Kuna High School

NNU LOGO CONCURRENT CREDIT SYLLABUS

1. Course Number and Title:

KHS NNU

Calculus MA 251 Calculus I

2. Course Description:

KHS- It is a full year course that will study limits, derivatives, integrals, and their applications. Daily written assignments are required in this class.

NNU- Limits, derivatives, integration and applications of the derivative, applications of integrals, integration techniques, logarithmic, exponential, trig and inverse trig functions.

3. Credit Hours: 2 high school math credits. 4 college credits from NNU Concurrent Credit.

4. Course Prerequisites:

KHS- A C-average in Pre-Calculus.

NNU- MA 130 – College Algebra with a grade of C or better.

5. Course Dates: August 26, 2008 to June 1, 2009

6. Course Times: Period 7

7. Course Location: Kuna High School room 213

8. Instructor: Pete Noteboom 955-0200 ext 2081 (classroom)

E-Mail: pnoteboom@kunaschools.org

9. Required Text and Other Learning Resources: Text provided by the school. It is recommended that students have a graphing calculator.

10. Course Overview: This course follows the one recommended for Calculus AB in the advanced placement program and Northwest Nazarene University. It is a full year course that will study limits, derivatives, integrals, and their applications. It is recommended that students have a graphing calculator. Daily written assignments are required in this class.

Functions, Graphs, and Limits

Analysis of graphs:

With the aid of technology, graphs of functions are often easy to produce. The emphasis is on the interplay between the geometric and analytic information and on the use of calculus both to predict and to explain the observed local and global behavior.

Limits of functions (including one-sided limits):

An intuitive understanding of the limiting process
Calculating limits using algebra
Estimating limits from graphs or tables of data

Asymptotic and unbounded behavior:

Understanding asymptotes in terms of graphical behavior
Describing asymptotic behavior in terms of limits involving infinity
Comparing relative magnitudes of functions and their rates of change. (For example, contrasting exponential growth, polynomial growth, and logarithmic growth.)

Continuity as Properties of Functions:

An intuitive understanding of continuity (Close values of the domain lead to close values of the range.)
Understanding continuity in terms of limits
Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme value Theorem)

Derivatives

Concept of the Derivative:

Derivative presented graphically, numerically, and analytically
Derivative interpreted as an instantaneous rate of change
Derivative defined as the limit of the difference of a quotient
Relationship between differentiability and continuity

Derivative at a Point

Slope of a curve at a point. Examples are emphasized, including points at which there are vertical tangents and points at which there are no tangents.
Tangent line to a curve at a point and local linear approximation
Instantaneous rate of change as the limit of average rate of change
Approximate rate of change from graphs and tables of values

Derivative as a Function

Corresponding characteristics of graphs of f and f’
Relationship between the increasing and decreasing behavior of f and the sign of f’
The Mean Value Theorem and its geometric consequences
Equations involving derivatives. Verbal descriptions are translated into equations involving derivatives and vice-versa

Second Derivatives

Corresponding characterists of the graphs of f, f’, and f’’
Relationship between the concavity of f and the sign of f’’
Points of inflection as places where concavity changes

Applications of Derivatives

Analysis of curves, including the notions of monotonicity and concavity
Optimization, both absolute (global) and relative (local) extrema
Modeling rates of change, including related rates problems
Use of implicit differentiation to find the derivative of an inverse function
Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration
Geometric interpretation of differential equations via slope fields and solution curves for differential equations

Computation of Derivatives

Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions
Basic rules for the derivative of sums, products, and quotients of functions
Chain rule and implicit differentiation

Integrals

Interpretations and Properties of Definite Integrals

Computation of Riemann sums using left, right, and midpoint evaluation points
Definite integral as a limit of Riemann sums over equal subdivisions
Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval:
Basic properties of definite integrals (Examples include additivity and linearity)

Applications of Integrals

Appropriate integrals are used in a variety of applications to model physical, biological, or economic situations. Although only a sampling of applications can be included in any specific course, students should be able to adapt their knowledge and techniques to solve other similar application problems. Whatever applications are chosen, the emphasis is on using the integral of a rate of change to give accumulated change or using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. To provide a common foundation, specific examples should include finding the area of a region, the volume of a solid with known cross sections, the average value of a function, and the distance traveled by a particle along a line.

Fundamental Theorem of calculus

Use of the Fundamental Theorem to evaluate definite integrals
Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined

Techniques of Antidifferentiation

Antiderivatives following directly from derivatives of basic functions
Antiderivatives by substitution of variables (Including change of limits for definite integrals)

Applications of Antidifferentiation

Finding specific antiderivatives using initial conditions, including applications to motion along a line
Solving separable differential equations and using them in modeling. In particular, studying the equation y’=ky and exponential growth

Numerical Approximations to Definite Integrals

Use of Riemann and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values

11. Course Objectives: Upon completion of this course, students should be able to do the following:

• To understand the statement and the uses of some theorems concerning limits.

• To understand the statement and some of the uses of certain basic theorems of differential and integral calculus (e.g. Max-Min Theorem, Mean Value Theorem, Fundamental Theorem of Calculus)

• To practice the techniques and applications of differentiation and integration

12. Course Calendar/Schedule: (May state as tentative).

a. 1st Quarter: Analysis of graphs, Limits of functions, Asymptotic and unbounded behavior, Continuity as Properties of Functions:

2nd Quarter: Derivatives, Concept of the Derivative, Derivative at a Point Derivative as a Function, Second Derivatives, Applications of Derivatives, Computation of Derivatives

3rd Quarter: .Integrals, Interpretations and Properties of Definite Integrals, Applications of Integrals, Fundamental Theorem of calculus, :

4th Quarter: Techniques of Antidifferentiation, Applications of Antidifferentiation, Numerical Approximations to Definite Integrals

b. Assignments will be given each class period and due the next class.

c. Chapter exams will be given on approximately the following dates:

NNU EXAM September 4, 2008

September 18-19, 2008 October 21-22, 2008

November 19-20, 2008 1st semester Final: Jan 12-16, 2009

February 10-11, 2009 March 12-13, 2009

April 23-24, 2009 2nd semester Final: May 19-22, 2009

There are lots of factors that can change these dates like shortened school days, assemblies, class meetings, weather, graduation, etc.

13. Grading Policy and Rubric:

All assignments, quizzes, and tests must be written in pencil. Work written in pen will not be accepted. Students must show their work and give thorough explanation to receive full credit. All work will be graded for accuracy of content, clarity of explanation, and presentation. Graded work may include but may not be limited to the following:

Your letter grade will be determined by the percentage of total points you have accumulated through homework and notes (25%), tests (50%), and the final exam each semester (25%). The grading scale is:

A 90-100%

B 80-89%

C 70-79%

D 60-69%

F Below 60%

14. Course Policies:

I do not give test retakes.

***All work missed due to an unexcused absence will receive a zero. ***

Late assignments will be accepted for one-half credit.

Make-Up Work:

If an absence is excused, students will be allowed to make-up the missed work. Each student will be given two (2) days for each day absent to make up work. It is the student’s responsibility to determine what work was missed on the day of the absence. It is the student’s responsibility to schedule a time with the instructor to make-up quizzes or tests. All work missed due to an unexcused absence will receive a zero. An absence is considered to be excused if a parent/guardian contacts the school, either in writing or by phone, by the second day of return to school.

Hall Passes:

In order for students to be successful in mathematics, attendance through out the entire class period is necessary. In some situations leaving a cell phone will be required to use the restroom. Hall passes may not be used during a lesson or in class activity. In addition, hall passes will not be issued during the first ten minutes of the period or the final ten minutes of the period. You will not be excused from class for any reason without a note from the office.

Discipline Policy

In this class you are expected to act in a mature manner and to follow all Kuna High School rules. In order to insure that all students will have the opportunity to learn, the following rules will be observed:

Follow directions.
Come to class prepared: on time (must be in the room when the bell rings), with paper, pencil (not pen), homework assignment and book.
Remain in your assigned seat unless directed to do otherwise by your teacher.
Use your class time well.
Do not disturb others.

Students who do not comply with the rules will be subject to the following consequences. All consequences are cumulative. Severe misconduct is subject to immediate office referral.

Warning by the teacher
Parents are notified.
Student referred to the office.

*The instructor reserves the right to make any necessary changes.

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NNU- Limits, derivatives, integration and applications of the derivative, applications of integrals, integration techniques, logarithmic, exponential, trig and inverse trig functions. 3. Credit Hours: 2 high school math credits. 4 college credits from NNU Concurrent Credit. 4. Course Prerequisites: KHS- A C-average in Pre-Calculus. NNU- MA 130 – College Algebra with a grade of C or better. 5. Course Dates: August 26, 2008 to June 1, 2009 6. Course Times: Period 7 7. Course Location: Kuna High School room 213 8. Instructor: Pete Noteboom 955-0200 ext 2081 (classroom) E-Mail: pnoteboom@kunaschools.org 9. Required Text and Other Learning Resources: Text provided by the school. It is recommended that students have a graphing calculator. 10. Course Overview: This course follows the one recommended for Calculus AB in the advanced placement program and Northwest Nazarene University. It is a full year course that will study limits, derivatives, integrals, and their applications. It is recommended that students have a graphing calculator. Daily written assignments are required in this class. Functions, Graphs, and Limits Analysis of graphs: With the aid of technology, graphs of functions are often easy to produce. The emphasis is on the interplay between the geometric and analytic information and on the use of calculus both to predict and to explain the observed local and global behavior. Limits of functions (including one-sided limits): An intuitive understanding of the limiting process Calculating limits using algebra Estimating limits from graphs or tables of data Asymptotic and unbounded behavior: Understanding asymptotes in terms of graphical behavior Describing asymptotic behavior in terms of limits involving infinity Comparing relative magnitudes of functions and their rates of change. (For example, contrasting exponential growth, polynomial growth, and logarithmic growth.) Continuity as Properties of Functions: An intuitive understanding of continuity (Close values of the domain lead to close values of the range.) Understanding continuity in terms of limits Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme value Theorem) Derivatives Concept of the Derivative: Derivative presented graphically, numerically, and analytically Derivative interpreted as an instantaneous rate of change Derivative defined as the limit of the difference of a quotient Relationship between differentiability and continuity Derivative at a Point Slope of a curve at a point. Examples are emphasized, including points at which there are vertical tangents and points at which there are no tangents. Tangent line to a curve at a point and local linear approximation Instantaneous rate of change as the limit of average rate of change Approximate rate of change from graphs and tables of values Derivative as a Function Corresponding characteristics of graphs of f and f’ Relationship between the increasing and decreasing behavior of f and the sign of f’ The Mean Value Theorem and its geometric consequences Equations involving derivatives. Verbal descriptions are translated into equations involving derivatives and vice-versa Second Derivatives Corresponding characterists of the graphs of f, f’, and f’’ Relationship between the concavity of f and the sign of f’’ Points of inflection as places where concavity changes Applications of Derivatives Analysis of curves, including the notions of monotonicity and concavity Optimization, both absolute (global) and relative (local) extrema Modeling rates of change, including related rates problems Use of implicit differentiation to find the derivative of an inverse function Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration Geometric interpretation of differential equations via slope fields and solution curves for differential equations Computation of Derivatives Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions Basic rules for the derivative of sums, products, and quotients of functions Chain rule and implicit differentiation Integrals Interpretations and Properties of Definite Integrals Computation of Riemann sums using left, right, and midpoint evaluation points Definite integral as a limit of Riemann sums over equal subdivisions Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval: Basic properties of definite integrals (Examples include additivity and linearity) Applications of Integrals Appropriate integrals are used in a variety of applications to model physical, biological, or economic situations. Although only a sampling of applications can be included in any specific course, students should be able to adapt their knowledge and techniques to solve other similar application problems. Whatever applications are chosen, the emphasis is on using the integral of a rate of change to give accumulated change or using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. To provide a common foundation, specific examples should include finding the area of a region, the volume of a solid with known cross sections, the average value of a function, and the distance traveled by a particle along a line. Fundamental Theorem of calculus Use of the Fundamental Theorem to evaluate definite integrals Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined Techniques of Antidifferentiation Antiderivatives following directly from derivatives of basic functions Antiderivatives by substitution of variables (Including change of limits for definite integrals) Applications of Antidifferentiation Finding specific antiderivatives using initial conditions, including applications to motion along a line Solving separable differential equations and using them in modeling. In particular, studying the equation y’=ky and exponential growth Numerical Approximations to Definite Integrals Use of Riemann and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values 11. Course Objectives: Upon completion of this course, students should be able to do the following: • To understand the statement and the uses of some theorems concerning limits. • To understand the statement and some of the uses of certain basic theorems of differential and integral calculus (e.g. Max-Min Theorem, Mean Value Theorem, Fundamental Theorem of Calculus) • To practice the techniques and applications of differentiation and integration 12. Course Calendar/Schedule: (May state as tentative). a. 1st Quarter: Analysis of graphs, Limits of functions, Asymptotic and unbounded behavior, Continuity as Properties of Functions: 2nd Quarter: Derivatives, Concept of the Derivative, Derivative at a Point Derivative as a Function, Second Derivatives, Applications of Derivatives, Computation of Derivatives 3rd Quarter: .Integrals, Interpretations and Properties of Definite Integrals, Applications of Integrals, Fundamental Theorem of calculus, : 4th Quarter: Techniques of Antidifferentiation, Applications of Antidifferentiation, Numerical Approximations to Definite Integrals b. Assignments will be given each class period and due the next class. c. Chapter exams will be given on approximately the following dates: NNU EXAM September 4, 2008 September 18-19, 2008 October 21-22, 2008 November 19-20, 2008 1st semester Final: Jan 12-16, 2009 February 10-11, 2009 March 12-13, 2009 April 23-24, 2009 2nd semester Final: May 19-22, 2009 There are lots of factors that can change these dates like shortened school days, assemblies, class meetings, weather, graduation, etc. 13. Grading Policy and Rubric: All assignments, quizzes, and tests must be written in pencil. Work written in pen will not be accepted. Students must show their work and give thorough explanation to receive full credit. All work will be graded for accuracy of content, clarity of explanation, and presentation. Graded work may include but may not be limited to the following: Your letter grade will be determined by the percentage of total points you have accumulated through homework and notes (25%), tests (50%), and the final exam each semester (25%). The grading scale is: A 90-100% B 80-89% C 70-79% D 60-69% F Below 60% 14. Course Policies: I do not give test retakes. *All work missed due to an unexcused absence will receive a zero. * Late assignments will be accepted for one-half credit. Make-Up Work: If an absence is excused, students will be allowed to make-up the missed work. Each student will be given two (2) days for each day absent to make up work. It is the student’s responsibility to determine what work was missed on the day of the absence. It is the student’s responsibility to schedule a time with the instructor to make-up quizzes or tests. All work missed due to an unexcused absence will receive a zero. An absence is considered to be excused if a parent/guardian contacts the school, either in writing or by phone, by the second day of return to school. Hall Passes: In order for students to be successful in mathematics, attendance through out the entire class period is necessary. In some situations leaving a cell phone will be required to use the restroom. Hall passes may not be used during a lesson or in class activity. In addition, hall passes will not be issued during the first ten minutes of the period or the final ten minutes of the period. You will not be excused from class for any reason without a note from the office. Discipline Policy In this class you are expected to act in a mature manner and to follow all Kuna High School rules. In order to insure that all students will have the opportunity to learn, the following rules will be observed: Follow directions. Come to class prepared: on time (must be in the room when the bell rings), with paper, pencil (not pen), homework assignment and book. Remain in your assigned seat unless directed to do otherwise by your teacher. Use your class time well. Do not disturb others. Students who do not comply with the rules will be subject to the following consequences. All consequences are cumulative. Severe misconduct is subject to immediate office referral. Warning by the teacher Parents are notified. Student referred to the office. *The instructor reserves the right to make any necessary changes.
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