SYLLABUS

Aztec High School Calculus

Articulated with San Juan College Math 188

2008-2009

 

 

Parent/Guardian Communication:

          It is the responsibility of the student and guardian to please ask or call me if you have questions

 or concerns about this class.  I will send a progress report home every other Friday.  I generally do not call about grades or attendance unless progress reports have not been returned or if a student has over five unverified absences.  If you need to have an update on grades, attendance, or any other matter, please call at anytime.  It is your responsibility to communicate with your student or call me to stay up to date on grades and attendance.  I do not answer the phone during class but if you leave a message I will return your call as soon as possible.  334-9414 ext 1356

Course Description:

This class will answer all of the important questions in life such as how to find the surface area and volume of Navajo Lake, the volume of a donut (torus), how long it takes for a cup of hot chocolate to cool down (Newton’s law of cooling), and the speed of a rocket when it hits the ground.  We will also find out how fast balloons blow up, find the angle that gives a discus maximum distance and how to build a better cereal box. We will be introduced to the ideas of Sir Isaac Newton, Gottfried Liebnitz, and Michel Rolle.  Other interesting topics include (but are not limited to) finding the area under a curve, solving simple differential equations, finding fluid forces (diving and engineering), calculating the work required to empty an oil tank, and finding the work required to open a screen door.  The course is divided into a study of limits, differentiation, integration, and applications.  Students will be encouraged to receive college credit either through San Juan College concurrent enrollment or through the Advanced Placement AP exam given in May.

1^st 9-weeks: Graphing, functions, slopes, limits, derivatives, product/quotient rules, chain rule, implicit differentiation and related rates

2^nd 9-weeks: Rolle’s Thm., mean value, optimization, Newtons method, Integration, Riemann Sums and Fundamental Thm. of Calc

3^rd 9-weeks: Logs, Exponentials, Transcendentals, area /volumes of solids, surfaces of revolution, arc lengths, centroids, fluid pressure

4^th 9-weeks: prep for AP Calc AB exam, advanced topics, integration by parts, trig substitutions, partial fractions and L’Hopitals Rule

This is a rigorous, college level AP class that will require consistent effort throughout the course.  Study groups are encouraged.

 

Expectations:

Each student will be given the opportunity to receive college credit for this course.   The preferred option is to take the AP CalcAB exam in early May.  A score of 3 or higher will grant college credit at most universities worldwide. Students are not required to take the AP exam, but will complete all class assignments and prepare for the exam regardless.  Successful completion of San Juan College concurrent enrollment will also grant credit at San Juan College for Calculus.   To qualify, each student will be required to pass a pretest, have a grade of C or better in Calculus and pass the San Juan College test with a 70% or better.  I expect each student to complete all tasks on time and be prepared to work each day, put forth honest effort, and contribute to our class in a positive manner.  I value hard work, responsibility, and integrity. 

 

 

Rules:

 

1.        NO TALKING OUT OF TURN

2.        NO CELL PHONES OR HEADPHONES

 

  -All other SCHOOL RULES as found in the AHS Student Handbook

 

Consequences:

 

1.        Verbal Warning 

2.        Classroom service and/or detention and/or student-teacher conference

3.        Classroom service and/or detention and/or parent-teacher conference

4.      Office Referral

 

Tardy Policy:

Students are expected to be in the classroom when the tardy bell rings

1^st & 2^nd :  Warning

3^rd – 5^th : Lunch Detention and Parent Contact

6^th + : After school detention

 

Grading Policy:

Daily Assignments: 35% of total grade

Tests/Quizzes:  50% of total grade

Midterm/Final: 15% of total grade

         

 All WORK MUST BE SHOWN on each problem or no credit will be given. Late work will be accepted up until the test on each unit is given.  If your semester homework average is >85%, one test score may be dropped.  Class notes will be required and will count 10% of each unit test.  Test retakes are permitted (deadlines and details will be given in class).   Some extra credit opportunities will be provided, details will be given in class.  As always, no credit will be given for cheating, so please don’t compromise your integrity!

 

If you have any questions or wish to contact me please call or email:

Mr. James Jacobs:  334-9414 ext 1356;   [email protected]

 

If you have additional questions about policies in my classroom, please refer to the AHS student handbook.  Please ASK if you have any question.

 

 

 

The Following is the Syllabus for San Juan College Math 188

 

 

COURSE # & TITLE:                       MATH 188, Calculus I                          # OF CREDITS: 4 (3+2P)

 

CATALOG DESCRIPTION:

Instructs the student in the methods of differential calculus.  Topics include elementary algebraic and transcendental functions, limits, continuity, differentiations and optimization.  Other topics include L’hopital’s rule, Newton’s method, Riemann sums, indefinite & definite integration, and the fundamental theorem of calculus.  Mathematical software will be utilized throughout the course to expose students to computer algebra systems.

 

Semester Offered:              Fall, Spring, Summer

Prerequisites:                      Grade of “C” or better in Math 185; College Algebra and Math 180; Trigonometry

 

 

GENERAL LEARNING OUTCOMES:

Upon completion of the course, the student should understand the following content areas:

 

1.)    Functions and their representations.

2.)    The Derivative.

3.)    Techniques of Differentiation.

4.)    Application of the Derivatives.

5.)    The Definite & Indefinite Integral.

6.)    Numerical Interpretations.

7.)    Emphasis on Theories & Theorems.

 

 

OUTCOMES:

Upon completion of this course, the student should be able to:

 

1.1   Good foundation of defining, recognizing and interpreting a Function.

1.2   Represent the following functions algebraically, graphically and numerically

-          Linear

-          Power

-          Inverse

-          Trigonometric

-          Exponential

-          Logarithmic

1.3   Recognize the types of problems that are modeled by the functions in 1.2

1.4   Explain the effect of varying parameters on the graphs of the functions in 1.2

1.5   Interpret the different definitions and formulas of the functions in 1.2

1.6   Recognize the functional notation, domain & range of a function and the composition of functions in 1.2

1.7   Understand the criteria for the existence of an inverse function, graph of an inverse function and inverse trigonometric functions and identities.

1.8   Describe the relationships between exponential and logarithmic functions.

 

2.1 Give a general description or definition of Calculus.

2.2 Describe the intuitive notion of limits by graphing and tables.

2.3 Recognize the existence or nonexistence of limits, the formal definition of a limit of a function.

2.4 Understand the Basic Properties & Rules for Limits

2.5 Algebraic methods to compute and find limits, also piecewise-defined functions.

2.6 Interpret the concept of Continuity/Discontinuity, involving the Intermediate Value Theorem.

 

3.1 Identify tangent lines, slope of a tangent line of a graph at a point.

3.2 Compute the Difference Quotient.

3.3 Know the concepts of the Derivative and recognize the graphical representation of the derivative.

3.4 Utilize the derivative of Constant, Power functions and the properties involved.  Along with higher

      derivatives.

3.5 Recognize the relationship between the graph of a function and the graph of its derivative.

3.6 Identify the derivatives of the sine, the cosine, and other trigonometric functions. 

3.7 Identify the derivatives of Exponential and Logarithmic functions.

3.8 Recognize and distinguish between Average & Instantaneous Rate of Change.

3.9 Understand the Chain Rule and justification of the Chain Rule.

3.10 Know the general procedure for Implicit Functions.

3.11 Model application problems involving rates of change.

3.12 Interpret results achieved by Local Linearization or Tangent Line Approximation & Differentials.

 

4.1 Describe the following concepts and their relationship to the first and second derivatives:

-          Maxima and Minima

-          Concavity

-          Inflection Points

4.2 Use the first and second derivative tests to find the relative and local extrema.

4.3 Find the absolute extrema of a function on an interval.

4.4 Describe the Mean Value Theorem and Rolle’s Theorem.

4.5 Recognize curves: limits involving Infinity and Asymptotes.

4.6 Model various Optimization applications

-          Physical Science

-          Engineering

-          Business

-          Economics

-          Life Sciences

4.7 Use l’Hopital’s Rule and identify Indeterminate forms.

 

5.1 Recognize Reverse Differentiation, Anti-derivative notation, Anti-differentiation formulas.

5.2 Describe the area as a limit of a sum.

5.3 Compute Right-Hand and Left-Hand Riemann Sums.

5.4 Know when the Riemann sum is an overestimate and an underestimate of areas.

5.5 Use the Fundamental Theorem of Calculus to evaluate definite integrals.

5.6 Use the Second Fundamental Theorem of Calculus.

5.7 Compute anti-derivatives and Indefinite Integrals.

5.8 Know how to use the Substitution Method of integration for definite and indefinite integrals.

5.9 Use the Mean Value Theorem for Integrals; Average Value.

5.10 Compute and recognize Numerical Integration: The Trapezoidal & Simpson’s Rule.

5.11 Use the Natural Logarithm as an integral.

 

6.1 Use technology to aid in the solution of calculus problems.

6.2 use a computer algebra system to make calculations and graph functions.

6.3 Describe the limitation of technology in finding the exact solution.

 

 

OTHER REQUIREMENTS:

The TI-82, TI-83, TI-84, TI-85 or TI-86 graphing calculator is required for the course.  A TI-83 Plus or TI-84 Plus Graphing Calculator is strongly recommended.  Graphing calculators capable of symbolic manipulation (such as TI-89 or TI-92 and other such calculators) will not be allowed on examinations, the final exam and where the instructor finds fit.

 

 

 

 

 

 

 

 

 

 

Please return this section to Mr. Jacobs

 

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I have read and understand the syllabus for Mr. Jacobs Calculus class.

 

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