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    Patrick Henry Community College


    MATH 263   Calculus of One Variable

    Spring, 2020 INSTRUCTOR: Lori Wagoner

    OFFICE LOCATION:  Bassett High School, Room 29

    OFFICE HOURS:  M – F 12:45  – 1:50 PM or by appointment

     

    OFFICE PHONE:  276-629-1731

    E-MAIL ADDRESS: law25117@email.vccs.edu

    CLASS MEETING TIME:   (Section 1) M – F, 8:25 – 10:00

                                                    (Section 2) M – F, 1:55 – 3:25

    CLASSROOM LOCATION: Bassett High School, Room 29

    MODE OF DELIVERY:  A variety of instructional methods will be utilized.  As a group we will work extensively on study habits, appropriate use of the graphing calculators, and student communication – both oral and written.  Students will be encouraged to actively participate in the learning process to help ensure that they understand the material.  Many examples will be provided through lecture and class activities.  The use of e-mail is essential.

    COURSE CREDITS: 4

     

    PREREQUISITE(S): a placement recommendation for MTH 263 and five units of high school mathematics including Algebra I, Algebra II, Geometry, Trigonometry, and Pre-Calculus or equivalent.

     

    COURSE DESCRIPTION

    This course presents differential calculus of one variable including the theory of limits, derivatives, differentials, anti-derivatives and applications to algebraic and transcendental functions. It is designed for mathematical, physical, and engineering science programs.

    COURSE INTRODUCTION

    Calculus was developed in the 17th century independently and simultaneously by Sir Isaac Newton and G. W. Leibniz. They actually argued over the ownership of calculus for 25 years. It has now been established that Newton developed calculus first, but Leibniz was the first to publish on the subject. The applications of calculus occurs in many disciplines: to compute the gravitational force of an object near the surface of the earth in physics; to compute reaction rates in chemistry; to model population growth in biology and sociology; and to model compound interest in economics. This course is a culmination of all high school math courses; therefore, a solid foundation in the prerequisite courses is essential.

    1. COURSE OBJECTIVES

    Upon successful completion of this course, the student should:

    • Develop effective study skills in order to master course content and objectives.
    • Demonstrate an understanding of the basic mathematical skills used in calculus.
    • Communicate clearly and effectively the principles of calculus using proper vocabulary.
    • Apply the principles and concepts of calculus to solve practical problems in mathematics.
    • Work with functions represented in a variety of ways and understand the connections among these representations.
    • Understand the meaning of the derivative in terms of a rate of change and local linear approximation, and be able to use derivatives to solve a variety of problems.
    • Model a written description of a physical situation with a function or a differential equation.
    • Use technology to help solve problems, experiment, interpret results, and verify conclusions.
    • Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
    • Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

     

     

    Unit 1 – Limits and Their Properties (7 days)

     

    • Finding limits graphically and numerically (Section 2.2)
    • Evaluating limits analytically (Section 2.3)
    • Continuity and one-sided limits (Section 2.4)
    • Infinite limits and limits involving infinity (Sections 2.5 and 4.5)
    • Asymptotic and unbounded behavior (Sections 2.5 and 2.5)
    • Understanding asymptotes in terms of graphical behavior (Sections 2.5 and 4.5)
    • Describing asymptotic behavior in terms of limits involving infinity (Section 4.5)
    • Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem) (Sections 2.4 and 4.1)

     

     

    Unit 2 Differentiation (16 days)

    • The concept of the derivative presented geometrically, numerically, and analytically (Section 3.1)
    • Definition of derivative: limit of the difference quotient (Section 3.1)
    • The tangent line problem (Section 3.1)
    • Slope of a curve at a point (Section 3.1)
    • Basic differentiation rules, velocity, and other rates of change (Section 3.2)
    • Product Rule, Quotient Rule, and higher order derivatives (Section 3.3)
    • Derivatives of trigonometric functions (Section 3.3)
    • Derivatives of logarithmic and exponential functions (Sections 3.2 and 3.4)
    • Chain Rule ( Section 3.4)
    • Differentiating functions involving radicals (Section 3.4)
    • Implicit differentiation (Section 3.5)
    • Logarithmic differentiation (Section 3.5)
    • Derivatives of inverse functions (Section 3.6)

     

    Unit 3 Applications of Differentiation (18 days)

    • Extrema on an interval (Section 4.1)
    • Rolle’s Theorem and The Mean Value Theorem (Section 4.2)
    • L’HÔpital’s Rule (Section 7.7)
    • Increasing and decreasing functions and the First Derivative Test (Section 4.3)
    • Concavity and the Second Derivative Test (Section 4.4)
    • Corresponding characteristics of graphs of 𝑓 and 𝑓′ (Section 3.3)
    • Relationship between the increasing and decreasing behavior of 𝑓 and the sign of 𝑓′ (Section 3.3)
    • Corresponding characteristics of the graphs of 𝑓, 𝑓 , and 𝑓" (Section 3.4)
    • Relationship between the concavity of 𝑓 and the sign of 𝑓" (Section 3.4)
    • Finding points of inflection (Section 3.4)
    • Graphing summary including zeros, domain and range, asymptotes, symmetry, extrema, and concavity (Section 4.6)
    • Optimization problems (Section 4.7)
    • Modeling rates of change, including related-rates problems (Section 3.7)

     

    Unit 4 Integration (22 days)

    • Understand the concept of area under a curve using a Riemann sum (Section 5.2)
    • Use the limit of a Riemann sum to calculate a definite integral (Section 5.3)
    • Computing definite integrals numerically using a graphing calculator (Section 5.3)
    • Definite integrals and Anti-derivatives (Section 5.1)
    • Fundamental Theorem of Calculus (Section 5.4)
    • The Second Fundamental Theorem of Calculus (Section 5.4)
    • Techniques of integration including u-substitution (Sections 5.5 and 8.1)
    • Integration of trigonometric functions (Section 5.8)
    • Integration of the natural logarithmic function (Section 5.6)
    • Integration of the exponential function (Section 5.1)
    • Differentiation and integration of bases other than 𝑒 (Section 5.5)
    • Differentiation and integration of inverse trigonometric functions (Section 5.8)
    • Integration by parts and simple partial fractions (Sections 7.2 and 7.5)
    • Numerical integration using the Trapezoidal Rule (Section 5.6)
    • Solving differential equations using separation of variables (Section 6.3)
    • Exponential growth and decay (Section 6.2)
    • Slope fields (Section 6.1)

     

    Unit 5 Applications of Integration (8 days)

     

    • Use definite integrals to find the area under a curve (Sections 5.2)
    • Average Value of a function (Section 5.4)
    • Use definite integrals to find the area between two curves (Section 7.1)
    • Volumes of solids of revolution using disks and washers (Section 7.2)
    • Volumes of solids of revolution using cylindrical shells (Section 7.3)
    • Volumes of solids with known cross sections (Section 7.2)

     

    Unit 6 More Integration Methods (10 days)

    • Basic integration rules (Section 7.1)
    • Integration by parts (Section 7.2)
    • Partial fractions (Section 7.5)

     

     

     

    1. VCCS CORE COMPETENCIES
    • Degree graduates will demonstrate the ability to

    1.1 Understand and interpret complex materials;

    2.6 Use problem solving skills;

    4.1 Determine the nature and extent of the information needed;

    4.2 Access needed information effectively and efficiently;

    6.1 Use logical and mathematical reasoning within the context of various disciplines;

    6.2 Interpret and use mathematical formulas;

    6.3 Interpret mathematical models such as graphs, tables and schematics and draw inferences from them;

    6.4 Use graphical, symbolic, and numerical methods to analyze, organize, and interpret data;

    6.5 Estimate and consider answers to mathematical problems in order to determine reasonableness; and

    6.6 Represent mathematical information numerically, symbolically, and visually, using graphs and charts.

     

     

    1. TEXTBOOK(S) AND REQUIRED TOOLS OR SUPPLIES

    Title:   

    • Calculus of a Single Variable: Early Transcendental Functions, 5th edition Ron Larson & Bruce Edwards Brooks/Cole, 2011
    1. Supplies:

    Notebook, pencils, colored pens, Binder, TI-84 plus calculator

     

     

    1. STUDENT EVALUATION

     

    • Students will have some type of graded work, either a quiz or a test, each week in addition to free-response questions that have been assigned. Tests are a combination of multiple choice and free-response questions taken from old AP exams. For some questions, no calculator is allowed; however, for some a calculator is required. There are at least four major tests and a final. The number of quizzes varies each unit. Homework is assigned daily and will be collected randomly. All homework should be kept in a three-ring binder, organized chronologically by date with the page number of the assignment included at the top of the paper.

    Students may be assigned free-response questions every three weeks and should write their solutions to these problems according to teacher guidelines discussed in class. Students may discuss these among themselves or get assistance from me. These problems are collected on Friday’s and graded on a nine-point scale.

     

    Grades will be based on the following:

    • 15% - Homework/Daily Assignments – announced or unannounced

       - Free-response questions (FRQs)

    • Announced at least three days to one week prior to being due
    • Gets students in the mind-set of college level assignments
    • 5% - Notebook checks
    • 5% - Participation
    • 25% - Quizzes
      • Announced, closed-book, and will cover two to three sections of material
      • Projects can be assigned periodically and will count as a quiz grade.
    • 50% - Tests
      • Will cover all material covered in a unit/chapter
      • 20% of the test will also be cumulative, reviewing material from previous chapters (Pre-Calculus material must be retained in order to be successful throughout all following math classes.)

     

    All work will be graded within two weeks of a student’s submission.

     

     

    A final comprehensive exam will be given at the end of the semester and will count one-seventh of the final semester grade.

    1. GRADING SCALE:

                A         90 - 100                                  

                B         80 - 89            

                C         70 - 79

                D         60 – 69 

                F          59 - below

    1. EXPECTATIONS FOR STUDENT SUCCESS (should include such things as)
    • Students should attend class daily.
    • Students should email instructor when missing a class to obtain assignments.
    • Students should submit note to Ms. Tonya Edwards within 24 hours of the student’s return with a valid reason for student’s absence. No make-up work will be allowed for unexcused absences.
    • Students should see instructor the day returning from a missed class to ask questions pertaining to the lecture and/or assignment.
    • Students should make arrangements to make up quiz/test if missed due to absence.
    • Students may have food and/or drink in the classroom but must leave area clean.
    • Students should show respect for classmates and instructor, listen carefully, and not interrupt someone who is talking.
    • Cell phones must be put away upon beginning each class. Cell phones will be placed in the cozy on the wall facing inward before the tardy bell rings.
    • Calculus is a time intensive course; therefore, it is critical that students demonstrate time management skills both inside and outside the classroom.

     

     

    1. EMERGENCY INFORMATION

    Evacuation procedures are posted near the door to the hallway. In the event of a lockdown, students will go to the wall and sit on the floor. In the event of a tornado, students will face the wall and drop and tuck.  In the case of a classroom emergency a designated student will deliver the green emergency card to the closest administrator.

     

    1. STUDENT SUPPORT/DISABILITY STATEMENT:
    • Patrick Henry Community College makes every effort to accommodate individuals with disabilities for all programs, services, and activities available to the public. If you have a disability or other need for reasonable accommodation in order to successfully complete the requirements of this course, please contact the 504/ADA Coordinator (Learning Resource Center #109D, 276-656-0257 or 800-232-7997 ext. 0257, disabilityresources@patrickhenry.edu) to discuss this matter confidentially.
    1. IMPORTANT DATES TO REMEMBER

    A school calendar is available at www.henry.k12.va.us

     

    1. SPECIFIC COLLEGE POLICIES

     

    • Academic Honesty
    • Students are expected to abide by the code of conduct and academic integrity found in the student handbook. Students will be required to sign a pledge on any take-home quizzes/tests stating “On my honor, I have neither given nor received aid on this assignment.” Infractions of the honor code will not be tolerated and will be reported to the director and will be addressed with the student and his/her parents. All violations of academic integrity will also be reported to each student’s honor organization.
    • - http://www.patrickhenry.edu/policies2018

    Internet Resources

    http://www.collegeboard.com/student/testing/ap/calculus_ab/samp.html?calcab

     

    1. Math Lab tutoring on-campus

     

    M. Brainfuse

    is an online tutoring service which gives students 24/7 access to highly qualified, experienced, and specially trained tutors. Virtual whiteboard technology lets students and tutors share the same screen. Students may submit writing assignments to be evaluated / proofread. Any PHCC student can access Brainfuse free of charge. Brainfuse can only be accessed through Canvus. Further information may be obtained from your instructor or the Writing Center Tutors.

     

     

     

     

     

     

     

     

    1. AFFIDAVIT


    My signature below indicates that I have read and understand this syllabus and have been given a copy of my own to keep.

     

    Student Signature

    Date

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    This syllabus conforms to the Patrick Henry Community College syllabus guidelines.