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Topics in Calculus Table of Contents

Topics in Calculus (MAT 131) Daily Syllabus (with homework)

JUMP TO CURRENT WEEK
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!)
  • fun math: creatively sharing a pizza with only one person
  • Read the First Day Handout so you're familiar with all course policies.
  • get text and supplies
  • write up index cards for next class
2 F, Jan 20
  • Section 1.1, Functions (most sections will not have this many cards; the first couple weeks are mostly review, so there will be more cards)
  • 1ab: what is a function; examples of functions
  • 2ab: function notation; examples, dummy variable
  • 3ab: more practice with function notation; example—a constant function
  • 4ab: domain and range of a function; examples
  • 5ab: composition of functions; example
  • 6ab: important functions in economics: demand, supply, revenue, cost, profit
 (Weekly quizzes will include randomly-generated questions from web exercises, and questions from text exercises.) text: Exercises 1.1:   57, 61, 63


WEEK #2
CLASS # DATE CLASS CONTENT HOMEWORK
3 M, Jan 23
  • Section 1.2, The Graph of a Function
  • 7ab: ordered pairs, the coordinate plane; practice with points
  • 8ab: the distance formula; finding $x$ and $y$-intercepts
  • 9ab: graphs of functions; reading information from a graph
  • 10ab: basic models you must know; end behavior of a graph
 text: Exercises 1.2:   39, 45, 49
4 W, Jan 25
  • Section 1.3, Linear Functions
  • 11ab: lines; $y=mx+b$ form; equal changes in the input give rise to equal changes in the output
  • 12ab: the slope of a line; slopes of horizontal and vertical lines
  • 13ab: graphing $y = mx + b$; graphing $ax + by + c = 0$
  • 14ab: writing equations of lines (examples)
  • 15ab: point-slope form; example
 text: Exercises 1.3:   37, 39, 43
Study for Friday's quiz!
5 F, Jan 27
  • Section 1.3, Linear Functions
  • 16ab: equations of horizontal and vertical lines
  • 17ab: parallel lines; perpendicular lines
  • Quiz over classes 1,2,3


WEEK #3
CLASS # DATE CLASS CONTENT HOMEWORK
6 M, Jan 30 Section 1.4, Functional Models
  • 18ab: elimination of variables technique; example
  • 19ab: proportionality: direct, inverse, joint; example
  • 20ab: market equilibrium; break-even analysis
7 W, Feb 1 Section 1.5, Limits
  • 21ab: limit of a function; three cases where $\displaystyle\lim_{x\rightarrow a} f(x) = \ell$
  • 22ab: examples: evaluating limits; infinite limits
  • 23ab: limits at infinity; limit rules
  • 24ab: some limits that don't exist; example
  • read Section 1.5, Limits
  • text exercises 1.5: 1–49 odd, 53, 61, 65
  • study for Friday's quiz
  • web exercise: Introduction to Limits
    Questions from this web exercise may be on Exam #1.
8 F, Feb 3 Questions over homework?
Quiz over classes 4,5,6 		(Write up index cards for next class!)


WEEK #4
CLASS # DATE CLASS CONTENT HOMEWORK
9 M, Feb 6 Section 1.6, One-Sided Limits and Continuity
  • 25ab: one-sided limits; examples
  • 26ab: continuity at a point; three ways a function can fail to be continuous
  • 27ab: key idea: when is evaluating a limit as easy as direct substitution?
  • read Section 1.6, One-Sided Limits and Continuity
  • text exercises 1.6: 1–45 odd
10 W, Feb 8 Section 2.1, The Derivative
  • 28ab: average rate of change; the tangent problem
  • 29ab: intuitive derivative (notation); example
  • 30ab: the derivative of $f$ at $a$; using the definition of derivative
  • read Section 2.1, The Derivative
  • web exercise: Average Rate of Change
    Questions from this web exercise may be on Exam #1.
  • text exercises 2.1: 1,3,5,9,13,15,17,19,21,25,27,29,37, 49a
11 F, Feb 10 Questions on homework?
Quiz over classes 7,8,9 		(Write up index cards for next class!)


WEEK #5
CLASS # DATE CLASS CONTENT HOMEWORK
12 M, Feb 13 lots of practice with card 30a Study for Exam #1;
bring questions to next class
13 W, Feb 15 REVIEW FOR EXAM #1 Study for Exam #1!
14 F, Feb 17 EXAM #1 (classes 1–12) (Write up index cards for next class!)


WEEK #6
CLASS # DATE CLASS CONTENT HOMEWORK
15 M, Feb 20 Section 2.2, Techniques of Differentiation
  • 31ab: position functions; velocity, acceleration
  • 32ab: derivative of a constant; the $\,\frac{d}{dx}$ operator; derivatives of sums and differences
  • 33ab: power rule for differentiation; examples
  • 34ab: derivative of a constant times a function; $\frac{d}{dx}(Kx^n)$
 text exercises 2.2: 1–45 odd, 55, 61
web exercise: Introduction to Limits (quiz on Wednesday)
web exercise: Basic Differentiation Shortcuts (quiz on Friday)
16 W, Feb 22 Section 2.3, Product and Quotient Rules;
Higher-Order Derivatives
  • 35ab: the product rule for differentiation; proof
  • 36ab: the quotient rule for differentiation; proof
  • 37ab: notation for higher-order derivatives
  • 38ab: examples: finding the equation of a tangent line; of a normal line
  • web exercise QUIZ: Introduction to Limits
Note: the proofs of the product and quotient rules will be EXTRA CREDIT on the next quiz! 		text exercises 2.3: 1–47 odd, as needed
(be sure to do several from each ‘section’)
word problems: 49, 53
17 F, Feb 24 web exercise QUIZ: Basic Differentiation Shortcuts

catch-up day; work lots of problems 		get caught up on homework;
write up index cards for next class


WEEK #7
CLASS # DATE CLASS CONTENT HOMEWORK
18 M, Feb 27 Section 2.4, The Chain Rule
  • 39ab: differentiating composite functions; motivation
  • 40ab: the Chain Rule: prime notation, Leibniz notation
  • 41ab: why is it called the Chain Rule; differentiating $\,(f(x))^n\,$
  • 42ab: pattern for generalizing all the basic differentiation formulas
 text exercises 2.4: 1, 5, 13, 21–41 odd, 43, 45, 51, 57
word problems: 69, 71, 77
19 W, Feb 29 Section 2.6, Implicit Differentiation and Related Rates
  • 43ab: explicit versus implicit; implicit differentiation
  • 44ab: related rate problems; falling ladder problem
 text exercises 2.6: 1, 3, 9, 11, 13, 17, 23, 27, 31
word problems: 45, 47, 53
20 F, Mar 2 Quiz over classes 15,16,17,18 get caught up on homework;
write up index cards for next class


WEEK #8
CLASS # DATE CLASS CONTENT HOMEWORK
21 M, Mar 5 Section 3.1, Increasing and Decreasing Functions; Relative Extrema
  • 45ab: Where can a function change its sign? Negating ‘and’ and ‘or’ sentences
  • 46ab: implications (and equivalent sentences); the contrapositive of an implication
  • 47ab: increasing and decreasing functions; getting increasing/decreasing behavior from the derivative
  • 48ab: local max/min; global max/min
 text exercises 3.1: 1–21 odd
22 W, Mar 7 continue Section 3.1;
Section 3.2, Concavity and Points of Inflection
  • 49ab: Where can a function have a local max/min?
  • 50ab: critical points and critical numbers; careful—a critical point does not have to be a max or min
  • 51ab: first and second derivative tests for identifying max/min
 3.1: 23–33 (classify critical points as max/min)
3.2: 1–11 odd; 13, 15, 27, 29
word problems: 57, 63, 65
23 F, Mar 9 finish Section 3.2
  • 52ab: info given by $f$, $f'$, $f''$; a basic sign analysis of a function
  • 53ab: inflection points; where can a function have an inflection point?
    • Quiz over classes 19,20,21
    Have a wonderful Spring Break!
 Have a wonderful Spring Break!


WEEK #9
CLASS # DATE CLASS CONTENT HOMEWORK
24 M, Mar 19 Section 3.4, Optimization
  • 54ab: review of absolute/global max/min; the Extreme Value Theorem
  • 55ab: optimization problems (finding max/min); example
  • 56ab: a first optimization problem; you try it!!
  • 57ab: another optimization problem; you try it!!
 3.4: 1–15 odd
word problems: 35, 43a
25 W, Mar 21 Monday was a snow day; cover Monday's material  
26 F, Mar 23 REVIEW FOR EXAM #2; catch-up day Study for Exam #2!


WEEK #10
CLASS # DATE CLASS CONTENT HOMEWORK
27 M, Mar 26 EXAM #2 (classes 15–25)  
28 W, Mar 28 Section 4.1, Exponential Functions
  • 58ab: exponential functions, graphs of exponential functions
  • 59ab: properties of exponential functions
 web exercise:
Introduction to Exponential Functions
You will have a worksheet from this exercise as part of your next quiz.
29 F, Mar 30 Section 4.2, Logarithmic Functions
  • 60ab: logarithmic functions; properties of logarithmic functions
  • 61ab: laws of logarithms; sample proof
  • 62ab: change of base formula; derivation
 You will have worksheets from each web exercise as part of your next quiz:
Introduction to Logarithms
Properties of Logarithms
Change of Base Formula for Logarithms
Introduction to Logarithmic Functions


WEEK #11
CLASS # DATE CLASS CONTENT HOMEWORK
30 M, Apr 2 Section 4.3, Differentiation of Exponential and Logarithmic Functions
  • 63ab: differentiating ${\text{e}}^x$; differentiating $a^x$
  • 64ab: derivatives of logarithms; generalizing the differentiation rules
 Section 4.3: 1–34 odd, 39, 45, 47, 53, 79
31 W, Apr 4 Section 5.1, Antidifferentiation, the Indefinite Integral
  • 65ab: antiderivatives; ‘undoing’ differentiation
  • 66ab: indefinite integrals; some antiderivatives you should know
  • 67ab: generalizing the formula for the derivative of $\ln x$; the antiderivatives of $\frac 1x$; example
  • 68ab: finding a particular antiderivative; example
 Section 5.1: 1–33 odd
32 F, Apr 6 Quiz over classes 28,29,30 catch up on homework;
write up index cards for next class


WEEK #12
CLASS # DATE CLASS CONTENT HOMEWORK
33 M, Apr 9 Section 5.2, Integration by Substitution
  • 69ab: substitution; the idea and format
  • 70ab: a substitution example: a long way, a compact version
 Section 5.2: 1–33 odd; 37, 39, 45, 53
34 W, Apr 11 Section 5.3, The Definite Integral and the Fundamental Theorem of Calculus
  • 71ab: the definite integral gives signed area under a curve; notation for the definite integral
  • 72ab: dummy variables in definite integrals; simple definite integrals (using area interpretation)
  • 73ab: properties of the definite integral
  • 74ab: the Fundamental Theorem of Calculus; examples
  • 75ab: more examples; using substitution with definite integrals
 Section 5.3: 1–29 odd
35 F, Apr 13 Quiz over classes 31,32,33 write up index cards for next class


WEEK #13
CLASS # DATE CLASS CONTENT HOMEWORK
36 M, Apr 16 Section 5.3 continued, The Definite Integral and the Fundamental Theorem of Calculus
  • 76ab: a very useful formula; integrating a rate of change gives total change
  • Work lots of examples!
 Section 5.3: 31–45 odd, 47, 49, 51
37 W, Apr 18 Section 6.1, Integration by Parts
  • 77ab: integration by parts (the integration ‘counterpart’ to the product rule for differentiation); basic strategy for using parts
  • 78ab: format for integration by parts; using parts with a definite integral
 Section 6.1: 1–13 odd, 41, 43
38 F, Apr 20 Quiz over classes 34,35,36 write up index cards for next class


WEEK #14
CLASS # DATE CLASS CONTENT HOMEWORK
39 M, Apr 23 Section 6.2, Improper Integrals
  • 79ab: improper integrals; writing improper integrals as limits
  • 80ab: two examples: a divergent improper integral; a convergent improper integral
 6.2: 1, 3, 5, 7, 9, 11, 13;
read over (but do not solve) 25, 29, 31, 37 to get a sense of the sorts of problems that improper integrals can address
40 W, Apr 25 REVIEW FOR EXAM #3 study for Exam #3
41 F, Apr 27 EXAM #3 (classes 27–39) start reviewing for final exam;
gather together your quizzes and tests, to get questions answered during review week


WEEK #15
CLASS # DATE CLASS CONTENT HOMEWORK
42 M, Apr 23 REVIEW FOR FINAL EXAM
(Exam #1 and associated quizzes) 		Study for final exam!
43 W, Apr 25 REVIEW FOR FINAL EXAM
(Exam #2 and associated quizzes) 		Study for final exam!
44 F, Apr 27 REVIEW FOR FINAL EXAM
(Exam #3 and associated quizzes)

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 final exam!

final exam:
Monday, May 7, 10:00–noon, Room 146