CALCULUS I – FALL 2006:
CALCULUS I – FALL 2006
67-171-002 MTuWF 9:10 - 10:10 Swart 4
67-171-003 MTuWF 10:20 - 11:20 Swart 4
Instructor: Dr. Kandasamy Muthuvel
Office: Swart 243
Phone: 424-0301
Email: muthuvel<at>uwosh.edu
Office Hours: MTuWTh F 11:30 - 12:30
MW: 12:40-1:40 (Other times by appointment)
Required Calculus Concepts and Contexts (3rd edition) by James Stewart
Materials: The textbook will also be used for Calculus II (67-172) and Calculus III (67-273).
TI 83 PLUS GRAPHICS PROGRAMMABLE CALCULATOR.
(If you already have a TI-83, TI-85 or TI-86, you do not need to buy a TI-83 PLUS.)
TI-89 and TI-92 will not be allowed on exams and quizzes.
Course Chapter 1: Functions and Models (1.1-1.3, 1.5-1.7)
Coverage: Chapter 2: Limits and Derivatives (2.1-2.9)
Chapter 3: Differentiation Rules (3.1-3.8)
Chapter 4: Applications of Differentiation (4.1-4.3, 4.5-4.9)
Chapter 5: Integrals (5.1 if time permits)
Prerequisite: Math 108 or, Math 104 and 106, with grade(s) of C or better or a satisfactory
score on a placement examination.
Exams: There will be four one-hour exams and a final exam. Final exam will cover
selected topics from Chapters 2, 3,and 4.
Exam dates will be announced at least one week in advance.
Homework: Homework will be assigned each class. It will be posted on D2L. Students are
expected to come to class with the assignment completed and the next section
read. Homework will not be collected.
Quizzes: Every week when there is no exam, there will be a quiz. Quizzes cannot be taken early or made up at a later time. It is important that you keep up with the homework. Most of the problems on the quizzes are very similar to the homework problems.
Grading: Exam I: 16%, Exam II: 16%, Exam III: 16%, Exam IV: 16%
Quizzes 16%, Class Participation: 2%(This will be discussed in class.),
Final Exam: 18%
[90, 100) A, [87, 90) AB, [79, 87) B, [77, 79) BC, [69, 77) C, [57, 69) D,
Below 57 F
Attendance: Regular attendance is required.
I will be taking attendance daily.
Those having 3 or more unexcused absences will be penalized.
Class attendance and effort will be considered to decide borderline cases.
Attendance: Regular attendance is required.
I will be taking attendance daily.
Those having 3 or more unexcused absences will be penalized.
Class attendance and effort will be considered to decide borderline cases.
Content Goals:
1. Limits and Continuity:
Upon completion of the course, students should be able to demonstrate:
- An informal understanding of the limit concept: how to calculate a limit algebraically, numerically, or graphically.
- An understanding of the formal definition of continuity at a point.
- An understanding of how limits “at infinity” provide information about the long-term behavior of functions.
- The Definition of the Derivative:
Upon completion of the course, students should be able to:
- State the formal definition of the derivative of a function as the limit of a difference quotient.
- Find the derivative at a point as well as the general derivative of simple functions formally using the definition of the derivative.
- Approximate the derivative of a function at a point numerically from either tabular or graphical data.
- View the derivative (at a point) as the slope of a tangent line.
- View the second derivative of a function as a statement about the rate of change of the derivative, and the concavity of the function.
- Recognize and argue the fundamental relationship of velocity as an instantaneous rate of change of a displacement function, and acceleration as an instantaneous rate of change of velocity.
- Sketch the graph of the derivative (and second derivative) of a function, given a graph of the function.
- Derivative Shortcuts:
Upon completion of the course, students should be able to demonstrate competence in:
- Finding the derivative of polynomials.
- Finding the derivative of the basic trigonometric functions (including sine, cosine, tangent, arcsine and arctangent).
- Finding the derivative of logarithmic and exponential functions.
- Finding the derivatives of sums, differences, products and quotients of functions.
- Finding the derivatives of compositions of functions, using the chain rule.
- Finding the derivative a parametric function, using the chain rule.
- Finding the derivative of a function defined implicitly.
- Finding the derivative of general power functions.
In addition, students should also be exposed to
The proof of the power, product, and quotient rules for taking derivatives. - An intuitive argument for the chain rule.
- Applications of the Derivative:
Upon completion of the course, students should be able to demonstrate competence in:
- Interpreting statements such as f’ (a)=b and f’’(a)=b in terms of physical applications.
- Describing a function given information about its first and second derivatives. This encompasses:
- Understanding how to apply the first and second derivative tests to classify local extrema.
- Understanding how to use the second derivative to determine concavity and inflection points.
- Sketching a graph of a function incorporating extreme features and concavity.
- Modelling a physical situation with a function and optimizing that function to solve an applied extreme value problem.
- Finding derivatives of functions involving parameters and interpreting the corresponding situations, as in analyzing a family of curves.
- Using the tangent line interpretation of the derivative at a point to
- Find the linear approximation to a function near a given point.
- Approximate the change in a function using the tangent line near a point.
- Find the limit of an indeterminate quotient by using L’Hopital’s rule.
- Find a solution to an equation iteratively using Newton’s method.
- Theorems about Derivatives:
Upon completion of the course, students should understand the statements of:
- The Intermediate Value Theorem
- Rolle’s Theorem
- The Mean Value Theorem
- The Extreme Value Theorem
Students should also understand that - Differentiability of a function at a point implies continuity at that point.