Room: B102 Phone: (503)673-7815 ext 4816
Office Hours: 7:30am-8:20am or after school with prior arrangement
Teacher recommendation and/or completion of Pre-Calculus
This course is the study of differential and integral calculus. Topics covered will include limits, tangent lines, def. of a derivative, derivative rules, area under a curve using summations and integrals, volume of solids, arc length of a curve, and applications of differential and integral calculus.
This course will foster an understanding of topics and applications of differentiation and antidifferentiation.
Student Learning Outcomes
· Estimate limits numerically and graphically.
· Determine limits numerically, graphically, and algebraically.
· Understand the limit definition of the derivative and its interpretation as an instantaneous rate of change.
· Find derivatives numerically, visualize derivatives graphically as the slope of the graph, and interpret the meaning of the first and second derivatives in various applications.
· Understand the derivative as a function in its own right and use the local linearity of functions to obtain approximations from the derivative.
· Demonstrate proficiency in differentiation and an understanding of why the various rules are true.
· Investigate families of functions using graphing technology to observe their properties and the first and second derivatives to verify these observations.
· Use derivatives in problem solving that requires sustained reasoning to reach successful conclusions.
· Reconstruct a function from its derivative graphically, numerically and analytically.
· Find the antiderivative of a variety of functions.
· Use Riemann sums to approximate the area under a curve and to demonstrate this graphically.
· Use the limit of Riemann sums to compute a definite integral.
· Use the Fundamental Theorem of Calculus to compute areas and to evaluate integrals.
· Sketch a given region and find its area by using integrals.
· Sketch a given three dimensional figure and find its volume by using method of disks, shells or washers.
· Sketch a given arc and find its length by using integrals.
· Sketch a given surface and find its area by using integrals.
· Use integrals to solve projectile motion, work and hydrostatic force problems.
· Explore different techniques used to evaluate an integral.
· Determine if an integral is proper or improper.
· Determine if an improper integral converges or diverges.
- Pencils, I will NOT accept any work done in pen.
- Graphing calculator is required for calculus. TI-83/TI-84 is best. TI-86 and TI-89 calculators will not be allowed on any test or quiz. They are however acceptable on the AP exam.
- Textbook, James Stewart, Calculus: Concepts and Contexts, Fourth Edition. I will check out books at the beginning of the year, please take care of them.
Classroom Rules and Expectations
· Be in your seat and ready to work when class starts. This means materials are out, pencils are sharpened, restroom breaks are taken, and socializing is done.
· Bring all materials (books, completed assignments, calculators, and pencils) to class each day.
· If quiet time is given, you are to work on your MATH assignment.
· Keep noise levels down when working in pairs or groups.
· Cheating is not tolerated. If you are caught cheating, you will get a zero and your parents will be notified. This includes if you let someone “borrow” the homework you have already completed.
· Absolutely no electronic devices are allowed in class during lecture/notes.
Assessments and Grading Policies
· If you have an excused absence you will be able to make up the test in a timely manner. There are NO TEST RETAKES. Missing a review day does not postpone a chapter test.
· If homework is not done when you enter the class it is considered late. Late work will be accepted for half credit before you take the chapter test.
· Work must be neat and complete for credit.
· Also homework scores are based on effort, all homework is worth 5 points. Full credit will only be given if all problems are attempted, not completing even one problem will result in only partial credit.
· If you are absent due to illness or family emergency you have one day to make-up the assignment after the one day the assignment is considered late and you will earn only half credit.
· Pre-arranged absences. If you will be out of class (this includes for all field trips, school events, and sporting events) you will be held accountable for the work due. For instance if you leave prior to my class and return after my class for a field trip it is your responsibility to come turn in homework and get your current assignment from me or a classmate. If you do not check that day’s assignment on the day it is due it become late work and will be treated accordingly. If you do not have the assignment prepared for the next day upon your return it also becomes late work.
· Because this class is a dual credit class, earning high school and college credit, you are held to student conduct policies for the high school and Clackamas Community College. Please refer to the HS Student Handbook and the College Handbook http://www.clackamas.edu/documents/handbook.pdf
A 90 and above
The same grading scale and policies do apply to the Advanced College Credit. However, the semester grades do not directly transfer to college grades. The Mth 251 grade is calculated based on chapters 1-4 and the Mth 252 grade is calculated based on chapters 5-7.
Advanced Placement Exam
· There is a fee of $93 dollars for the AP Calculus AB Exam.
· Test Format:
Section I: Multiple Choice
Part A: no calculator, 30 questions, 60 minutes
Part B: calculator, 15 questions, 45 minutes
Section II: Free Response
Part A: calculator, 2 questions, 30 minutes
Part B: no calculator, 4 questions, 60 minutes
· Each section is 50% of the overall score.
Day: Sections and topics/themes covered:
1 1.1 Four Ways to Represent a Function
2 1.2 Mathematical Models: A Catalog of Essential Functions
3 Poster of 1.2 topics
4 Summer packet questions
5 Test Summer packet and ways to rep. a function
6 2.1 Tangent and velocity problem (calculated numerically, graphically)
7 2.2 Limit of a function. (calculated numerically, graphically)
8 2.3 Calculating limits using the limit laws (analytically)
9 2.3 Calculating limits using the limit laws (analytically)
10 Limits (analytically, numerically, graphically)
11 2.4 Continuity
12 2.4 Continuity (Intermediate Value Theorem)
13 2.5 Limits involving infinity
14 2.5 Limits involving infinity
15 Review 2.1-2.5
16 Review 2.1-2.5
17 Test 2.1-2.5
18 2.6 Tangents, velocities, and other rates of change (calculated numerically, graphically)
19 2.6 Tangents, velocities, and other rates of change.
20 2.7 Derivatives (calculated analytically using the difference quotient)
21 2.8 The derivative as a function (calculated analytically using the difference quotient)
22 2.8 What does f’ and f” say about f and f’, and local extrema
23 Review 2.6-2.10
24 Test 2.6-2.10
25 3.1 Derivatives of polynomial and exponential functions
26 3.1 Derivatives of polynomial and exponential functions
27 3.2 The product and quotient rules.
28 3.3 Derivatives of the trigonometric functions
29 3.8 Rates of change in the natural and social sciences
30 3.4 The Chain Rule
31 3.4 The Chain Rule Day 2
32 3.5 Implicit Differentiation
33 3.5 Implicit Differentiation
34 3.6/3.7 Derivatives of inverse trig. And logarithmic functions
35 3.7 Logarithmic Differentiation
36 Review of chapter 3
37 Review of chapter 3
38 Test Ch 3
39 4.2 Global maximum and minimum. (analytically, verify graphically)
40 4.1 Related rates
41 4.1 Related rates continued
42 4.1 Related rates continued
43 4.3 Derivatives and the shape of curves (the first derivative test, concavity)
44 4.3 Derivatives and the shape of curves (The Mean Value Theorem, the second derivative test)
45 Review 4.1-4.3
46 4.5 Indeterminate forms and l’Hospital’s Rule
47 4.6 Optimization problems.
48 4.6 Including optimization problems and applications to economics.
49 Review of 4.1-4.6
50 Test 4.1-4.6
51 4.8 Antiderivatives
52 5.1 Areas and distances (numerically and graphically
53 5.2 The definite integral (graphically, verbally)
54 5.3 Evaluating definite integrals.( analytically)
55 5.3 Evaluating definite integrals and the Total Change Theorem
56 5.4 The Fundamental Theorem of Calculus (graphically)
57 5.4 The Fundamental Theorem of Calculus (analytically)
58 Review 4.9-5.4
59 Test 4.9-5.4
60 Semester Review
61 Semester Review
62 Semester Review
63 Semester Review
64 Final Exam
65 5.5 The substitution rule
66 5.5 The substitution rule
67 5.6 Integration by Parts
68 5.6 Integration by Parts
69 5.5/5.6 Review
70 5.9 Approx. integration (numerically, graphically, analytically) (Trapezoid Rule)
71 5.10 Improper Integrals
72 5.10 Improper Integrals
73 6.1 More about areas
74 6.2 Volumes (slices, disks and washers)
75 6.2 Volumes day two
76 6.2 Volumes day three
77 6.1/6.2 Review
78 6.4 Arc Length (parametric and functions of x or y)
79 6.5 Average value of a function, and applications of definite integral
80 6.6 Applications to Physics
81 Review of chapter six
82 Test over chapter six
83 7.2 Direction fields
84 7.3 Separable equations
85 7.4 Exponential growth and decay
86 Review of chapter seven
87 Quiz ch 7
Remaining days will cover review for the final and the AP test as well as projects after the AP test