

To read: All

Be sure to understand: All bold terms and blue boxes

Reading Questions:

  1. Identify the following quantities as a scalar or vector.  Explain your reasoning.
    1. The air temperature in a room
    2. The weight of a car
  2. Give geometric descriptions of the operations of addition of vectors and multiplication of a vector by a scalar.

Section 11.2 – Space Coordinates and Vectors in Space

To read: All

Be sure to understand: example 1

Reading Questions:

  1. Give the formula for the distance between the points (x1, y1, z1) and (x2, y2, z2).
  2. State the definition of parallel vectors.

Section 12.1 – Vector-Valued Functions

To read: All

Be sure to understand: Blue boxes.

Reading Questions:

  1. If r(t) is a vector-valued function, is the graph of the vector-valued function u(t) = r(t-2) a horizontal translation of the graph of r(t)?  If not, what is it?  Explain your reasoning.
  2. State the definition of continuity of a vector-valued function.  Give an example of a vector-valued function that is defined but not continuous at t = 2.

Section 12.2 – Differentiation and Integration of Vector-Valued Functions

To read: All

Be sure to understand: Blue boxes!

Reading Questions:

  1. Describe, in your own words, how to find the derivative of a vector-valued function and give its geometric interpretation.
  2. How do you find the integral of a vector valued function?  How is this similar to parametric equations?
  3. The z-component of the derivative of a vector-valued function u is 0 for t in the domain of the function.  What does this information imply about the graph of u?

Section 12.3 – Velocity and Acceleration

To read: All

Be sure to understand: Definitions of Velocity and Acceleration

Reading Questions:

  1. In your own words, explain the difference between the velocity of an object and its speed
  2. What is known about the speed of an object if the angle between the velocity and acceleration vectors is (a) acute and (b) obtuse?