Jim Meyers
832-668-7200 x72308
AP CALCULUS AB
Syllabus
Course Description
Calculus is the mathematics behind the dynamic universe in which we live. Prior to this course, mathematics is mostly the study of static systems. Calculus offers students practice with the mathematics that drives the perennially changing world. In addition to this, students have the opportunity to see the beauty of Calculus. After this course, students should have the understanding and ability to succeed in future mathematics courses.
Technology
Students are required to use a TI-84 plus (or higher) graphing calculator. Throughout the course, students are taught various problem solving methods using the calculator.
Students use graphing functions to identify zeroes, estimate slopes and approximate areas under curves on the TI-84 plus and some internet-based graphing programs. Students are taught basic programming on the TI-84 plus in order to watch functions as they approach asymptotes and examine sequences and series. Students will learn to use the TI-84 plus graphing calculator to test hypotheses and draw conclusions. Students will interpret the results of their experimentation with data and functions in order to find mathematical truth.
Course Planner
Functions (1 week)
· Viewing functions numerically, graphically, verbally and analytically
· Linear Models and Rates of Change
· Fitting models to data
Limits and Derivatives (6 weeks)
· Tangent and Velocity problems
· Limit of a Function
· Calculating Limits Using the Limit Laws
· Continuity
· Limits Involving Infinity
· Tangents, Velocities and Other Rates of Change
· Derivatives
· Derivative as a Function
· f and f’
Differentiation Rules (4 weeks)
· Derivatives of Polynomials and Exponential Functions
· The Product Rules
· Rates of Change in the Natural and Social Sciences
· Derivatives of Logarithmic Functions
· Linear Approximations and Differentials
Applications of Differentiation (4 weeks)
· Related Rates
· Maximum and Minimum Values
· Derivatives and the Shapes of Curves
· Indeterminate Forms and l`Hospital’s Rule
· Optimization Problems
· Applications to Economics
· Newton’s Method
· Antiderivatives
Integrals (3 weeks)
· Areas and Distances
· The Definite Integral
· Evaluating Definite Integrals
· The Fundamental Theorem of Calculus
· The Substitution Rule
· Integration by Parts
· Additional Techniques of Integration
· Approximate Integration
· Improper Integrals
Applications of Integration (3 weeks)
· More about Areas
· Volumes
· Arc Length
· Average Value of a Function
· Applications to Physics and Engineering
· Applications to Economics and Biology
· Probability
Differential Equations (4 weeks)
· Modeling with Differential Equations
· Direction Fields and Euler’s Method
· Separable Equations
· Exponential Growth and Decay
· The Logistic Equation
· Predator-Prey Systems
Infinite Sequences and Series (3 weeks)
· Sequences
· Series
· The Integral and Comparison Tests; Estimating Sums
· Other Convergence Tests
· Power Series
· Representations of Functions as Power Series
· Taylor and Maclaurin Series
· The Binomial Series
· Applications of Taylor Polynomials
· Using Series to Solve Differential Equations
The schedule leaves about 5 weeks flexibility to add time to topics as learners need.
Teaching Strategies
Directed teaching introduces and proves theorems from calculus. Throughout the course, students work together, applying calculus in a project-based environment. Students are encouraged to work together on homework assignments. Technology is applied to the course with the use of TI-84 plus calculators and computer graphing software.
Student Evaluation
Class participation is a major aspect of student evaluation. Students demonstrate their understanding of material by interacting with me as they work through problems or projects. Students present and explain their group work before the class.
Formal written assessments are given at the end of each major topic and account for the majority of the student’s classroom grade. These allow each student to demonstrate the extent of their understanding of each topic. The final exam in the course is a written assessment.
For each six weeks:
· Major grades- 70%. Tests and Projects.
· Minor grades- 30%. Quizzes, Homework, Classwork and Participation as appropriate.
Primary Textbook
Larson, Hostetler, Edwards. CALCULUS of a Single Variable, 10th edition. Houghton
Mifflin, Co. 2006.