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Syllabus for Calculus I

1) Name & Title: Richard Ganns, Instructor
2) Office location: 35-256; office hours: 7:20 – 7:50 and 10:00 – 10:30 a.m. daily, and any
time my door is open. Office hours are subject to adjustment;
Phone number: (360) 596-5482.

1) Title: Math 151 Calculus I; Section: F ; Quarter: Winter 2009;
Room number: 35-351; Hours: noon – 1:05 p.m. MTWF.
2) List of prerequisites and their justification: Math 141 and Math 142 or appropriate testing.
These skills and knowledge are essential foundations for continuing development in Math
151 and beyond. 3) Supplemental materials: see below.

1) Calculus, Volume 1, 2nd Edition, by Ostebee and Zorn.
2) Instructor’s Supplement Packet (sold in the bookstore)
3) Homework Solutions Supplement Packet (sold in the bookstore)
4) An inexpensive scientific calculator: If you want a graphing calculator (optional), Texas
Instruments (TI) calculators are popular on many campuses. This brand is not required, but
is recommended because support is usually readily available, and the use of TI models is
required in some courses and programs both at SPSCC and at other schools. Bring your
calculator to class daily; do not plan to borrow one in class. A graphing calculator is helpful
but not required. Calculator tutorials may be available through the bookstore or Mathware
(phone 1-800-255-2468). Note that calculators
will not always be allowed on quizzes. An optional but useful freeware program “MPP” can
be obtained from the instructor; it will run on Windows, and provides a wide range of useful

1) College Wide Abilities for AA that are addressed in this course:
• Effective oral and written communication
• The ability to apply fundamental quantitative skills
• The ability to think logically and critically
• The ability to integrate and synthesize knowledge
2) Specific Learning Objectives for this course:
Upon the successful completion of this course, the student will be able to (with regard to
the leading topic):

Define and compute average and instantaneous rates of changes of functions
Construct accurate graphs of functions via pencil and paper
Define and compute first and second derivatives
Estimate derivatives graphically and numerically
Describe the geometry of first and second derivatives
Define continuity at a point and on an interval
Compute derivatives of elementary functions
Define limit and compute limits of functions
State and use basic derivative formulas for various elementary functions
Recognize selected simple ordinary differential equations and their use in modeling motion
State and use the product and quotient rules for derivatives
State and use chain rule for derivatives
Execute implicit differentiation and interpret the results geometrically
Solve simple optimization problems
Solve simple related rates problems
State and describe: Intermediate, Extreme, and Mean Value Theorems
Describe the bisection method for determining roots of functions
Use personal computer graphing technology in selected exercises
Solve additional selected physical application problems as time permits
State and use Newton’s method as time permits

1) General description, topics to be covered: The first course in a series of four in calculus.
Topics include:

Estimating derivatives
Geometry of derivatives
Geometry of Second derivatives
Defining the derivative
Derivatives of polynomials, EVT
Derivative formulas
Log/Exp derivatives
Sine, cosine derivatives.
Product, quotient rules
Chain rule
Implicit differentiation
Derivatives: more practice
Related rates
IVT, EVT, bisection method
Newton’s method [if time]
Use of computer algebra and graphing technology
Selected physical applications as time permits
ODEs, modeling motion (if time permits)

2) General instructional methods: Lecture, class discussion, group work in and out of class.

Final Grades: will be available through the touch-tone system early in the week following final exams
and via the campus website. You may also request notification via e-mail (give
the instructor you address).

Plagiarism: All work submitted for a grade must be the student's own: copying from any
unacknowledged source may result in a failing grade for the course and possible disciplinary action by
the college including expulsion. On in-class tests, this simply means: don't look at your neighbor's
paper, and don't use unapproved notes or calculators.

More formally: “Academic honesty: Breach of any of the categories (cheating and plagiarism) found in
the document Statement of Academic Honesty may result in dismissal from the college as outlined in
the Code of Student Rights and Responsibilities. A copy of the document on Academic Honesty may
be found on the SPSCC intranet. Knowledge of the information contained in these documents is the
student’s responsibility.”

1) Daily or weekly schedule for this section of this course: see attached tentative calendar.
2) Due dates for exams: see attached tentative calendar.
3) Use of packets that students might buy at the bookstore: a supplement packet is required (be
sure to get the one with the instructor’s name on it), and a scientific calculator.


* Topics from Math 140 College Algebra and Math 141 Precalculus I:

- Exponents, radicals : ability to manipulate, simplify, rationalize numerator/denominator
- Expressions: manipulate, simplify
- Equations: manipulate & solve linear, quadratic, radical, rational
- Story problems: variable declaration , organization, justification of equations;
- Inequalities : linear, compound, nonlinear, absolute-valued; sign diagram method of solving
- Cartesian plane graphs: linear, quadratic, power function, root function, rational; symmetry
tests for relations;
- Elementary functions: notation, domain, range, even/odd, combinations, composites; NOTE:
this includes log and exponential functions;
- Absolute value function:
- Quadratic functions : factoring, completing the square, graphing, solving for roots:
- Inverse functions: definition, notation, domain & range, graphing;
- Polynomial functions: factoring , dominant terms ;
- Division; remainder theorem; polynomial long division , synthetic division
- Solving Pn(x) = 0 using Descartes’ rule of signs, root theorems, rational root theorem, synthetic
- Rational functions: domain, asymptotes, graphing;
- Exponential functions: base-e and general base, notation, properties , graphs, growth and decay
- Logarithmic functions: base-e and general base, notation, properties, graphs, equations;
- Log & exponential models: fitting curves to data; finding doubling times and half-lives;
- Log/exp. equations; base change formula;
- Compound interest formula;
- Geometric objects: circle, sphere, cone, cylinder, triangle;

* Topics from Math 142 Precalculus II:

- Angles: definition of radian; conversion between radians and degrees;
- Trig functions : names, relations, domains, ranges, graphs, right-triangle & unit circle
- Identities: basic knowledge, ability to manipulate, develop, prove
- Equations: solving on intervals and on
- Reference angle and standard reference triangles, use in evaluating functions and solving
- Addition formulas, multi-angle formulas;
- Inverse functions: graphs, use in solving problems, trigonometric substitution ;
- Laws of sines, cosines use in applications;
- Trigonometric substitution;
- Vectors: notation, definitions, properties, unit vectors, use in applications, force, velocity,
- Polar coordinates: conversions from/to Cartesian; polar graphs;
- Parametrized curves;
- Conic sections: able to complete the square in second degree expressions and equations and
graph the conic sections (focus, directrix not needed);
- Nonlinear systems involving second degree equations: represent solution sets as intersections of
conic sections


Text # Days Topics Assigned Homework Problems
1.1 Functions 1-41 odd
1.2 3 Graphs 1-53 odd, 59-65 odd
1.3 3 Functions 1-49 odd
1.4 Rates 1-33 odd, 34, 35, 41, 43, 44, 45-63 odd
1.5 1 Estimating derivatives 1-27 odd, 30
1.6 Geometry of derivatives 1-15 odd, 16-19, 21-23, 25-32, 34, 46, 49, 50, 53, 54
1.7 ½ Geometry of 2nd derivatives 1-15 odd, 16-19, 24-27, 30-33, 35, 36
2.1 2 Defining the derivative 1, 3, 5, 7-11, 29, 31, 33-37, 41-45, 47-53, 55, 57
2.2 1 Derivatives of polynomials EVT; 1-37 odd, 45-55 odd, 61, 63, 65, 66, 68, 69
2.3 5 Limits 1-9 odd, 4, 8, 10-26, 27-35 odd, 37, 39-55, 57, 58,
      61, 63-68
2.4 1 Derivative formulas 1-11, 13-19, 21-27 odd, 31-47 odd, 56, 57, 61
2.6 Log/Exp derivatives 1-47 odd (DE’s optional; 15-25 graphing optional), 51, 53, 61,
      65, 67, 69
2.7 1 sine, cosine derivatives 1-4, 7-35 odd, 43, 45, 65, 67; use grapher to
      check sketches.
3.1 1 Product, quotient rules 1-41 odd, (21-41 graphs optional).
3.2 2 Chain rule 1-27 odd, 37, 39
3.3 1 Implicit differentiation 1, 3, 5, 6, 8-11, 15, 16, 19, 20, 21, 27
3.5 Derivatives: more practice 1-61every other odd, 39. Skip antiderivatives.
4.3 2 Optimization 1-29 odd (#17 optional), 4, 10, 24, 26, 28, 30
4.5 2 Related rates 1-29 odd (#15 optional), 18-28 even
As time permits:    
4.8 1 IVT, EVT, bisection method 1-10, 17, 19, 30, 35-39
4.9 ½ MVT 1-15 odd, 16-27, 29, 31, 33
4.6 ½ Newton’s method [if time 1, 3, 4, 15, 21
2.5 1 ODEs, modeling motion 1-27 odd, 28-31

Homework also includes selected items in the supplement packet.

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