Syllabus for SM121, SM121A    

           Calculus I           

       Fall Semester, 2004-2005

TEXT: CALCULUS, Concepts and Contexts, Second Edition, by James Stewart

NOTES:

  1. A web site at http://www.nadn.navy.mil/MathDept/courses/fall04/calc1/calc1.html will have the most up to date information about the course, including this syllabus, practice exams, web links, etc.

  2. All students in this course are expected to have a calculator like the VOYAGE 200 with the capabilities to do symbolic calculations. There will be assignments that use such a calculator as well as questions on the common final exam on which it is expected that the student has such a calculator. The above web site also has a list link to a file with a list of the minimal competences expected of all students.

  3. If you would like help in the course, you should contact your instructor for extra-instruction. If your instructor is not available, try the Math Lab. It is staffed all six class periods every class day with instructors who should be able to answer your questions. Also, hard copies of web page information will be kept there (syllabi, practice tests, etc.). There is also peer tutoring available in the evenings provided by upper classmen.

  4. Exercises that ask for verbal explanations should be answered with complete sentences.

  5. In the syllabus below, the LABS in the PROBLEMS column are considered part of the course

    LESSON

    SECTION

     TOPIC

    PROBLEMS

    1 (review)

    Appendix B

    (excluding conics)

    p. A16: 1,3,9,10,12,17,21,26,38,39  (interval notation p.A2)

    2 (review)

    Appendix C

    (thru equ. 8 & graphs)

    p. A27: 1,3,5,8,12,13,17,29,30  (WAVE LAB)

    3

    1.1

    Representing Functions

    p. 22: 2,6,8,16,30,35,41,49

    4

    1.2

    Mathematical Models

    p. 35: 3,6,11,13,14,17,19

    5

    1.3

    New Functions from Old

    p. 46: 1,3,5,10,11,17,21

    6

    1.3

    (continued)

    p. 46: 15,28,32,35,49,51

    7

    1.5

    Exponential Functions

    p.63: 1,4,11,13,15,20,23 (PARACHUTE LAB)

    8

    1.6

    Inverse Functions and Logs

    p. 73: 4,5,6,13,15,16,17,20,35,37 

    9

    Appendix C

    Inverse Trig Func.

    p. A28: 41,42,43,45,48

    10

    1.7

    Parametric Curves

    p. 81: 5,6,9,13,16,25,29,30

    11

    1.1-1.7

    Review

    p. 24: 48; p.37: 16; p.48: 53; p. 64: 26; p.74: 58

    12

     

    Test 1

     

    13

     

    Test 1 debrief

     

    14

    2.1

    Tangent and Velocity

    p. 99: 1,3,5,8  (TOWER LAB)

    15

    2.2

    Limit of a Function

    p. 108: 1,2,5,6,9,13,17 

    16

    2.3

    Limit Laws

    p. 117: 1,2,9,15,19,23,33

    17

    2.4

    Continuity

    p. 128: 1,2,4,7,9,16,26,30,32

    18

    2.5

    Limits Involving Infinity

    p. 139: 1,2,4,6,16,21,22,35

    19

    2.6

    Tangents, etc.

    p. 148: 1,2,3,4,5,13,14,20,22 

    20

    2.7

    Derivatives

    p. 155: 1,2,3,4,9,28 

    21

    2.8

    Derivative as a Function

    p. 167: 1,3,4,8,9,10

    22

    2.8

    (continued)

    p. 167: 26,31,35,48

    23

    2.9

    Linear Approximations

    p. 173: 5,8, 9,13

    24

    2.10

    What does f’ say about f ?

    p. 178: 1,2,4,12,19

    25

    2.10

    (continued)

    p. 178: 5,8,10,28

    26

     

    Review

    p. 182: 1,2,5,10,21,27,28,33,36,37,43,46

    27

     

    Test 2

     

    28

     

    Test 2 debrief

     

    29

    3.1

    Differentiation Rules

    p. 196: 4,5,13,18,24,31,45

    30

    3.1

    (continued)

    p. 196: 1,2,7,9,15,19,56

    31

    3.2

    Product and Quotient Rules

    p. 204: 1,2,3,8,22,28,29,31,34

    32

    3.3

    Rates of Change

    p. 215: 1,5,11,14,27

    33

    3.4

    Derivatives of Trig

    p. 223: 1,4,6,14,28,31,37

    34

    3.5

    Chain Rule

    p. 233: 3,6,16,38,41,42

    35

    3.5

    (continued)

    p. 233: 45,55,62,65,66,73

    36

    3.6

    Implicit Differentiation

    p. 243: 1,2,5,20,27,29,35  skip orthogonal fns..

    37

    3.7

    Derivatives of Logs

    p. 250: 1,2,5,18,25,37  skip logarithmic differentiation

    38

    3.8

    Linear Approximations...

    p. 256: 1,10,15,19,20

    39

    3.5-3.8

    Review

    p.233: 7,26,57; p. 243: 18; p.250: 17,31,36; p.256: 2,8

    40

     

    Test 3

     

    41

     

    Test 3 debrief

     

    42

    4.1

    Related Rates

    p. 269: 1,2,5  (RATES LAB)

    43

    4.1

    (continued)

    p. 269: 7,14,30

    44

    4.2

    Max and Min Values

    p. 276: 1,2,3,6,7,9,13,39,52

    45

    4.3

    Derivatives and Shapes

    p. 288: 1,2,3,4,5,7,9

    46

    4.3

    (continued)

    p. 288: 12,17,24,38,45

    47

    4.4

    Graphing with Calculus...

    p. 297: 2,4,6,20,23,27,30

    48

    4.5

    Indeterminate Forms

    p. 305: 7,9,10,11,14,15 

    49

    4.5

    (continued)

    p. 305: 27,30,31,33,41

    50

    4.6

    Optimization Problems

    p. 312: 7,8,19,23,40 

    51

    4.6

    Optimization Problems

    p. 312:  12,21,27,42

    52

    4.8

    Newton’s Method

    p. 327: 1,3,4,6,9,22

    53

    4.9

    Antiderivatives

    p. 334: 2,7,10,11,27,30,33,37,44  (DECK LAB)

    54

    5.1

    Area

    p. 355: 2,3,4,11

    55

    5.2

    The Definite Integral

    p. 367: 1,5,6,8,12,17,30

    56

     

    Review

    p. 305: 10,25,47; p. 327: 16,30; p.334: 6,36; p.355: 12,13,18; p.367: 32,36,41; p. 377:30,37,57,60

    57

     

    Test 4

     

    58

     

    Test 4 debrief

     

    59

     

    Review for Final Exam

     

    CALCULATOR NOTES

    The latest version of the VOYAGE 200 guidebook in PDF format is at
    http://education.ti.com/product/pdf/gb/eng/8992p/$8992book-eng.pdf

    Appendix C: Note, for example,  that tExpand(sin(x+y)) gives the sum formula. One way to change from degrees to radians is to enter 2nd D (for degrees) in radian mode.  One way to reverse is to use 2nd Y D D (decimal degrees).

    1.1   Be sure you can define your own functions on the calculator, either by define or store. (Piecewise functions are hard to enter - beyond the course expectations.)

    1.4   Using Y=, GRAPH, TABLE gives a function algebraically, visually, and numerically.  If a graph is taking too long to draw, the ON key interrupts.  Zoomdec (F2 4) gives correct aspect ratio - makes circles circular.
    To get roughly Figure 6, change the xmin/xmax window to plus or minus a)15, b)12.5, c)11.25, d)7.5.
    To get Figure 11, try x^(1/3.) - note decimal point

    1.4   Use the calculator to compose functions. Sometimes g(f(x))will give an error.  It can be avoided by defining f and g using a variable other   than x (say t) but then using x for the composition.  Try drawing shifted and stretched graphs with the calculator.  In the Y= screen, F4 unchecks/checks a function to not draw/draw it and F3 may be needed to edit (change) a function or clear and re-enter it.

    1.7   The MODE key allows one to change Graph-parametric. Under Y= menu, F1 toolkit, 9 Format, Graph order 2 simultaneous, allows checking for simultaneous collision.  Lead cursor ON to see cos(3t) sin(3t) 3 times.

    2.1   All the many points in a problem like number 9 can be done quickly by defining a secant slope function on the calculator.  For example, define f(x) then  use ((f(x)-f(1))/(x-1))|x={2,1.5,1.4,1.3,1.2,1.1}.  Old assigned variables can cause errors - recommend using single letter variable names and then erasing with F6. 

    2.2   The VOYAGE 200 takes limits!  For example define g(x)=x/x.  Then g(0) is undefined. But limit(g(x),x,0)=1.  And it does one sided limits, e.g. limit(abs(x)/x,x,0,-7) = -1 (where -7 can be any negative) for limit from the   negative side.

    2.3   Graph the floor and ceiling functions and understand in what way the calculator graphs are wrong.

    2.4   Graph functions with infinite limits and understand how the calculator graphs can be wrong (drawing vertical asymptotes). The VOYAGE 200 can use (2nd J) in both ways.

    2.5   The VOYAGE 200 will draw tangent lines and give the equation (graph and then use F5 math A).

    Created by Prof Sanders, tjs@usna.edu.