Text: Calculus by Larson, Hostetler, and Edwards, 8th Edition.  D. C. Heath and Company, 2005.

Instructor: Mr. G. Davidson

Outcomes: Students will know basic concepts and demonstrate calculus techniques in the following areas:

I           Pre-Calculus Review – algebra and trigonometry and use of technology such as graphing calculators, graphical utilities, and spreadsheets (goal 6).  We will make heavy use of graphing calculators to assist us in finding zeros, relative maximums and minimums, and other characteristics of functions.

2.         Limits – develop the notions of closeness, continuity, function, and limit (goal 2).  Limits at infinity and delta-epsilon proofs will also be studied.

3.         Differentiation – students will learn the definition and how a function and its derivative are related graphically and algebraically.   Differentiation rules will be applied to algebraic, trigonometric, logarithmic, exponential, and hyperbolic functions. Proper notation and development of rules will be emphasized (rules such as product, quotient, and chain and techniques such as implicit differentiation) (goal 3).  We will utilize graphing calculators to assist us in approximating derivatives and in applications such as Newton’s method.

4.         Application of Differentiation – students will apply what they learned in part 3 with most applications in the areas of graphing, business, and science (goal 1).  Students will understand the dual concepts of rate of change and slope of the tangent line, how they are related, and how they are applied.

5.         Integration – students will understand the concept of integration as an “antiderivative”, as an area, and its use in graphing (goal 4).  Students will apply the Fundamental Theorem of Calculus and recognize when the 2^nd Fundamental Theorem of Calculus can be applied.  Students will also understand how the concept of Integration was derived and its culmination in the Riemann Integral.

6.         Applications of Integration – students apply integration in finding area, volume, solutions to motion problems, and in graphing.  The science concepts of work, fluid pressure and force will also be examined.  We will utilize graphing calculators to approximate definite integrals using methods such as Simpson’s rule. (goal 4)

7.         Exponential and Logarithmic Functions – students apply the derivative and integration to this class of functions.  Also problems of growth and decay and how these are applied in science and business are studied.

8.                  Trigonometric Functions – Students also apply the derivative and integration to trigonometry functions and their inverses and apply these functions to practical problems in science and in triangle and circle measurement.

9.                  Differential Equations – Students learn a variety of techniques of solving differential equations and apply these techniques in problem solving.  Also Euler’s method and slope fields in approximating solutions will be examined and we will utilize graphic calculators to assist us in making calculations and in examining the graphs of solutions.

10.              Students will be performing many problem solving activities which require responses verbally as well as written.  In addition, most of my tests have open ended essay questions which require clear, concise, and complete responses.  I expect students to know the language of calculus and to use it appropriately.  Also, I use a response system in class where all students respond to questions that I pose in class.  These responses are graded and will count as a quiz grade. (goals 1 and 5).

Policies:         1. Daily homework will be assigned.

2. Homework is due the day after it is assigned.  Unexcused late homework will not be accepted.  Occasionally there will be some class time for homework.  Failure to use this time properly will result in a demerit.

3. A one hour test will follow each chapter.

4. A short quiz may be given at any time covering a specific topic.  Responder questions will count as a quiz.

5. A comprehensive semester exam will be given each semester.

6. Students will need a scientific calculator, preferably a TI-83 graphing calculator or better.  Knowledge of MicroSoft Excel is helpful.

7. Any evidence of communicating during an exam will result in a zero for that exam.

8. All policies in the student handbook will be followed.

9. This course may be taken for 5 hours of Kansas Newman credit and credit may also be obtained from other Universities by taking the AP exam in May.

10. Extra help is available in room 402, before or after school.  Since I administrate the school's computer network, I can occasionally be found in the network server room at those times (200 hall).   Please have me paged in the main office if you have difficulty finding me.  My email address is davidsongreg@bcchs.org. My voice mail phone number is 722-2390 extension 511

11. A number of resources within the school will also be used.  Students will make use of one of our computer labs in studying differentiation and integration.  We will also apply technology in student numeric methods such as Newton’s method and the Trapezoidal rule.  We will also view several films on differentiation and integration.  Usually, late in the fall, we have a former student visit us and give students an understanding of the use of calculus in college.

Grading: Grades will be computed using weighted averages.  The weights of each area are given below.

                        Tests                        3

                        Quizzes                    1

                        Homework                1

The Diocesan grading scale will be used.

Newman University grade will be the average of the Bishop Carroll semester grades.  

Calculus 2

Course:           Calculus II BC

Calculus II BC builds upon the foundation laid in Calculus I AB.  Calculus I AB is a prerequisite for this course.    In this class students will learn basic concepts and demonstrate skill in problem solving in topics such as techniques of integration, series, conic sections, parametric equations, and vectors.  Upon successful completion of this course, students will be prepared to take the advanced placement test for BC Calculus.

Text:               Calculus by Larson, Hostetler, and Edwards, 8th Edition.  D. C. Heath and Company, 2005.

Instructor:      Mr. G. Davidson

Outcomes:      Students will know basic concepts and demonstrate calculus techniques in the following areas:

1          Calculus I Review – The student must have shown sufficient progress in Calculus I in order to be in Calculus II.  A grade of C or higher in Calculus I is required to be in Calculus II.  We will review the major concepts of Calculus I and some of its application including volumes of rotation, arclength, work, and pressure problems.  The concept of function is explored and knowledge of representations of functions such as graphs, formulas, ordered pairs, and verbal descriptions is expected.  Students will be able to convert from one function representation type to another with and without use of technology.  This will be accomplished by giving students graphs or tables of ordered pairs without knowing the function analytically (no formula) and making sure they can analyze properties of the function such as derivative, area under the curve, limits, etc.  Students will understand the Fundamental Theorem of Calculus and how it connects the two fundamental concepts of Integration and Differentiation.  The final project will test their ability to construct a function from raw data and analyze its properties.

2            Techniques of Integration – A look at some basic techniques such as substitution, Partial Fractions, Integration by Parts, and Tables.  Also, we will review the concepts that were learning in Calculus I such as numeric methods of computing integrals (trapezoidal, Simpson’s, etc.), techniques of substitution, areas, volumes, arclength and position, velocity, and acceleration problems.  We will also use integration to assist us in solving separable differential equations.

3              Limits -  Students will have a basic intuitive understanding of limits and be able       

            to find those limits using algebra, graphs, and other numeric methods.  Students   will be able to find vertical and horizontal asymptotes and use these to assist them in graphing.  Students will student the relative growth rates of various functions such as polynomial, exponential, and logarithmic.  Students will use limits to further their understanding of continuity and apply it in the Intermediate and Extreme Value Theorems.

4.         Infinite Series – Students will study the concepts and notation of infinite Series as well as know a number of types of Series.  Included will be topics such as L’Hopital’s rule, convergence and divergence, bounded and oscillating sequences, polynomial, trigonometric, and exponential function approximations, integral and derivative approximations, geometric series, Harmonic series, Maclaurin and Taylor series, and various limit convergence tests.

5.         Conic Sections – Students will study the various formulas and attributes of conic sections.

6.         Parametric Equations and Polar Coordinates – Students will study parametric, rectangular, and polar plane equations and points.  Students will also be able to convert between the forms in both point and equation.

7.         Solid Analytic Geometry – student will study the various classifications of space figures and be able to find formulas, convert between rectangular, cylindrical, and spherical equations.

7.         Vectors – Students will expand their understanding of vectors in 3 dimensional space.

8.                  Vector-Valued Functions – Students will understand the techniques and applications of functions of vectors and perform Calculus on these functions.

9.                  Derivatives – Students will have an understanding of the derivative as an instantaneous rate of change and as a slope of a tangent line.  Students will also study higher order derivatives and use the concept of derivative to solve problems in business and science.  Concepts such as relative extrema, points of inflection, concavity, implicit differentiation, and differential equations will be explored.  All rules for differentiation (product rule, chain rule, etc.) will be studied as well as numeric approximations for evaluating derivatives.  Also, the relationship between derivatives and continuity (studied along with the limit concept) will be explored.  Students will be able to generate a derivative function from either numeric data, written description, or a graph of a function.

10.              Differential equations – students will learn a number of techniques of solving differential equations such as separation of variables and numeric methods such as Euler’s method.  They will apply these techniques in solving problems in science and business.

11.              Students will demonstrate their knowledge of Calculus by performing a final project.  Students will submit a written summary of their project and give an oral presentation of their solution.  Additional verbal and written projects will be presented as a regular classroom feature as we put solved problems on the board and students will give rationale for their solution.

Policies:           1.         Daily homework will be assigned.

2.         Homework is due the day after it is assigned.  Unexcused late homework will not be accepted.  Occasionally there will be some class time for homework.  Failure to use this time properly will result in a demerit.

3.         A one hour test will follow each chapter.  Some chapters may require two tests.

4.         A 15 minute quiz may be given at any time covering a specific topic.

5.         A comprehensive semester exam will be given each semester.

6.         Students will need a graphing calculator, preferably a TI-83 graphing calculator or better.  Knowledge of MicroSoft Excel is helpful.  Students will demonstrate their ability to use calculus functions on their calculator to analyze problems, experiment, verify solutions, and to solve problems.  The graphing calculator is used on a daily basis and students must be adept at using it.

7.         Any evidence of communicating during an exam will result in a zero for that exam.

8.         All policies in the student handbook will be followed.

9.         If you are interested in gaining college credit for this course, the AP Calculus BC test may be taken in May.

10.       Extra help is available in room 402, before or after school.  Since I administrate the school's computer network, I can occasionally be found in the network server room at those times (200 hall).   Please have me paged in the main office if you have difficulty finding me.  My email address is davidsongreg@bcchs.org. My voice mail phone number is 722-2390 extension 511.

Grading:         Grades will be computed using weighted averages.  The weights of each area are given below.

                                                Tests........................... 3

                                                Quizzes....................... 1

                                                Homework.................. 1

The Diocesan grading scale will be used.  

Course: PreCalculus Mathematics

Test: Advanced Mathematics by Richard G. Brown.  Houghton Mifflin Company, 2003

Instructor: Mr. G. Davidson

Outcomes: Students will demonstrate skill in problem solving in the following areas:

1.                  Linear and Quadratic Functions – Graphical and algebraic aspects of these functions.  Complex numbers and modeling will be examined.

2.                  Polynomial Functions – solving equations, max/min problems, and classical theorems on polynomial functions are examined.

3.                  Inequalities – graphing and solving inequalities

4.                  Functions – concept of function, notation, and graphical analysis

5.                  Exponents and Logarithms – solving equations, simplifying expressions, and practical applications in growth and decay will be examined.

6.                  Probability and Combinatorics – techniques of counting and basic techniques in computing probabilities.

7.                  Matrices – operations and applications of matrices.

8.                  Trigonometric Functions and Equations – Basic 6 functions, their inverses and techniques of solving equations and simplifying expressions.  Proofs using identities will also be examined.

9.                  Triangle Trigonometry – techniques of solving triangles in practical applications as well as identities and trigonometric laws

10.              Polar Coordinates and Vectors – conversions and operations with these concepts.  Practical applications in navigation and forces will be examined.

11.              Sequences and Series – identify and define a variety of sequences and series as well as find infinite and partial sums.

Policies:         1. Daily homework will be assigned.

2.  Homework is due the day after it is assigned.  Late homework will not be accepted.  Occasionally there will be some class time for homework.  Failure to use this time properly will result in a demerit.

3. A one hour test will follow each chapter.

4. A short quiz may be given at any time covering a specific topic.  Responder questions will count as a quiz.

5.  A comprehensive semester exam will be given each semester.  It will cover the above outcomes and the emphasis will be on demonstrating basic skills in problem solving.

6. Students will need a scientific calculator, preferably a TI-83 or TI-86 graphing calculator, to complete assignments.  A knowledge of MicroSoft Excel is helpful.

7. Any evidence of communicating during an exam will result in a zero for that exam.

8. All policies in the student handbook will be followed.

9. This course can be taken for college credit through Newman University.  First semester gives credit for College Algebra and second semester for Trigonometry.  A total of 6 credit hours are given.

10.  Extra help is available in room 402, before or after school.  Since I administrate the school’s computer network, I can occasionally be found in the network server room.  Please have me paged in the office if you have difficulty finding me.  My email address is davidsongreg@bcchs.org . My voice mail phone number is 722-2390 extension 511

Grading:  Grades will be computed using weighted averages.  The weights of each area are given below.

Tests………………………………            7

Quizzes……………………………            2

Homework…………………………            1

The Diocesan grading scale will be used. 

Newman University grade will be the same as the Bishop Carroll grade.