HONORS CALCULUS
Course Description and Syllabus
Lynn Pearson Ph. # 210-3283
Welcome to Honors Calculus! This course will provide you with the same information and material as a college level Calculus course, but try not to let that scare you.
Calculus is.... a branch of mathematics dealing with maxima and minima of definite integrals
which have an integrand that is a function of independent variables and of dependent variables and their derivatives. Huh?
Calculus provides the tools for describing the real world in mathematical terms.
This course is designed to teach Calculus using a multidimensional approach. We will be solving problems numerically, graphically, analytically, and in combination. Your understanding of a concept will also be reinforced verbally and through your writing. You must have a solid mathematical background (in arithmetic, algebra, geometry, and trigonometry) to be successful in this course. You should be comfortable and proficient in working with functions of all kinds (linear, polynomial, rational, exponential, logarithmic, trigonometric, and piece-wise defined). As in previous math courses, you will be asked to solve problems both with and without your graphing calculator.
Please have these materials with you in class everyday :
A writing utensil and a large 3-ring binder with notebook paper (2 ½ - 3” binder)
The TI-83/Plus or the TI-84/Plus graphing calculator is required for this course.
(Please be aware that the use of a graphing calculator with capabilities beyond those of the TI-84 Plus will
not be allowed on graded assignments, quizzes, and tests.)
Your textbook: Calculus: Graphical, Numerical, Algebraic by Finney, Demana,
Waits, & Kennedy, Pearson/Prentice Hall, Boston, MA © 2007
3 rd edition
This Calculus course will be challenging. It is based around the information found in a college level course. Don't be shy about asking questions or asking for help.
Calculus concepts will be found throughout the higher level math, physics, and engineering classes you will encounter in college. They may also be found in many of your business and computer science courses. Honors Calculus will provide a solid foundation for future coursework.
Honors Calculus Curriculum or What you should expect to learn in this course
* Functions, Graphs, and Limits
- Analysis of graphs
- Limits of functions
* Limits at a point
* Properties of limits
* One and two-sided limits
- Asymptotic and unbounded behaviors
* Limits involving infinity
* End behavior
- Continuity of functions
* Definition of continuity and Continuity as a property of functions
* Types of discontinuities (Removable, Asymptotic, Jump)
* Derivatives
- Concept and definition of the derivative
* Rates of change
* How the derivative relates to continuity
- Derivative at a point
- Derivative as a function
* Curve sketching (function to derivative and vice versa)
- Second derivatives
* And other higher order derivatives
* The relationship of a function to its various derivatives
- Computation of derivatives
* Using power, product, quotient, and chain rules
* Trigonometric, inverse trigonometric, exponential, logarithmic,
and other derivative formulas
* Implicit Differentiation
* Logarithmic Differentiation
- Applications of derivatives
* Distance, velocity, and acceleration
* Particle motion
* Marginal cost/revenue
* Local and Global (Relative and Absolute) Extrema
* Concavity and Points of Inflection
* Optimization
* The Mean Value Theorem
* Rolle’s Theorem
* Linearizaton
* Related Rates
* Integrals
- Interpretations and properties of Indefinite Integrals
* Using power rule, algebraic manipulation, and u-substitution
* Trigonometric, inverse trigonometric, exponential, logarithmic,
and other integration formulas
- Fundamental Theorem of Calculus
- Numerical approximations of definite integrals
* Trapezoidal Rule
* Reimann Sums (Left, Right, and Midpoint Approximation)
- Interpretations, properties, and calculations of Definite Integrals
* Using power rule, algebraic manipulation, and u-substitution
* Trigonometric, inverse trigonometric, exponential, logarithmic,
and other integration formulas
- Applications of integrals
* Area under a curve and between curves
* Volume of a solid (Disk and Washer methods)
* Separable Differentiable Equations
* Slope Fields
* Exponential Growth and Decay
Grading :
* You can expect homework almost every night, regardless of what day of the week it is.
* Each homework assignment is worth 10 points. Every 10 homework assignments is worth a quiz grade
(for a total of 100 points). Daily homework will NOT be accepted late. Some homework
assignments may be collected for a quiz grade. You will be given notice of this when the work is assigned. Graded homework submitted late, will lose points each day it is overdue.
* I GIVE POP QUIZZES! Always be prepared.
* You will always be given notice of upcoming tests.
* Both a Mid-term and a Final Exam are required.
* To compute grades at the end of each 6 weeks: All quizzes count once; all tests (except the Midterm
and Final) count twice. The mean is then used with these numbers.
* The highest possible report card grade is 100.
* There is no extra credit available and there are no bonus questions on quizzes or tests. Therefore, it is
extremely important that you are familiar and comfortable with the material as we go along. Ask
questions and/or come in for extra help so you don’t fall behind.
HOT TIPS!!
Do NOT be afraid to ask relevant questions or to ask for extra help.
Show your work. That way I can show you where and how you can improve.
Organize your work. Keep a notebook! Take good notes. Stay organized. If you get organized and remain organized,
your grades will improve. You will accumulate a great deal of paper as we go along in this course.
Attend class everyday. If you must be out, get the notes from a friend (who takes good notes!) and make up your work immediately or you will fall far, far behind.
When I assign odd numbered questions for homework, check your answers to these questions in the back of your
book. I give Pop quizzes. If you don't practice the skills, you won’t pass the quizzes. If you can’t pass the
quizzes, you won’t pass the tests. If you can’t pass the tests, you probably shouldn’t pass the course!
I am here to help you succeed. I cannot force you to succeed.
Good luck. Be willing to work. Don’t give up.
General Classroom Procedures:
* When you first get to class: sharpen your pencil, be seated, and have your homework on your desk with your name on it. I
usually check homework first thing, and if it’s not on your desk - it doesn't count!! This is a very good reason to
organize your notebook! It’s also a very good reason to be in class and ready to go on time.
* Seating arrangements will be assigned. Please let me know if you need to sit someplace specific and I will try to
accommodate you.
* Keep your bookbag and other personal belongings under your desk, where they do not pose a safety hazard in the aisles.
* Use the restroom and get water between classes.
Rules :
Follow all school rules. Be respectful. Be appropriate. Do your personal best.
*** Behaviors that prevent others from learning will not be tolerated.
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