MATH 1AHP: HONORS CALCULUS I SEMINAR
Foothill College Course Outline of Record
Heading | Value |
---|---|
Effective Term: | Summer 2022 |
Units: | 1 |
Hours: | 1 lecture per week (12 total per quarter) |
Corequisite: | MATH 1AH. |
Degree & Credit Status: | Degree-Applicable Credit Course |
Foothill GE: | Non-GE |
Transferable: | CSU/UC |
Grade Type: | Letter Grade Only |
Repeatability: | Not Repeatable |
Student Learning Outcomes
- Use formal definitions and theorems with mathematical proof techniques to prove limits, derivative values, and relevant theorems.
- Complete applied real world problem projects with solutions and relevant explanations, accompanied with the use of mathematical typesetting software.
Description
Course Objectives
The student will be able to:
- State and prove limits.
- State and prove derivatives.
- State and prove theorems.
- Demonstrate an understanding of applications of the derivative.
Course Content
- State and prove limits
- Epsilon-delta proofs of limits
- Proofs of limit laws
- Proofs involving continuity
- L'Hospital's Rule
- State and prove derivatives
- Epsilon-delta proofs
- Derivative values
- Second derivative values
- Proofs of derivative rules
- Power rule
- Product rule
- Derivatives of logarithmic functions
- Derivatives of trigonometric functions
- Derivatives of inverse functions
- Epsilon-delta proofs
- State and prove theorems
- Mean Value Theorem
- Rolle's Theorem
- Intermediate Value Theorem
- Extreme Value Theorem
- The Squeeze Theorem
- Mean Value Theorem
- Demonstrate an understanding of applications of the derivative
- Related rates
- Optimization
- Linear approximations
- Differentials
Lab Content
Not applicable.
Special Facilities and/or Equipment
2. Access to mathematical typing software.
3. When taught via Foothill Global Access, ongoing access to computer with email software and hardware; email address.
Method(s) of Evaluation
Typed formal proofs
Special applied projects
In-class presentations
Method(s) of Instruction
Lecture
Discussion
Cooperative learning projects
Representative Text(s) and Other Materials
Briggs, W., L. Cochran, and B. Gillett. Calculus Early Transcendentals, 3rd ed.. 2018.
Instructor-generated materials, such as excerpts from:
1. Trench, William F. Introduction to Real Analysis. Free Edition Open Textbook Online.
2. Lay, Steven R. Analysis With an Introduction to Proof, 5th ed. 2014.
Types and/or Examples of Required Reading, Writing, and Outside of Class Assignments
- Homework problems covering the subject matter from the text. Honors students will be assigned more of the challenging problems from the text on a regular basis.
- Special applied projects: At least one applied real world project which will be typed using appropriate math typing software. Projects will also be presented in class.
- Typed proofs: Formal proofs which will be typed and accompanied with math typing software.