homepage: Dr. Carol JVF Burns

Calculus I (MAT 136) Daily Syllabus (with homework)

WEEK #1
CLASS # DATE CLASS CONTENT HOMEWORK
1 W, Jan 18
  • Welcome! I'll introduce myself.
  • go over highlights of the First Day Handout (tomorrow's QQ, 3 points!)
  • sign roster; get your course number
  • take your first “Quick Quiz” (use your number!)
  • talk about WebWorks (online, graded homework)
  • fun math: creatively sharing a pizza with only one person
2 Th, Jan 19
  • (Note: no index cards this review week, to give you time to get your cards, notebook, dividers)
  • Quickly go over a few web exercises, to show you how they work. Talk about next Wednesday's major Prerequisite Review Quiz.
  • Sample Prerequisite Problems (PreCalculus) (Solutions included)
    Questions over #1 and #2?
Try Sample Prerequisite Problems (PreCalculus): 3–7
Bring questions to the next class.

Next Wednesday, there will be an 80-pt PREREQUISITE REVIEW QUIZ (full period).
It will include questions from the Sample Prerequisite Problems (PreCalculus).
It will also include questions from each of the following web exercises:
multi-step exponent law practice
practice with radicals
introduction to sets
interval and list notation
introduction to functions
introduction to function notation
more practice with function notation
factoring a difference of squares
factoring trinomials, all mixed up
graphs of functions
basic models you must know
composition of functions
advanced set concepts
3 F, Jan 20 Try Sample Prerequisite Problems (PreCalculus): 8–15
Bring questions to the next class.

web exercises:
graphing tools: vertical and horizontal translations
graphing tools: vertical and horizontal scaling
reflections and the absolute value transformation
graphical transformations: all mixed up
quadratic functions and the completing the square technique
introduction to logarithms
properties of logarithms
introduction to logarithmic functions
properties of logarithms
introduction to exponential functions



WEEK #2
CLASS # DATE CLASS CONTENT HOMEWORK
4 M, Jan 23 STUDY FOR PREREQUISITE REVIEW QUIZ!
5 W, Jan 25 PREREQUISITE REVIEW MAJOR QUIZ (80 pts)  
6 Th, Jan 26
  • finish worksheets, as needed
  • web exercise: Average Rate of Change
    short in-class quiz on Monday
  • WebWorks: Average Rate of Change
    (2 problems, 4 pts each, 8 pts)
    DUE: Friday, Jan 27, end of day
  • WebWorks: Rate of Change
    (5 problems, 2 pts each, 10 pts)
    DUE: Friday, Jan 27, end of day
7 F, Jan 27
  • 3ab
    intuitive derivative (notation); finding derivative values
  • 4ab
    limit of a function; 3 cases where the limit of $f(x)$, as $x$ approaches $a$, equals $\ell$
  • 5ab
    one-sided limits; the Squeeze (Pinching) Theorem
  • text, Exercises 2.4.15 and 2.4.16, finding limit values (finish for homework, as needed)
 WebWorks: Intuitive Derivative (12 pts)
DUE: Friday, Feb 3, end of day

WebWorks: Limits (13 pts)
DUE: Friday, Feb 3, end of day

web exercise: Introduction to Limits



WEEK #3
CLASS # DATE CLASS CONTENT HOMEWORK
8 M, Jan 30
  • 6ab
    continuity at a point; three ways a function can fail to be continuous at $c$
  • 7ab
    key idea: if $f$ is continuous at $c$, then evaluating a limit is as easy as direct substitution
  • 8ab
    an important type of continuity problem; relationship between differentiability and continuity
  • short in-class quiz; Average Rate of Change web exercise
 WebWorks: Continuity
(7 problems, 2 pts each, 14 pts)
DUE: Friday, Feb 3, end of day
DUE: Monday, Feb 6, end of day
9 W, Feb 1 WebWorks: Limit Rules
(20 problems, 1 pt each, 20 pts)
DUE: Friday, Feb 3, end of day
DUE: Monday, Feb 6, end of day
10 Th, Feb 2
  • 11ab
    the derivative of $f$ at $a$
  • 12ab
    more examples: using the definition of derivative
WebWorks: Basic Derivatives
(8 problems, 1 pt each, 8 pts)
DUE: Friday, Feb 3, end of day
DUE: Monday, Feb 6, end of day
11 F, Feb 3
  • 13ab
    the linearization of $f$ at $a$
  • 14ab
    local/global max/min (extreme values)
WebWorks: Local Linearization
(6 problems, 2 pts each, 12 pts)
DUE: Friday, Feb 10, end of day

WebWorks: Extreme Values
(6 problems, 2 pts each, 12 pts)
DUE: Friday, Feb 10, end of day



WEEK #4
CLASS # MWThF DATE CLASS CONTENT HOMEWORK
12 M, Feb 6
  • 15ab
    strictly increasing and decreasing functions;
    getting inc/dec behavior from the first derivative
  • 16ab
    concavity;
    getting concavity info from the second derivative
WebWorks: Direction and Sign of the Derivative
(2 problems, 2 pts each, 4 pts)
DUE: Friday, Feb 10, end of day
Hint: you will need to know the vertex formula for a quadratic function

WebWorks: Concavity
(9 problems, 2 pts each, 18 pts)
DUE: Friday, Feb 10, end of day

Suggestion: Do these homework sets before the first exam!
13 W, Feb 8 Finish the in-class worksheets.
Study for Exam #1.
Bring good questions to class tomorrow!
14 Th, Feb 9 catch-up; review  
15 F, Feb 10 EXAM #1  



WEEK #5
CLASS # DATE CLASS CONTENT HOMEWORK
16 M, Feb 13
  • 17ab
    the Power Rule for differentiation;
    examples of using the power rule
  • 18ab
    partial proof of the Power Rule (nonnegative integers)
WebWorks: Power Rule
(10 problems, 1 pt each, 10 pts)
DUE: Friday, Feb 17, end of day
17 W, Feb 15
  • 19ab
    derivative of a constant times a function;
    finding $\frac{d}{dx}(Kx^n)$
  • 20ab
    derivatives of sums and differences; proof
WebWorks: Derivatives of Linear Combinations
(11 problems, 1 pt each, 11 pts)
DUE: Friday, Feb 17, end of day
18 Th, Feb 16
  • 21ab
    differentiating composite functions—motivation;
    differentiating composite functions—the idea
  • 22ab
    the Chain Rule (prime notation);
    the Chain Rule (Leibnitz notation)
  • 23ab
    Why is it called the Chain Rule?
    Using the Chain Rule to differentiate $(f(x))^n$
  • 24ab
    pattern for generalizing all the basic differentiation formulas; examples
WebWorks: Derivatives of Compositions
(5 problems, 2 pts each, 10 pts)
DUE: Friday, Feb 17, end of day
19 F, Feb 17
  • 25ab
    the Product Rule for differentiation;
    Proof of the Product Rule
  • 26ab
    When is $\displaystyle\lim_{h\rightarrow 0} f(x+h) = f(x)\,$?
    When is this true? As $x\rightarrow c\,,$ $f(x) \rightarrow f(c)$
  • 27ab
    the Quotient Rule for Differentiation;
    Proof of the Quotient Rule
WebWorks: Derivatives of Products and Quotients
(19 problems, 1 pt each, 19 pts)
DUE: Friday, Feb 24, end of day

Practice this web exercise to firm up your understanding of limits: Introduction to Limits

Also practice this web exercise: Basic Differentiation Shortcuts

Next week (Wednesday and Thursday) there will be quizzes over these two web exercises (in the form of printed, randomly-generated worksheets)



WEEK #6
CLASS # DATE CLASS CONTENT HOMEWORK
20 M, Feb 20
  • 28ab
    the irrational number e;
    equivalent limit statements defining e
  • 29ab
    evaluating a limit involving e;
    why is $\displaystyle\lim_{n\rightarrow\infty} [(1+\frac 1n)^n]^{2k} = {\text{e}}^{2k}\,$?
  • 30ab
    derivatives of logarithms;
    proof that $\displaystyle\frac{d}{dx} \ln x = \frac 1x$
  • 31ab
    more notation for derivatives;
    notation: evaluating a derivative at a point
WebWorks: Natural Base e
(3 problems, 1 pt each, 3 pts)
DUE: Friday, Feb 24, end of day

WebWorks: Derivatives of Logarithmic Functions
(6 problems, 1 pt each, 6 pts)
DUE: Friday, Feb 24, end of day

web exercise: Introduction to Limits (quiz on Wednesday)
web exercise: Basic Differentiation Shortcuts (quiz on Thursday)
21 W, Feb 22 WebWorks: Derivatives of Exponential Functions
(4 problems, 1 pt each, 4 pts)
DUE: Friday, Feb 24, end of day
22 Th, Feb 23
  • 33ab
    what is $\displaystyle\,\lim_{x\rightarrow 0}\frac{\sin(x)}{x}\,$; an example
  • 34ab
    derivatives of sine and cosine;
    derivatives of tangent and cotangent
  • 35ab
    derivatives of secant and cosecant;
    a useful observation—derivatives of co-functions
  • web exercise QUIZ: Basic Differentiation Shortcuts
WebWorks: Derivatives of Trigonometric Functions
(20 problems, 1 pt each, 20 pts)
DUE: Friday, Feb 24, end of day
23 F, Feb 24
  • 36ab
    finding the derivative of an inverse function;
    two methods of finding $\,(f^{-1})'(x)$
  • 37ab
    What does $\,(f^{-1})'(x) = \frac{1}{f'(f^{-1}(x))}\,$ really mean?
WebWorks: Derivatives of Inverse Functions
(4 problems, 1 pt each, 4 pts)
DUE: Friday, Mar 2, end of day

Prepare for next week's Gateway Differentiation Quizzes



WEEK #7
CLASS # DATE CLASS CONTENT HOMEWORK
24 M, Feb 27 WebWorks: Derivatives of Inverse Trigonometric Functions
(6 problems, 1 pt each, 6 pts)
DUE: Friday, Mar 2, end of day
25 W, Feb 29
  • short Gateway Differentiation Quiz at end of class (20 pts)
  • 39ab
    differentiating variable stuff to variable powers—the log trick;
    example (differentiating $x^x$)
WebWorks: the Log Trick
(5 problems, 1 pt each, 5 pts)
DUE: Friday, Mar 2, end of day
26 Th, Mar 1  
27 F, Mar 2 EXAM #2  



WEEK #8
CLASS # DATE CLASS CONTENT HOMEWORK
28 M, Mar 5
  • 40ab
    l'Hopital's Rule (for investigating indeterminate forms); motivation for the ‘$\frac 00$’ case
  • 41ab
    examples: using l'Hopital's Rule (basic; more advanced)
WebWorks: l'Hopital's Rule
(6 problems, 1 pt each, 6 pts)
DUE: Friday, Mar 9, end of day
29 W, Mar 7
  • 42ab
    where can a function change its sign (from positive to negative, or negative to positive); negating ‘and’ and ‘or’ sentences
  • 43ab
    information given by the sign of $f$, $f'$, and $f''$; a basic sign analysis of a function
  • 43cd, math language material:
    implications; the contrapositive of an implication
continue WebWorks: l'Hopital's Rule
(6 problems, 1 pt each, 6 pts)
DUE: Friday, Mar 9, end of day
30 Th, Mar 8
  • 44ab
    Where can a function have a local max/min? At a horizontal tangent line; at a place where the function is not differentiable; at an endpoint of the domain
  • 45ab
    definition: critical numbers (points) for a function; these give the candidates for places where there are max/min; careful—you may not have max/min at critical points
  • 46ab
    inflection points;
    Where can a function have an inflection point?
    At a place where $f''(x) = 0$ or where $f''(x)$ does not exist
begin WebWorks: Function Analysis
(9 problems, 1 pt each, 9 pts)
DUE: Friday, Mar 9, end of day
31 F, Mar 9
  • 47ab
    an algorithm for thorough function analysis;
    example: implementing the algorithm for thorough function analysis (creating a derivative chart)
  • 48ab
    deciding if candidates are local max/min:
    the first derivative test; the second derivative test
  • Have a wonderful Spring Break!! (March 12–16)
 continue WebWorks: Function Analysis
(9 problems, 1 pt each, 9 pts)
DUE: Friday, Mar 9, end of day



WEEK #9
CLASS # DATE CLASS CONTENT HOMEWORK
32 M, Mar 19
  • 49ab
    open/closed intervals; bounded subsets of $\Bbb R$
  • 50ab
    review of absolute/global max/min;
    the Extreme Value Theorem
  • 51ab
    optimization problems; finding the absolute max/min of a continuous function on a closed bounded interval
  • 52ab
    a first optimization problem; you try it!
begin WebWorks: Optimization
(8 problems, 3 pts each, 24 pts)
Keep working on it all week!
DUE: Friday, Mar 23, end of day
33 W, Mar 21
  • 53ab
    an optimization problem; you try it!
 
34 Th, Mar 22
  • 53cd
    a useful observation (if $f \gt 0$ and $f$ has a max/min at $c$, then $f^2$ also has a max/min at $c$)
  • 54ab
    an optimization problem; you try it!
 
35 F, Mar 23
  • 55ab
    explicit versus implicit; implicit differentiation
WebWorks: Implicit Differentiation
(6 problems, 2 pts each, 12 pts)
DUE: Friday, Mar 30, end of day



WEEK #10
CLASS # DATE CLASS CONTENT HOMEWORK
36 M, Mar 26
  • 56ab
    related rate problems; example (falling ladder)
WebWorks: Related Rates
(3 problems, 4 pts each, 12 pts)
DUE: Friday, Mar 30, end of day
37 W, Mar 28
  • 57ab
    Is the car speeding? (another related rate problem)
 
38 Th, Mar 29
  • 58ab
    the Mean Value Theorem; interpretation and intuition
  • 59ab
    the Mean Value Theorem: examples
WebWorks: the Mean Value Theorem
(4 problems, 2 pts each, 8 pts)
DUE: Friday, Mar 30, end of day
39 F, Mar 30
  • 60ab
    bounded functions; the definite integral of a function
  • 61ab
    a definite integral may or may not exist;
    notation for the definite integral
  • 62ab
    dummy variables in definite integrals;
    simple definite integral examples
WebWorks: Definite Integrals as Signed Area
(7 problems, 2 pts each, 14 pts)
DUE: Friday, Apr 6, end of day



WEEK #11
CLASS # DATE CLASS CONTENT HOMEWORK
40 M, Apr 2
  • Optimization problem quiz (10 minutes, 20 points)
  • 63ab
    properties of the definite integral; linearity of the integral
  • 64ab
    definite integral examples
continue working on:
WebWorks: Definite Integrals as Signed Area
(7 problems, 2 pts each, 14 pts)
DUE: Friday, Apr 6, end of day
41 W, Apr 4 more practice with complete function analysis study for Exam #3
42 Th, Apr 5 review study for Exam #3
43 F, Apr 6 EXAM #3  



WEEK #12
CLASS # DATE CLASS CONTENT HOMEWORK
44 M, Apr 9
  • 65ab
    how might we estimate areas beneath a curve;
    general notation for the area problem
  • 66ab
    summation notation;
    left and right estimates using summation notation
  • 67ab
    precise definition of a definite integral; Riemann sums
  • 68ab
    estimating a definite integral using a Riemann sum; finding a very simple definite integral using the definition of definite integral
  • Read and study this online web exercise:
    Summation Notation
    Print out a worksheet, write in all the answers, and pass it in as tomorrow's Quick Quiz.
    There will be a QUIZ (a randomly-generated worksheet) on THURSDAY, APRIL 19.
  • WebWorks: Riemann Sums
    (6 problems, 2 pts each, 12 pts)
    DUE: Friday, Apr 13, end of day
45 W, Apr 11
  • 69ab
    the Fundamental Theorem, Part I;
    proof of the Fundamental Theorem
  • 70ab
    antiderivatives;
    ‘undoing’ differentiation—antidifferentiation
  • 71ab
    every differentiation formula gives an antidifferentiation formula;
    some antiderivatives you should know
  • 72ab
    examples: using the Fundamental Theorem
  • 73ab
    a very useful formula; integrating a rate of change gives total change
  • WebWorks: Fundamental Theorem
    (9 problems, 2 pts each, 18 pts)
    DUE: Friday, Apr 13, end of day
46 Th, Apr 12
  • 74ab
    connection between area and antiderivatives;
    making it precise
  • 75ab
    continuing: making it precise
  • practice: print out this worksheet and fill in the blanks
  • 76ab
    summary: the Fundamental Theorem of Calculus
  • 77ab
    examples: derivatives involving integrals
WebWorks: Antiderivatives
(7 problems, 2 pts each, 14 pts)
DUE: Friday, Apr 13, end of day
47 F, Apr 13
  • 78ab
    indefinite integrals (general antiderivatives); more antiderivative formulas
  • 79ab
    finding a particular antiderivative; example
  • 80ab
    generalizing the formula for the derivative of $\ln x$;
    the antiderivatives of $\frac 1x$
WebWorks: Indefinite Integrals
(6 problems, 2 pts each, 12 pts)
DUE: Friday, Apr 20, end of day


WEEK #13
CLASS # DATE CLASS CONTENT HOMEWORK
48 M, Apr 16
  • 81ab
    the substitution technique for integration;
    format for substitution problems
  • 82ab
    a substitution example;
    same problem; more compact version
  • 83ab
    substitution with definite integrals;
    two approaches
WebWorks: Substitution
(7 problems, 2 pts each, 14 pts)
DUE: Friday, Apr 20, end of day
49 W, Apr 18 Lots of substitution problems! Study for tomorrow's quizzes!
50 Th, Apr 19  
51 F, Apr 20
  • 84ab
    integration by parts;
    strategies for using parts
  • 85ab
    format for integration by parts problems;
    using parts with a definite integral
get started on:
WebWorks: Integration by Parts
(8 problems, 2 pts each, 16 pts)
DUE: Friday, Apr 27, end of day



WEEK #14
CLASS # DATE CLASS CONTENT HOMEWORK
52 M, Apr 23
  • 86ab
    periodically differentiable functions;
    using parts with products of polynomials and periodically differentiable functions
  • 87ab
    inverse functions with simpler derivatives;
    using parts for inverse functions
  • 88ab
    using parts with products of periodically differentiable functions; it doesn't always work
continue working on:
WebWorks: Integration by Parts
(8 problems, 2 pts each, 16 pts)
DUE: Friday, Apr 27, end of day
53 W, Apr 25
  • 89ab
    analyzing falling objects: $m x''(t) = mg$;
    integrate to find velocity and position (height)
  • Integration problems—all mixed up!
    (from textbook, Section 5.8)
WebWorks: Integration Mixed Practice
(6 problems, 2 pts each, 12 pts)
DUE: Friday, Apr 27, end of day
54 Th, Apr 26
  • review for Exam #4
    (68b and 69b will be EXTRA CREDIT on this exam)
Study for Exam #4!!
55 F, Apr 27 EXAM #4
This exam will include a worksheet from:
Differentiation Formula Practice 		Study for the first mixed integration quiz!
Study for the final exam!



WEEK #15 (end-of-term week)
CLASS # DATE CLASS CONTENT HOMEWORK
56 M, Apr 30 Study for the second mixed integration quiz!
Study for the final exam!
57 W, May 2 Study for the third mixed integration quiz!
Study for the final exam!
58 Th, May 3 Study for the last mixed integration quiz!
Study for the final exam!
59 F, May 4
  • mixed integration quiz #4
    (5 problems, 25 pts, recorded as 20 pts)
  • review for final exam (third hour exam)
  • review for final (fourth hour exam)

Bring INDEX CARDS to FINAL EXAM to be graded:
-- they MUST have a rubber-band around them, or be in a plastic bag or zippered pouch
-- your name and number must clearly appear on the top of the pile
-- they must be in INCREASING ORDER 		Study for the final exam!

final for 8:00 class:
Monday, May 7, 7:30–9:30 AM, ROOM 221

final for 11:30 class:
Wednesday, May 9, 10:00–noon, ROOM 147