Calculus Syllabus - Pacific Lutheran High School

Mr. Schreier

2011-2012

Course Summary:

This AP Calculus AB topic outline is coordinated with the California State Standards. The two primary objectives for this course are to generate and/or enhance the problem solving skills of the students’ through various applications of material from each chapter and to focus the students’ attention on the goal of passing the AP Calculus AB exam.

Class Materials Needed:

Textbook - Stewart, James: Calculus – Early Transcendentals 5th Edition

Graphing calculator

Note paper

pen/pencil

Assessment:

Students will be assessed through homework, quizzes, and tests/exams. Calculus AB follows P.L.H.S. policy for grading which is found in the Student Handbook. Course emphasis will be on concepts rather than on repetition.

Course Sequence:

	Week 1	Introduction

	Week 2-4	Functions and Models
		Four ways to represent a function Mathematical Models New f\Functions from Old Functions Graphing Calculators and Computers Exponential Functions Inverse Functions and Logarithms
	Week 5-7	Limits and Derivatives
		The Tangent and Velocity Problems The Limit of a Function Calculating Limits Using the Limit Laws The Precise Definition of a Limit Continuity Limits at Infinity, Horizontal Asymtotes Tangents, Velocities, and Other Rates of Change Derivatives The Derivative as a Function
	Week 8-12	Differentiation Rules
		Derivatives of Polynomials and Exponential Functions The Product and Quotient Rules Rates of Change in the Natural and Social Sciences Derivatives of Trigonometric Functions The Chain Rule Implicit Differentiation Higher Derivatives Derivatives of Logarithmic Functions Hyperbolic Functions Related Rates Linear Approximations and Differentials
	Week 13-15	Applications of Differentiation
		Maximum and Minimum Values The Mean Value Theorem How Derivatives Affect the Shape of a Graph Indeterminate Forms and L’Hospital’s Rule Summary of Curve Sketching Graphing with Calculus and Calculators Optimization Problems Application to Business and Economics Newton’s Method Antiderivatives
	Week 16-18	Integrals
		Areas and Distances The Definite Integral The Fundamental Theorem of Calculus Indefinite Integrals and the Net Change Theorem The Substitution Rule The Logarithm Defined as an Integral
	Week 19-21	Applications of Integration
		Areas Between Curves Volumes Volumes by Cylindrical Shells Work Average Value of a Function
	Week 22-25	Techniques of Integration
		Integration by Parts 25tion of Rational Functions by Partial Fractions Strategy for Integration Integration Using Tables and Computer Algebra Systems Approximate Integration Improper Integrals
	Week 26-29	Further Applications of Integration
		Arc Lengths Area of a Surface of Revolution Applications to Physics and Engineering Applications to Economics and Biology Probability
	Week 30-31	Differential Equations

	Week 32-33	Review for AB Examination

	Week 32-35	Infinite Sequences and Series (This topic is not covered on the AB Exam but is in the State Standards)
		Sequences Series The Integral Test and Estimates of Sums The Comparison Tests Alternating Series Absolute Convergence and the Ration and Root Tests Power Series Representation of Functions as Power Series Taylor and Maclaurin Series The Binomial Series Applications of Taylor Polynomials

All of the above items will be touched upon at varying degrees of depth throughout the school year.

White Board Formula:

Each class period, students will be given at least one educational objective (what skill is being taught during the class), an activity to reinforce this educational objective (what students/teachers will be engaged in to achieve the objective), and an assessment for the activity. Educational objectives are pulled from California Content Standards or other standards appropriate for each course.

ELSR Integration:

P - Students will Put Christ first through their study of His Word, meditation upon his teachings/doctrines, and discussion of his saving message
L - Students will Learn academics when they daily delve into the correct approach to the Bible(hermenutics), understand God’s plan of salvation centered on the person and work of Jesus Christ, and study alternate viewpoints to the classical Christian position.
H - Students will Hone life skills through their application of the knowledge they receive in this course. They will personalize the gospel message and work to improve in the area of Sanctification
S - Students will learn ways to Serve school, church, and community after they have been built up themselves in the Christian faith. Examples of others who have served their churches and communities will be studied