Honors Calculus #
Course Description #
Explore the concepts, methods, and applications of differential and integral calculus. You’ll work to understand the theoretical basis and solve problems by applying your knowledge and skills. You’ll learn how to determine expressions and values using mathematical procedures and rules; connect representations; justify reasoning and solutions; and use correct notation, language, and mathematical conventions to communicate results or solutions.
Units of Study #
- 1 Limits and Continuity
- Explore how limits allow solving problems involving change and to better understand mathematical reasoning about functions.
- 2 Differentiation: Definition and Fundamental Properties
- Apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.
- 3 Differentiation: Composite, Implicit, and Inverse Functions:
- Master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.
- 4 Contextual Applications of Differentiation
- Apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms.
- 5 Analytical Applications of Differentiation
- Explore relationships among the graphs of a function and its derivatives, and learn to apply calculus to solve optimization problems.
- 6 Integration and Accumulation of Change
- Apply limits to define definite integrals and how the Fundamental Theorem connects integration and differentiation. Apply properties of integrals and practice useful integration techniques.
- 7 Differential Equations
- Solve certain differential equations and apply that knowledge to further understand exponential growth and decay.
- 8 Applications of Integration
- Make mathematical connections that will allow solving a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions.
You will have access to TI-84 Plus calculators in class, and an emulator of the same is on your Chromebooks. Purchasing your own is not a bad idea if you have the means, but not required in any way shape or form. I still have a TI-89 from my freshman year of college over 20 years ago, so it’s worth considering if you anticipate using it after this course.
If you intend to purchase a calculator and take the AP exam, see this list of acceptable calculators from College Board. You want calculators with an asterisk after their name.
- Grading is point-based. Homework assignments are worth 1 point, quizzes 10 points and exams 25.
- Late work loses two percentage points per day with a floor of 70%
- The official gradebook will exist on Canvas, with Genesis only having the overall grade
- Ask your classmates first when you have a question about the material