Teacher: Fred Kral, Ph.D.

Telephone: 925-283-2101 x3307

Email Address: fkral

Homework and more information: http://teach.kralsite.com reachable through the usual Bentley School faculty page.

Course Description

The Advanced Placement Calculus AB course is equivalent to a first course in a college calculus sequence. The three major areas covered are functions, graphs and limits (analysis of graphs, limits, asymptotic and unbounded behavior, and continuity), derivatives (concept of a derivative, derivative at a point, derivative as a function, second derivatives, applications, and computation of derivatives) and integrals (interpretations and properties of definite integrals, applications of integrals, Fundamental Theorem of Calculus, techniques of anti-differentiation, applications of anti-differentiation, numerical approximations to definite integrals, and differential equations including slope fields). Graphical, numerical, algebraic, and verbal methods are stressed throughout the course. Students are expected to take the Advanced Placement examination.

Required text and supplemental materials

Course Outline

Prerequisites        
    Chapter 1   Review of Advanced Algebra, Mathematical Analysis, and Trigonometry
Basic Calculus        
    Chapter 2   Velocity, Limits, Derivative at a Point, Derivative Function
    Chapter 3   Derivatives of Polynomial, Exponential, Trigonometric and Logarithmic Functions, Product and Quotient Rules, Chain Rule
    Chapter 4   Maxima, Minima, Concavity, Antiderivatives
    Chapter 5   Areas, Distances, Definite Integrals, Fundamental Theorem of Calculus, Net Change Theorem, Indefinite Integrals, Differential Equations
More Topics and Applications        
    Chapter 2   Precise Definition of a Limit, Continuity, Intermediate Value Theorem, Limits at Infinity
    Chapter 3   Implicit Differentiation, Applications of Derivatives, Exponential Growth and Decay, Related Rates, Linear Approximations, Differentials
    Chapter 4   The Mean Value Theorem, Curve Sketching and Graphing, Optimization
    Chapter 5   Integration by Substitution
    Chapter 6   Areas between Curves, Volumes, Average Value of a Function
    Chapter 7   Trapezoidal Rule
    Chapter 9   Modeling with Differential Equations, Direction (Slope) Fields, Separable Differential Equations
Course Review        
        Review including Practice AP Examinations

Assessment

Homework: timely completion of homework assignments. Assessed formally and informally. 1 point per homework
Review homework: timely completion of representative problems in preparation for tests and exams. 4 points per review
Quizzes: written and graphical solutions of problems similar to homework problems. 10 points per quiz
Mid-Trimester Tests: written and graphical solutions of problems from recent material. 100 points per test
End-Trimester Examinations: written and graphical solutions of problems from the whole trimester (comprehensive). 20% of course grade
In-Class work: positive energy and interest level, relative to individual capability, during in-class work including discussion, working on investigations, and practice during class. Assessed informally. 5 points per week

Course Rules

Each student is expected to abide by the Bentley rules in the Student Handbook. In addition, you may not re-take quizzes, tests or exams for credit and there is no extra credit. You may work with other students as long as you share the work. It is wise to put the name of each contributing student on an assignment to avoid issues with plagiarism. I encourage study groups.

 

Please see the web site for other information including assignments.