BC Calculus Syllabus 2014-15 Instructor: Jim Moser Office: 203 AcLab: 206 Email: jmoser@ladueschools.net Attendance: You are expected to attend class every day that the class meets. Please be on time for each class. If you know you will be missing a class, please notify me before the class. If you miss a class, contact me before the next class to find out what you missed. The best way to avoid problems is to communicate with me as much as possible.

Grading Scale: 97-100%=H 87-89%=B+ 77-79%=C+ 67-69%=D+ 93-96% =A 83-86%=B 73-76%=C 63-66%=D 90-92% =A- 80-82%=B- 70-72%=C- 60-62%=D- 59-0%=F Homework: Practice is the key to success. It is imperative that you reinforce new concepts outside the classroom. Assignments should be completed by the next class. Many days class will begin with a homework quiz. If you have difficulty completing assignments, see me during AcLab or after school in Room 203. I expect you to attempt all parts of the homework. Each of you can succeed as long as you are willing to learn from your mistakes and reinforce your success. Homework is an important part of the learning process in math courses. You should expect to spend two hours outside of class for every hour spent in class. You will receive a homework assignment for each section we cover in this class. These assignments will be only a minimum of what you should complete in order to be successful. It is important to develop good work habits now in order to be successful in all of your mathematics coursework. Homework will not be collected, but quizzes will be based on the homework problems.

Quizzes: Eleven or more short quizzes will be given during each semester. Each

quiz will consist of one or more problems similar to recent homework problems. Quizzes will be unannounced and closed book. Quizzes will be given at the beginning of class; make-ups will not be allowed for late or absent students. Only your ten best quiz grades will be counted as part of your final grade.

COURSE DESCRIPTION: This course is designed to follow the AP Calculus BC course guidelines as set by the College Board for AP Calculus. The primary focus of the course is to develop a thorough understanding of the concepts covered in Calculus BC and master the skills necessary to solve problems related to those concepts. Students will learn through a variety of methods. Classroom activities will emphasize graphical representations of calculus concepts with and without graphing calculators. Students may work in groups to discuss homework problems as well as solve more open ended applications problems requiring discussion and written explanations. EVALUATION: Student work will be assessed on a regular basis. Assessments will include daily homework problems, quizzes, tests and AP problem sets assigned with each chapter from the text. The problem sets are intended to help students grasp the foundations of the topics and their applications and answer in precise mathematical language, both verbally and in written sentences. They also serve to help familiarize the students with the style of the AP questions. Quizzes and tests will include, but not be limited to, problems like those in the homework and problem sets. Quizzes and tests may include both calculator and non-calculator sections. FINAL EXAM: Each semester a cumulative exam will be given during the period designated on the semester final exam schedule. REFERENCE MATERIALS: Primary Textbook Ross L. Finney, Franklin D. Demana, Bert K. Waits, Daniel Kennedy, Calculus: Graphical, Numerical, Algebraic, Boston, Massachusetts, 2007 David Lederman, Multiple-choice & Free-Response Questions in Preparation for the AP Calculus (BC) Examination (Sixth Edition), Brooklyn, New York, D & S Marketing Systems, Inc., 1999. Web Resources AP Central Visual Calculus Website www.ies.co.jp/math/java/calc/index.html (various calculus applets) Calculator Students are required to have and to use a graphing calculator. Demonstrations will be done in class using TI-83, TI-83+, TI-84, and TI-nSpire calculators.

TOPIC OUTLINE: Chapter 1: Prerequisites for Calculus

Lines Functions and Graphs

Analysis of graphs, with and without graphing calculator Exponential Functions

Students will discuss and identify situations that may result in and exponential growth or decay situation.

Parametric Equations Functions and Logarithms Trigonometric Functions

Asymptotic and unbounded behavior Comparing relative magnitudes of functions and their rates of change including discussion of the various types of functions.

Chapter 2: Limits and Continuity Rates of Change and Limits

Intuitive understanding of the limiting process Demonstration of limits of functions at asymptotes and at infinity using graphing calculator including discussion of these limits in verbal as written form Calculating limits using algebra Estimating limits from graphs or tables of data

Limits Involving Infinity Limits of functions (including one-sided limits)

Continuity Continuity as a property of functions Intuitive understanding of continuity Continuity in terms of limits Intermediate Value Theorem

Rates of Change and Tangent Lines Estimating limits from graphs or tables of data, describing in groups what mathematics lead to these conclusions. Demonstration of tangent lines on the graphing calculator Group discussion of what these tangent lines mean--setting up the discussion of the derivative in the next chapter.

Chapter 3: Derivatives

Derivative of a Function Concept of the derivativegraphically, numerically, and analytically Definition of the derivative as a limit of the difference quotient and as the limit of average rate of change Derivative as an instantaneous rate of change analytically, graphically, and numerically

Discussion as to what the rate of change represents. Differentiability

Differentiability implies continuity Differentiability implies local linearity Demonstration of local linear linearity on the graphing calculator Finding a numerical derivative on a graphing calculator

Rules for Differentiation Derivative at a point Slope of a curve at a point Power rule, product rule, quotient rule Second derivatives

Velocity and Other Rates of Change Approximate average and instantaneous rate of change from tables and graphs Equations involving derivatives Verbal descriptions are translated into equations involving derivatives and vice versa. Approximate average and instantaneous rate of change from tables and graphs Equations involving derivatives. Verbal descriptions are translated into equations involving derivatives and vice versa.

Derivatives of Trigonometric Functions Chain Rule Implicit Differentiation Derivatives of Inverse Trigonometric Functions

Using implicit differentiation to derive derivatives of inverse trigonometric functions

Derivatives of Exponential and Logarithmic Functions Computation of derivatives During this chapter, students can start doing free response type questions involving discussion about what one is actually doing when taking a derivative.

Chapter 4: Applications of Derivatives Extreme Values of Functions

Absolute and local extrema Demonstration of extreme values of functions using graphing caculators Extreme Value Theorem

Mean Value Theorem Increasing and decreasing functions, monotonicity

Connecting f, and f with the Graph of f Derivative as a function Concavity, points of inflection Using a graphing calculator to show the connection between f, and f with the graph of f Discussion of what type of behavior one would observe in f when f is positive or negative. Discussion of what type of behavior one would expect in f when f is positive or negative.

Modeling and Optimization

Interpretation of the derivative as a rate of change in varied applied contexts including velocity, speed, and acceleration. Describe solutions both verbally and in written sentences. Solving verbal optimization problems analytically and graphically with a graphing calculator. Describe solutions both verbally and in written sentences.

Linearization and Newtons Method Local linear approximation

Related Rates Simulation of sliding ladder using a graphing calculator Solving verbal problems involving related rates. Describe solutions both verbally and in written sentences

Chapter 5: The Definite Integral

Estimating with Finite Sums Definite Integrals

Definite integral as a limit of Riemann sums Definite Integrals and Antiderivatives

Antiderivatives following directly from derivatives of basic functions Mean Value Theorem for Integral

Fundamental Theorem of Calculus Using a graphing calculator to evaluate a definite integral

Trapezoidal Rule Chapter 6: Differential Equations and Mathematical Modeling

Slope Fields and Eulers Method Demonstrating slope fields on the graphing calculator. Demonstration of Eulers Method with program on graphing calculator.

Antidifferentiation by Substitution Antidifferentiation by Parts Exponential Growth and Decay

Solving separable differential equations with and without initial conditions Demonstration of Newtons Law of Cooling. Students solve similar problems and describe solutions both verbally and in written sentences. Modeling exponential growth and decay verbal problems. Describe solutions both verbally and in written sentences.

Logistic Growth Partial Fractions Solving verbal logistic differential equations and using them in modeling, Describe solutions both verbally and in written sentences. Demonstration of logistic growth problems using a graphing calculator

Chapter 7: Applications of Definite Integrals Integral As Net Change Areas in the Plane

Volumes Volumes of with known cross sections including circular and square Cylindrical Shells

Lengths of Curves Vertical tangents and cusps

Applications from Science and Statistics Students solve problems in groups and describe solutions both verbally and in written sentences.

The following topics are covered only in the BC curriculum. Chapter 8: Sequences, LHpitals Rule, and Improper Integrals

Sequences LHpitals Rule Relative Rates of Growth

Demonstration comparing rates of growth using a graphing calculator Students discuss types of equations how one might determine relative rates of growth using calculus.

Improper Integrals Chapter 9: Infinite Series

Power Series Motivating examples, including decimal expansion Geometric series with applications Technology will be used to explore convergence or divergence

Taylor Series Constructing series Series for sin x and cos x Demonstration using a graphing calculator of relationship between sin x and Maclaurin series approximation Maclaurin series and the general Taylor series centered at x = a

Maclaurin series for the functions

Combining Taylor Series, substitution, differentiation, and antidifferentiation Taylors Theorem

Remainder Remainder Estimation Theorem (LaGrange error bound) Class discussion as to why error bound is important, and why the formula works mathematically.

Radius of Convergence Comparing series Ratio test

Testing Convergence at Endpoints Integral test Harmonic series and p-series Comparison tests

Alternating series with error bound. Class discussion as to why error bound is important, and why the formula works mathematically. Absolute and conditional convergence Intervals of convergence

Chapter 10: Parametric, Vector, and Polar Functions Parametric Functions

Parametric curves in the plane Slope and Concavity Arc length

Vectors in the Plane Two-dimensional vectors Vector operations Modeling planar motion Velocity, acceleration, and speed Displacement and distance traveled Students will be able to describe motion concepts learned in physics in mathematical terms both verbally and in written sentences.

Polar Functions Polar curves Slopes of polar curves Polar areas