Approved by University Studies sub-committee 2/21/07. A2C2 action pending.
Math 160 - Calculus I
Fall 2006
Text: Early Transcendentals by James Stewart
Chapters Covered:
Chapter 1: Functions and Models
Chapter 2: Limits and Derivatives
Chapter 3: Differentiation Rules
Chapter 4: Applications of Differentiation
Chapter 5: Integrals
Chapter 6: Applications of Integration
Chapter 7: Techniques of Integration
For additional information about the learning outcomes for this course please see below.
Instructor: Felino G. Pascual
Office: Gildemeister 303
Office Phone: 457-5378 (Gi 303)
457-5370(Math and Stat Office)
Email Address:
Fax: 457-5376
URL: http://course1.winona.edu/fpascual
Office Hours: 9:00 - 9:50 MF
11:00 am - 12:00 pm MF
1:30 - 4:00 pm M
2:00 - 3:00 pm TTh
1:30 - 3:00 pm F
or by appointment
Evaluation Procedure: Exams, homework and quizzes will be used for the determination of the
final grade. There will be 4 exams (100 points each) and one cumulative final exam
(200 points). The total score from the homework and quizzes will be scaled so as to add up to
200 points.
4 exams (100 points each) 400
1 Final Exam 200
Homework and Quizzes 200
------
Total 800 points
90% will be sufficient for a grade of A 70% will be sufficient for a grade of C
80% will be sufficient for a grade of B 60% will be sufficient for a grade of D
IMPORTANT: There will be no make-up for any of the exams or quizzes except for emergency cases. Homework must be submitted by the due date. Cheating and unruly behavior will not be tolerated. Warnings will be issued. Students who disregard the warnings will merit a grade of "E" for the course.
The Schedule for the Fall
Sept. 5 - 8
Sept. 11 - 15
Sept. 18 - 22
Sept. 25 - 29
Oct. 2 - 6
Oct. 9 - 13
Oct. 16 - 20
Oct. 23 - 27
Oct. 30 - Nov. 3
Nov. 6 - 10
Nov. 13 - 17
Nov. 20 - 21
Nov. 27 - Dec. 1
Dec. 4 - 6 / Overview of Chapter 1, 2.1 - 2.3
2.4 - 2.6
2.7 - 2.9
3.1 - 3.5
3.5 - 3.7
3.8 - 3.11
4.1 - 4.3
4.4 - 4.7
4.9*, 4.10, 5.1
5.1 - 5.2
5.3 - 5.5
5.6
6.1 - 6.3
6.5
7.1
Midterm Exams:
Sept. 21
Oct. 17
Nov. 7
Nov. 30
Final Exam:
Part I: 10:00 - 10:50 am on Dec. 7, Thursday
Part II: 10:00 - 10:50 am on Dec. 8, Friday
This course can be used to satisfy the University Studies requirements for Basic Skills in Mathematics. This course includes requirements and learning activities that promote students’ abilities to...
a. use logical reasoning by studying mathematical patterns and relationships;
· provide examples of functions which are differentiable, continuous, both, either, or neither and explain which condition(s) implies the other and why
· explain why continuous functions satisfy intermediate value theorem
· explain the implication of speed with derivatives
· explain why and how x has to be close to a number a for f(x) to be close to a number L
· explain the connection of rise/run with derivatives when run is too small
· explain the limitations on the conclusions that can be drawn about a function from knowledge of its first derivative, providing an example from a physical phenomenon which demonstrates these limitations
· explain the limitations on the conclusions that can be drawn about a function from knowledge of its second derivative, providing an example from a physical phenomenon which demonstrates these limitations
· explain the relationship of composition of two or more functions with chain rule
· accurately apply the logical understanding of the inverse function to find the derivatives of the inverse trig functions
· apply chain rule to understand implicit differentiation
· understand logical reasoning behind local linearity
· understand logical reasoning behind the concept of first and second derivative tests
b. use mathematical models to describe real-world phenomena and to solve real-world problems - as well as understand the limitations of models in making predictions and drawing conclusions;
· accurately model situations using related rates and solve the resulting equations using implicit differentiation and/or the chain rule.
· accurately model situations involving optimization, identify the constraints, and find the optimal value of the relevant variable
· accurately graphs involving optimization of real-world problems
· accurately apply the theory of optimization to marginality
· find total value of a relevant function knowing its rate of change
c. organize data, communicate the essential features of the data, and interpret
the data in a meaningful way;
· accurately sketch a graph using data
· accurately interpret the behavior of a function representing a physical phenomenon using the given data set
· use data to find average and instantaneous rate of change of a function and/or the rate of increasing or decreasing of a function
· use data to find the limiting value of a function
· use data to find upper and lower estimates for a certain quanity for e.g. given a data relating speed (mph) and corresponding fuel efficiency (mpg) find the lower and upper estimates of the quantity of fuel used
d. do a critical analysis of scientific and other research;
· do assigned projects or group work which requires mathematical research and investigations using course topics.
e. extract correct information from tables and common graphical displays, such as line
graphs, scatter plots, histograms, and frequency tables;
· given the graph of a rational function or a polynomial, f(x), determine a reasonable form for its algebraic expression
· given a graph, what does the concavity of the graph says about the growth of the function
· given the graph of position, s(t), of an object in directed linear motion, correctly the intervals for t over which the object is moving right/left, accelerating/decelerating, speeding up/slowing down, and any combination of these.
· given a graph of a function find the total change
· given the graph of the velocity, v(t), of an object in directed linear motion, correctly the intervals for t over which the object is moving right/left, accelerating/decelerating, speeding up/slowing down, and any combination of these, when possible.
· given the graph of a function, f(x), correctly sketch the graph of its derivative, labeling the critical points and points of inflection for f(x) and determining the corresponding points on the derivative.
· given the graph of the derivative of a function, sketch the original function.
f.use appropriate technology to describe and solve quantitative problems.
· demonstrate proficiency in using the TI-89 to solve messy algebraic equations and compute integrals and derivatives that arise from real-world problems with real data.
· use a spreadsheet and various numerical methods to estimate the value of the integral of an unknown function whose values we know at a finite number of points