# Syllabusap Calculus

## Publish Date

Calculus, Volume 1: One-Variable Calculus, with An Introduction to Linear Algebra. Waltham, Mass: Blaisdell, 1967. 2 will be needed for those who wish to continue on to 18.024 Multivariable calculus with theory.). MATH 2413 Calculus I. Syllabus and First-Day Handout. MATH 2413-012, 013, Calculus I Michael McCarthy, Ph.D. Fall 2012 223 3294.

08/02/2012 17:52:23

## Calculus I

MATH-2413

Fall 2012
08/27/2012 - 12/16/2012

## Syllabus For Ap Calculus Bc

Please note that is just a sample syllabus, actual syllabi for the various sections of the course will likely be different each semester. Different instructors may choose somewhat different material. The number of class sessions varies between fall and spring semesters, Monday-Wednesday and Tuesday. Calculus AB: Sample Syllabus 1 Syllabus 1544617v1. Advanced Placement Calculus AB The overall goal of this course is to help students understand and apply the three big ideas of AB Calculus: limits, derivatives, and integrals and the Fundamental Theorem of Calculus. Imbedded throughout the big ideas are the. An outline of topics to be covered in AP Calculus AB is provided within this syllabus. This course is designed to provide students with instruction and a learning experience equivalent to a college course in single variable calculus.

Section 012
Lecture
MW 14:50 - 16:35
RGC1 336
Paul Wright

Section 013
Lecture
MW 19:30 - 21:15
RGC1 337
John Vawter

## Office Hours

No office hours have been entered for this term

## Course Requirements

MATH 2413 Calculus I

MATH 2413-012, 013, Calculus I Michael McCarthy, Ph.D.

Fall 2012 223 3294

Synonym: 14495, 14496 [email protected]

MW 2:50 - 4:35 Office: RGC 332

RGC 336 Hours: MW 1:40 - 2:40

Other hours by appointment

Course Description: MATH 2413 CALCULUS I (4-4-0). A standard first course in calculus. Topics include inequalities; functions; limits; continuity; the derivative; differentiation of algebraic functions and trigonometric functions; Newton's method; applications of the derivative; the integral; integration of algebraic functions and the sine and cosine functions; numerical integration; and applications of the integral. Prerequisites: MATH 2412 with C or better or equivalent. Another option is an appropriate secondary school course (one year of precalculus or the equivalent, including trigonometry, with a B or better) and a satisfactory entrance score on the ACC Mathematics Assessment Test.

Required Text and Optional Materials:The required textbook for this course is: Calculus: Concepts and Contexts,4th ed., by James Stewart, Brooks/Cole 2010

Optional:Student Solutions Manual, Single Variable ISBN 0-495560618 by Jeffrey A. Cole, Study Guide ISBN 495560642 by Dan Clegg, Scientific Notebook software, single version, Doing Calculus with Scientific Notebook, by Daniel W. Hardy, Carol L. Walker.

Technology required: You must have access to technology which enables you to (1) Graph a function, (2) Find the zeroes of a function. Most ACC faculty are familiar with the TI family of graphing calculators. Hence, TI calculators are highly recommended for student use. Other calculator brands can also be used.

Instructional Methodology: This course is taught in the classroom primarily as a lecture/discussion course.

Course Rationale:This course is the first course in the traditional calculus sequence for mathematics, science and engineering students. It is part of what could be a four-semester sequence in calculus courses. The approach allows the use of technology and the rule of four (topics are presented geometrically, numerically, algebraically, and verbally) to focus on conceptual understanding. At the same time, it retains the strength of the traditional calculus by exposing the students to the rigor of proofs and the full variety of traditional topics: limits, continuity, derivative, applications of the derivative, and an introduction to the definite integral.

MATH 2413 Calculus I Objectives:

1. Find limits of functions (graphically, numerically and algebraically)
2. Analyze and apply the notions of continuity and differentiability to algebraic and transcendental functions.
3. Determine derivatives by a variety of techniques including explicit differentiation, implicit differentiation, and logarithmic differentiation. Use these derivative to study the characteristics of curves. Determine derivatives using implicit differentiation and use to study characteristics of a curve.
4. Construct detailed graphs of nontrivial functions using derivatives and limits.
5. Use basic techniques of integration to find particular or general antiderivatives.
6. Demonstrate the connection between area and the definite integral..
7. Apply the Fundamental theorem of calculus to evaluate definite integrals.
8. Use differentiation and integration to solve real world problems such as rate of change, optimization, and area problems.

Required Text and Optional Materials:The required textbook for this course is: Calculus: Concepts and Contexts,4th ed., by James Stewart, Brooks/Cole 2010

## Course Subjects

 Lecture Topic(s) 1 Function representations, Essential functions, 2 Arithmetic of functions, Graphing, Exponential functions, Inverse functions, 3 Parametric curves, 4 Tangent and velocity, 5 Limit of a function, 6 Calculating limits, 7 Continuity, Limits at infinity, 8 TEST ONE 9 Derivatives and rates of change, Relationship of f' to f, 10 Derivatives of polynomials, Derivative of exponential functions, 11 Product rule, Quotient rule, 12 Derivative of trigonometric functions, 13 Chain rule, 14 Implicit differentiation, 15 Derivatives of inverse trigonometric functions, 16 Linear approximation and differentials, 17 TEST TWO 18 Related rates, 19 Maximum and minimum values, 20 Derivatives and curves, 21 Graphing with Calculus, 22 L’Hospital’s rule, 23 Optimization, 24 Newton’s method, 25 Antiderivatives, 26 TEST THREE 27 Area and distance, 28 Definite integral, 29 Evaluation theorem, 30 Fundamental theorem of Calculus, 31 Substitution rule 32 TEST FOUR

## Student Learning Outcomes/Learning Objectives

MATH 2413 Calculus I Objectives:

1. Find limits of functions (graphically, numerically and algebraically)
2. Analyze and apply the notions of continuity and differentiability to algebraic and transcendental functions.
3. Determine derivatives by a variety of techniques including explicit differentiation, implicit differentiation, and logarithmic differentiation. Use these derivative to study the characteristics of curves. Determine derivatives using implicit differentiation and use to study characteristics of a curve.
4. Construct detailed graphs of nontrivial functions using derivatives and limits.
5. Use basic techniques of integration to find particular or general antiderivatives.
6. Demonstrate the connection between area and the definite integral..
7. Apply the Fundamental theorem of calculus to evaluate definite integrals.
8. Use differentiation and integration to solve real world problems such as rate of change, optimization, and area problems.

Course Syllabus

Donovan, Room 104

## Syllabus For Ap Calculus Ab

 Unit Time Content Curricular Requirements 1 2.5 weeks Limits –investigation of limits through the table feature of the calculator, graphs and analytic methods; definition of limit; limit properties, Squeeze Theorem and its use for finding limits of functions that cannot be found analytically; one-sided limits; infinite limits and vertical asymptotesContinuity – definition and 3-step verification; continuity of composite functionsIntermediate Value Theorem and its proof C2, C3, C5C3, C4C2 2 5-6 weeks The derivative – limit definition of derivative; using the definition to find derivatives of some of the basic functions; graphical investigation of local linearity extending into the tangent line concept and the slope of a curve at any given point; when derivatives fail to exist – explored graphically and analytically; product and quotient rules; proof of the theorem that differentiability implies continuity; derivatives of all 6 trig functions; higher order derivatives and their application to the position function, velocity, and acceleration functions (the derivative as a rate of change);Chain rule; derivatives of transcendental, logarithmic, and exponential functions;Implicit differentiation, logarithmic differentiationInterpreting graphs – the relation between the graph of a function and the graph of its derivativeDerivative of inverse functions, including inverse trig functionsRelated RatesNewton’s Method of Approximating zeros of a function – derivation of this method C2, C3, C5C4C4C2C3, C4C3C4, C5C3,C4, C5 3 5 weeks Extrema – graphically and analytically; Extreme Value Theorem and its proof; critical numbers; relative and global extremaRolle’s Theorem and the Mean Value Theorem – proofs of bothFunctions – increasing/decreasing; concavity; first and second derivative tests for extrema; second derivative test for points of inflection/concavityLimits at infinity and horizontal asymptotesCurve sketching – applying the above concepts; more investigation/interpretation of the relation between a function’s graph and the graphs of its first and second derivatives, using graphs and tables to make the connectionsOptimization – applications of the derivativeDifferentials C3, C5C3, C4C3, C4, C5C3C3,C4, C5C4, C5C3 4 5 weeks Antiderivatives and indefinite integrals – preview onlyArea (of nonnegative function between the function and the x-axis) using sigma notation; investigation of lower, upper, and midpoint sums,Riemann Sums and the definite integral – formal definition of the integralThe Fundamental Theorem of Calculus and its proof; The Mean Value Theorem for Integrals (its proof) and the Average Value of a Function; the Second Fundamental Theorem of Calculus and its proof;Displacement versus total distanceIntegration techniques: integration by substitution; using the Trapezoidal Rule (when an antiderivative of the given function cannot be found); integration of the natural logarithmic function; integration by parts C2C3C3C3C3, C5C2, C3 5 2.5-3 weeks Differential Equations – solved by separation of variablesApplications – Exponential Growth and Decay, Newton’s Law of Cooling, etc.Slope Fields C3, C5C4, C5C3, C4 6 1.5-2 weeks Area between two curvesVolumes of revolution – disc, washer, and shell methodsVolumes using cross-section areas perpendicular to one of the axes C2, C3, C5C2, C3, C5C2, C3,C5 7 2 days L’Hopital’s Rule for finding limits of functions in indeterminate form C2

Curricular Requirements, as referenced above:

C2 – The course teaches all topics associated with Functions, Graphs, and Limits; Derivatives; and Integrals as delineated in the Calculus AB Topic Outline in the AP Calculus Course Description.

C3 – The course provides students with the opportunity to work with functions represented in a variety of ways - - graphically, numerically, analytically, and verbally - - and emphasizes the connections among these representations.

C4 – The course teaches students how to communicate mathematics and explain solutions to problems both verbally and in written sentences.

C5 – The course teaches students how to use graphing calculators to help solve problems, experiment, interpret results, and support conclusions.

AP Calculus AB

Course Overview: The purpose of the course is to learn and apply various techniques of differentiation and integration. The course presents these concepts from four perspectives: numerical, graphical, algebraic, and verbal.

Required Skills: Students must have completed Trigonometry/Precalculus prior to enrolling in this course and must have a working knowledge of a graphing calculator.

Homework: There are daily assignments. These assignments are checked for completion and process of solution. Most daily assignments will require students to watch a video online. They will be required to join Educreations. Some homework assignments will be collected randomly and graded for correctness on up to 4 problems.

Tests: Most tests have a calculator and a non-calculator portion and are modeled on the free response section of the AP exam. The student is expected to show the set up of the problem and, usually, the solution process. The student must often justify in writing a particular answer.

Quizzes: Quizzes are routinely given throughout the course. Each quiz can consist of multiple-choice questions and/or free response questions.

Calculator: The TI-nSpire CAS graphing calculator is required for AP Calculus AB.

Textbook: Calculus: Early Transcendental Functions, 4th edition

Larson, Hostetler, Edward; Houghton Mifflin, 2003

Resources: Calculus - Graphical, Numerical, Algebraic

Finney, DeMana, Waits, Kennedy; Addison Wesley Longman, Inc. 1999

Multiple Choice and Free-Response Question in Preparation for the

AP Calculus (AB) Examination, 8th edition

David Lederman with assistance of Lin McMullin;

D & S Marketing Systems, Inc., 2003

Preparing for the (AB) AP Calculus Examination

George Best and J. Richard Lux; Venture Publishing, 2006

A 95-100%

A- 92-94.9%

B+ 89-91.9%

B 86-88.9%

B- 83-85.9%

C+ 80-82.9%

C 77-79.9%

C- 74-76.9%

D+ 71-73.9%

D 68-70.9%

D- 65-67.9%

Tests 50 %

Quizzes/Writing 20%

Homework/Projects 10%

Exam 20 %

CLASSROOM PROCEDURES AND EXPECTATIONS:

1. Students are held accountable for their own learning. Thus, students are expected to be able to explore, explain, support, collaborate, and participate in all classroom activities and learning
2. Every student will have a folder which they will use to turn in all work and to receive all work to be done for that day. Work will not be accepted unless it is found in the students’ folder
3. Every class will begin with a warm-up/homework check followed by brief homework review and class activities
4. Students are expected to be ON TIME. 3 tardies will equal one incomplete homework
5. Students are expected to work together with Mrs. Donovan as a facilitator
6. Consult the calendar on the school website to determine any assignments which you missed after returning from an absence. The student is responsible to obtain all notes or information missed from their peers or on the portal.
7. If additional assistance is needed, it is the students’ responsibility to approach the teacher during free time to request extra help
8. If extra time occurs in class, students are expected to use that time to work on math assignments only
9. Students are expected to Be Prepared, Be Responsive, and Be Engaged at all times

ABSENCE POLICY:

1. Excused absences have as many days as the absence to make up missing work. It is the student’s responsibility to check their folder, the calendar or website, and their peers for any work that they have missed
2. If a student has an excused absence on the day of a test, they have 1 week to make up the test before or after school. If there is failure to do so, student will receive a 0 for that test.
3. If the absence is due to a school activity, the test or quiz make-up day/time must be arranged before the student leaves for the activity. This appointment must be made by the student with Mrs. Donovan.
4. Unexcused absences do not get credit for missed work

CONSEQUENCES: Students who fail to abide by classroom rules and expectations will be subject to the following consequences:

1. Change of seat
2. Student/teacher conference
3. Loss of credit on assignment or test/quiz
4. Call home to parent/guardian, and/or detention
5. Parent conference