Course Description
Grade 11 to 12 Math
Course Objective: Calculus is designed to give students an overview of Calculus topics such as limits and continuity, derivatives, anti-derivatives, integrals and differential equations. While this course covers many of the same concepts found in Advanced Placement Calculus, it is not bound by the pace and rigor necessary for success on the AP Calculus exam. Therefore, this course best suits the student who is mathematically ready to learn Calculus but does not want the “stress” of AP Calculus. Students have the option of taking the AP Calculus exam after completing this course
Textbook: Math 11 to 12
- Contemporary Calculus I and II by Dale Hoffman.
Materials:
- Student textbook
- Practice and enrichment worksheets
- Manipulative materials
- Calculators
Time Allotment:
- 45 minutes per day, 2 days per week
Course Content:
1. Functions, Limits, Continuity
2. Derivatives
3. Applications of Derivatives
4. Integration
5. Applications of Definite Integrals
6. Transcendental Functions
7. Integration Techniques
The instructor reserves the right to modify this syllabus for the needs of the class.
Course Outline
Chapter 1 — Functions, Graphs, Limits and Continuity
• 1.0 Slopes & Velocities
• 1.1 Limit of a Function
• 1.2 Limit Properties
• 1.3 Continuous Functions
• 1.4 Formal Definition of Limit
Chapter 2 — The Derivative
• 2.0 Slope of a Tangent Line
• 2.1 Definition of Derivative
• 2.2 Differentiation Formulas
• 2.3 More Differentiation Patterns
• 2.4 Chain Rule (!!!)
• 2.5 Using the Chain Rule
• 2.6 Related Rates
• 2.7 Newton’s Method
• 2.8 Linear Approximation
• 2.9 Implicit Differentiation
Chapter 3 — Derivatives and Graphs
• 3.1 Introduction to Maximums & Minimums
• 3.2 Mean Value Theorem
• 3.3 f’ and the Shape of f
• 3.4 f” and the Shape of f
• 3.5 Applied Maximums & Minimums
• 3.6 Asymptotes
• 3.7 L’Hospital’s Rule
Chapter 4 — The Integral
• 4.0 Introduction to Integrals
• 4.1 Sigma Notation & Riemann Sums
• 4.2 The Definite Integral
• 4.3 Properties of the Definite Integral
• 4.4 Areas, Integrals and Antiderivatives
• 4.5 The Fundamental Theorem of Calculus
• 4.6 Finding Antiderivatives
• 4.7 First Applications of Definite Integrals
• 4.8 Using Tables to Find Antiderivatives
• 4.9 Approximating Definite Integrals
Chapter 5 — Applications of Definite Integrals
• 5.0 Introduction to Applications
• 5.1 Volumes
• 5.2 Arc Lengths & Surface Areas
• 5.3 More Work
• 5.4 Moments & Centers of Mass
• 5.5 Additional Applications
Chapter 6 — Introduction to Differential Equations
• 6.0 Introduction to Differential Equations
• 6.1 Differential Equation y’=f(x)
• 6.2 Separable Differential Equations
• 6.3 Exponential Growth, Decay & Cooling
Chapter 7 — Inverse Trigonometric Functions
• 7.0 Introduction to Transcendental Functions
• 7.1 Inverse Functions
• 7,2 Inverse Trigonometric Functions
• 7.3 Calculus with Inverse Trigonometric Functions
Chapter 8 — Improper Integrals and Integration Techniques
• 8.0 Introduction Improper Integrals & Integration Techniques
• 8.1 Improper Integrals
• 8.2 Integration Review
• 8.3 Integration by Parts
• 8.4 Partial Fraction Decomposition
• 8.5 Trigonometric Substitution
• 8.6 Trigonometric Integrals
Areas to be evaluated:
- Class participation
- Homework assignments
- Computation time tests
- Tests
- Quizzes
Additional activities:
- Math vocabulary journals
- Math games