Math 123 Calculus I  Syllabus (4 credits)

Contact Information:

                Instructor:             Mr. Hogie

                Room #:                  126

                Office Hours:        Available to assist students before school (7:25 am) and after school every day.

                Home Phone:        582-2106     E-mail:  Allen.Hogie@k12.sd.us Web Page:  http://ah002.k12.sd.us

Course Description:        The study of limits, derivatives, applications of the derivative, antiderivatives, the definite and indefinite integral, and the    fundamental theorem of calculus.

 Prerequisites:   Pre-Calculus/Trigonometry; Full Math COMPASS test of 40 or higher OR Math ACT of 25 or higher and Trig Compass score 40 or higher.

Course Goals:

BOR Goal #5         Students will understand and apply fundamental mathematical processes and reasoning.

SLO(5.1)                 As a result of taking this course, students will be able to use mathematical symbols and mathematical structure to model and solve real world problems.

                             *Students ability to use mathematical symbols and structure from calculus I (derivatives and integrals) that are used in solving real world problems will be assessed using homework, quizzes, tests, and a final exam.

 SLO(5.2)                 As a result of taking this course, students will demonstrate appropriate communication skills related to mathematical terms and concepts.

                                *Communication skills will be assessed using homework, quizzes, and tests and making sure proper grammar is used.

 SLO(5.3)                 As a result of taking this course, students will demonstrate the correct use of quantifiable measurements of real world situations.

                                *Correct units are applicable to most word problems in the text that are similar to problems that arise in the real world and student understanding will be assessed using homework, quizzes, tests and a final exam.

Course Requirements:  CALCULUS of a Single Variable, 8^th Edition, Larson-Hostetler-Edwards   

                                    A graphing calculator is required for the course.  The TI-84 Plus is recommended.

Evaluation Procedures:

Every hour examination will count 50 - 100 points each.  Quizzes will vary from perhaps 10 to 50 points each.  Hour exams will be announced in advance but you may not be given advance notice of all quizzes.  Grades will be taken on a) tests, b) quizzes, c) homework assignments, and d) participation in class.

Grading:                                                                                                Weight                                   Scale

Quarter Grade                      Homework                             30%                                        A              90 - 100%

                                                Tests/Quizzes                       70%                                        B              80 - 89%               

                                                                                                                                             C              70 - 79%               

Semester Grade                    Quarter 1                              40%                                        D             60 - 69%

                                                Quarter 2                              40%                                        F              Below 60%

                                               Semester Test                       20%    (All students must take each semester test for credit.)

Final Grade           The Final Grade will be calculated by averaging a students Semester 1 and Semester 2 grades.

 The Final Grade will appear on a NSU transcript and will become part of your permanent transcript within the SD university system.  Official transcripts are not necessary if the student is attending a SD state university, as those credits are in the SD Regental system computer.  Official transcripts need to be requested for students attending out-of-state or private institutions.  Official transcripts may be ordered at:  http://www.northern.edu/academics/pages/registrar/transcripts.aspx

 PLEASE NOTE:  NSU earned credits are transferable to any SD Board of Regents University and to most public and private colleges and universities.  It is the student’s responsibility to check and confirm that NSU credits earned through the NSU Rising Scholars Program will be accepted as college credits at the institution of higher education that s/he plans to attend.

One Caution: Students must be very diligent in this class and do more than the “minimum” required to pass.  A passing grade in a dual-credit course does not always mean the student is prepared for the next MATH course.

NORTHERN STATE UNIVERSITY ADA STATEMENT:

Northern State University recognizes its responsibility for creating an institutional climate in which students with disabilities can thrive.  If you have any type of disability for which you require accommodations, please contact Karen Gerety at the NSU Office of Disability Services (ODS) as soon as possible to discuss your particular needs.

 The mission of the Office of Disability Services is to provide equal access to university programs, as mandated by the Americans with Disabilities Act (ADA) and Section 504 of the Rehabilitation Act of 1973.  Any student requesting accommodations must submit adequate documentation of disability before accommodations can be provided.                Contact Information for the ODS:    Phone: 605-626-2371;   FAX: 605-626-3399

E-mail: geretyk@northern.edu; Location: Graham Hall 202 

ACADEMIC FREEDOM STATEMENT:  FREEDOM IN LEARNING

Under Board of Regents and University policy student academic performance may be evaluated solely on an academic basis, not on opinions or conduct in matters unrelated to academic standards.  Students should be free to take reasoned exception to the data or view offered in any course of study and to reserve judgment about matters of opinion, but they are responsible for learning the content of any course of study for which they are enrolled.  Students who believe that academic evaluation reflects prejudiced or capricious consideration of student opinions or conduct unrelated to academic standards should contact the dean of the college which offers the class to initiate a review of the evaluation.

 NORTHERN STATE UNIVERSITY DIVERSITY STATEMENT:     Northern State University strives to build an academic community of people from diverse backgrounds and experiences who are committed to sharing diverse ideas in a mutually respectful environment. We value open discourse and consideration of multiple perspectives on issues of regional, national, and international importance, in which individuals are free to express their points of view. Our goal is a diverse learning community with equal opportunity for all.

HOMEWORK:

 To learn mathematics, one needs to focus on understanding skills and knowledge required to solve problems.  Homework provides an opportunity to reflect upon learning and synthesize understanding.  How hard a student works at his/her homework determines the depth and breadth of learning that takes place.  Active participation is also necessary.  Homework will be collected periodically and graded.  Once assigned, it is due at the beginning of class the next day.  Late homework up to one day will result in a minus five points.  After one day, a grade of zero will be given but the student is expected to complete the assignment.  All work turned in will be graded, not only on correct answers, but also on the neatness, organization, and steps used to derive answers.  Show all work!

Academic Dishonesty:        Cheating is not tolerated.  If a student is caught cheating on homework, a quiz, or a test, no credit will be given and will be dealt with according to district policy.

 When given time in class to work on homework, use it wisely.  DO NOT QUIT EARLY!

I allow students to work in small groups quite often, but only when the time is being used wisely.

 ABSENCES:

Students who are absent are responsible for any make-up work.  This includes missed tests and quizzes.  I will not chase after you to see that you make it up.  Make-up work is due the day after you return back to school. (One day allowed for each day absent.)

 If you know you are going to be absent, I expect you to complete and turn in your work before you leave.  This includes school-sponsored activities.  It is in a student's best interest to make up any work A.S.A.P.

 DISCIPLINE:

It is my philosophy that each student is responsible for his/her own behavior both inside and outside the school environment.  My policy is as follows:

1^st Offense:                                            Warning. Written Referral to the Office

2^nd Offense:                                           Referral.  Trip to the office. Saturday School points given.

3rd Offense:                                          Conference with parents and principal;  Contracting will be done.

EXPECTATIONS:    My job is to TEACH.  Your job is to LEARN.     BEWARE OF TOO MUCH NOISE.

                                                                                                                BE SURE TO DO YOUR OWN WORK.

                                                                                                                BELIEVE IN YOURSELF.

                                                                                                                BE ON TIME.

                                                                                                                BEHAVE.

My biggest pet peeve is someone talking while I am talking.

No pop, candy or gum is allowed in the classroom unless permission is granted.

GOALS for ALL Students:                   Learn to apply mathematics to a variety of different situations.

                                                                Class average of 83%

                                                                Develop communication skills.

                                                                Learn to work with others and develop self-discipline.

To be successful in Calculus a student should:

·         Read ahead.  Make a note of everything you do not understand and ask in class.

·         Take notes, write down examples, and review them.

·         Complete all assigned homework and show all steps to the solution for each problem.  Take the time to check your work and make corrections.   Learning mathematics is a step by step process.  Always keep up with and complete your assignments because you must understand each topic in order to learn the next one.  Show all work!

·         Work the problems in class as though you were practicing for a test.

·         Pay attention all period. When working in a group or with a partner stay focused on the task at hand.

·         Seek help beyond the class period.

·         Participate in classroom discussions because it builds confidence.

·         Use the time in class wisely.  Do not quit early!

 ·         Put forth an excellent EFFORT.  Work on tasks until they are completed.  Push yourself to continue working on tasks even when difficulties arise or when a solution is not immediately apparent.  View difficulties that arise as opportunities to strengthen your understanding.

CALCULUS TENTATIVE COURSE OUTLINE

SEMESTER ONE

Chapter P             Preparation for Calculus                                  {13 days}

                                In this chapter students will learn how to:

·          Sketch the graph of an equation.

·          Find the intercepts of a graph.

·          Test a graph for symmetry with respect to an axis and the origin.

·          Find points of intersection of two graphs.

·          Interpret mathematical models for real life data.

·          Find the slope of a line passing through two points.

·          Write the equation of a line with a given point and slope.

·          Interpret slope as a ratio or as a rate in a real-life application.

·          Sketch the graph of a linear equation in slope-intercept form.

·          Write equations of lines that are parallel or perpendicular to a given line.

·          Use function notation to represent and evaluate a function.

·          Find the domain and range of a function.

·          Sketch the graph of a function.

·          Identify different types of transformations of functions.

 Chapter 1              Limits and Their Properties                             {17 days}

                                In this chapter students will learn how to:

·          Estimate a limit using a numerical or graphical approach.

·          Determine different ways that a limit can fail to exist.

·          Use a formal definition of a limit.

·          Evaluate a limit using properties of limits.

·          Develop and use a strategy for finding limits.

·          Evaluate a limit using dividing out and rationalizing techniques.

·          Determine continuity at a point and continuity on an open interval.

·          Determine one-sided limits and continuity on a closed interval.

·          Use the Intermediate Value Theorem

·          Determine infinite limits from the left and from the right.

·          Find and sketch the vertical asymptotes of the graph of a function.

 Chapter 2              Differentiation                                                     {33 days}

                                In this chapter students will learn how to:

·          Find the slope of the tangent line to a curve at a point.

·          Use the limit definition to find the derivative of a function.

·          Understand the relationship between differentiability and continuity.

·          Find the derivative of a function using the Constant rule, Power rule, Constant Multiple rule, Sum and Difference rules, Product rule, and Quotient rule.  Find a higher-order derivative of a function.

·          Find the derivative of a trigonometric function.

·          Use derivatives to find rates of change.

·          Find the derivative of a composite function using the Chain Rule and General Power Rule.

·          Find the derivative of a trigonometric function using the chain rule.

·          Use implicit differentiation to find the derivative of a function.

·          Find a related rate.

·          Use related rates to solve real-life problem.

 Chapter 3              Applications of Differentiation                        {17 days}

                                In this chapter students will learn how to:

·          Apply the definition of extrema of a function on an interval.

·          Apply the definition of relative extrema of a function on an open interval.

·          Find extrema on a closed interval.

·          Apply Rolle’s Theorem and the Mean Value Theorem.

·          Determine intervals on which a function is increasing or decreasing.

·          Apply the First Derivative Test to find extrema of a function.

·          Determine intervals on which a function is concave upward or concave downward.

·          Find any points of inflection of the graph of a function.

·          Apply the Second Derivative Test to find relative extrema of a function.

 SEMESTER TWO

 Chapter 3              Applications of Differentiation (continued)                   {18 days}

                                In this chapter students will learn how to:

·          Determine limits at infinity.

·          Determine the horizontal asymptotes, if any, of the graph of a function.

·          Determine infinite limits at infinity.

·          Analyze and sketch the graph of the function.

·          Solve applied minimum and maximum problems.

·          Approximate a zero of a function using Newton’s Method.

·          Apply the concept of a tangent line approximation.

·          Compare the value of the differential, dy, with the actual change in y, delta y.

·          Estimate propagated error using a differential.

·          Find the differential of a function using differentiation formulas.

 Chapter 4              Integration                                                                            {36 days}

                                In this chapter students will learn how to:

·          Write a general solution of a differential equation.

·          Use indefinite integral notation for antiderivatives.

·          Use basic integration rules to find antiderivatives.

·          Find a particular solution of a differential equation.

·          Use Sigma notation to write and evaluate a sum.

·          Apply the concept of Area.

·          Approximate the area of a plane region.

·          Find the area of a plane region using limits.

·          Evaluate a definite integral using limits.

·          Evaluate a definite integral using properties of definite integrals.

·          Evaluate a definite integral using the Fundamental Theorem of Calculus.

·          Find the average value of a function over a closed interval.

·          Apply the Second Fundamental Theorem of Calculus.

·          Use pattern recognition, change of variables, and the general power rule to evaluate an indefinite integral.

·          Use a change of variables to evaluate a definite integral.

·          Evaluate a definite integral involving an even or odd function.

Chapter 5              Logarithmic, Exponential, and Other Transcendental Functions           {16 days}

                                In this chapter students will learn how to:

·          Develop and use properties of the natural logarithmic function.

·          Find derivatives of functions involving the natural logarithmic function.

·          Use the Log Rule for Integration to integrate a rational function.

·          Integrate trigonometric functions.

·          Develop properties of the natural exponential function.

·          Differentiate natural exponential functions.

·          Integrate natural exponential functions.

Chapter 7              Application of Integration                                 {11 days}

                                In this chapter students will learn how to:

·          Find the area of a region between two curves using integration.

·          Find the area of a region between intersecting curves using integration.

·          Describe integration as an accumulation process.

·          Find the volume of a solid of revolution using the disk, washer and shell methods.

·           Arc Length and Surfaces of Revolution, Work, and Fluid Pressure as time permits.

Extra Credit Offered (4th quarter only)

Chapter 9              Conics, Parametric Equations, and Polar Coordinates           

                                In this chapter students will learn how to:

·          Apply the definition of a conic section.

·          Analyze and write equations of circles, parabolas, ellipses, and hyperbolas.

Pre-Calculus/Geometry Syllabus

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