Introduction to Calculus I
Course presentation
- Name, syllabus;
- Plan:
1) Present resources; objectives (direct/indirect benefits)
2) How the course is organized
3) Using technology
4) Background information (not test);
…
1) - Objectives:
1) To introduce the basic ideas of real analysis with proofs;
- Will involve some algebraic structures;
- The 1st part (Ch.2-3) is also a general introduction to Topology (metric);
2) To teach students how to designing mathematical proofs, starting with:
- Idea: picture (graphical representation);
- Plan: “flow chart” of the proof’s logic;
- Math code: the details of the proof (the program in “low level” math language).
This would help students think conceptually, intuitively and globally, but read and write rigorous mathematics.
3) To help students develop a rigorous understanding of the theorems of calculus;
4) To enhance student’s ability to communicate abstract ideas (written & oral form);
- Course format:
- Course format is “Lecture – Recitation”: more details …
- Learning cycle:
- Basic idea: repeat a topic to learn it;
- Read before lecture; write an outline; work HW problems; read next section before lect.
- “Journal of activities”: testing it to be used w. Calc. students;
- Please provide feedback on its utility
- Class activities:
- Answering questions;
- Student practice: proofs; no grading; 1 pt. for turning them in (reasonably completed);
- Presenting solutions (depending on time / # students);
2) Background information;
3) 5 min break;
4) Sections 1.1 & 1.2
Resources for Calc I
- Instructor: Lucian Ionescu
- Office hours: MWRF 1:00-2:00 p.m., STV 303G;
- Appointments: in person or by e-mail;
- Web site: LI homepage/mat145
- Text: Calculus by James Stewart, 2nd ed., 2001;
Content:
Ch.1 – Functions as mathematical models
(Calculus 1,2,3 … “theme”)
Ch.2,3,4 – Studying functions (models):
- Limits and derivatives, applications;
Ch.5 – Finding functions from Differential Equations:
- Introduction to integration.
Objectives:
- General: building knowledge and learning skills;
- Specific: calculus methods applied to sciences.
- Calculator with a Computer Algebra System (CAS): TI-89/92
(Symbolic differentiation, integration, solving D.E. etc.)
- Solving a problem: understanding versus computing.
- Syllabus
1) Lecture – recitation format
2) Learning cycle
3) List of homework assignments; timing …
4) Evaluation / grading scale
The Learning Cycle
- What is “learning”?
- Acquisition of Knowledge
- Building Skills.
- How “to learn”? (Many “good answers” possible!)
1. BEFORE class, skim through the assigned section (1/2 hour)
(Know “what’s on the menu” - next class).
2. Come to class and:
- Answer questions from the previous section;
- Ask questions from the current section;
- Take class notes; do not just “follow the explanations”;
- Focus on concepts and methods.
3. After class,
- Review the material, write an OUTLINE of the section;
- Attempt all the homework problems:
a) First, without the help of the book;
b) If it doesn’t work, use the book (Review as above);
c) Write a list of questions to ask (group/instructor).
- Impact on grade (usually): 1-4 leads to A!
“Calculus: 1,2,3…”
Solving a Problem:
- Find the quantities involved-> variables;
- Find the relations among variables-> equations;
- Translate the questions into tasks (solving eq.);
- Apply the appropriate method;
- Interpret the result.