初級微積分第 1 學期：第 1-7 章（彈性安排）

This is a flexible schedule class, which means there are no scheduled live meetings. I will upload videos as YouTube links every Monday morning to the Outschool classroom page that students will watch on their own time throughout the week. The pacing is about one chapter of material every two weeks. 

Students will watch the video lessons and complete homework assignments for each chapter. Answer keys and worked solutions will be provided so students can self-check their homework. Chapter tests will be assigned for each chapter that I will grade (with feedback!) and return. Students can message me with questions at any time, and I will answer with a step-by-step video explanation or written explanation as soon as I can! 

Each week, I will start a discussion thread for a chapter on the Outschool classroom page. This thread is meant for students to ask questions about and discuss homework problems with each other and with me. As a way to keep the discussion alive throughout the course, students will be required to post at least 1 comment per discussion thread. This post has to be related to the chapter and can be a question, an answer to someone else's question, or just a comment about something interesting that they learned during that chapter. Participation in discussions will count towards the student's participation grade, which will be 15% of their grade for the course. The other 85% of the grade will come from the 7 tests that the student takes and submits throughout the course. 

I will be running the class through the Outschool classroom page, but students will need access to YouTube to be able to click the video links and watch the lessons. 

The pre-requisites for this course are the completion of pre-algebra, algebra 1, geometry, and algebra 2 with trigonometry. 

Here are the topics we will cover in the class: 
Chapter 1: Graphs
1-1: The Distance and Midpoint Formulas
1-2: Graphs of Equations in Two Variables
1-3: Lines
1-4: Circles

Chapter 2: Functions and Their Graphs
2-1: Functions
2-2: The Graph of a Function
2-3: Properties of Functions
2-4: Libraries of Functions; Piecewise-defined Functions
2-5: Graphing Techniques: Transformations
2-6: Mathmatical Models: Building Functions

Chapter 3: Linear and Quadratic Functions
3-1: Linear Functions and Their Properties
3-2: Linear Models: Building Linear Functions
3-3: Quadratic Functions and Their Properties
3-4: Build Quadratic Models from Verbal Descriptions
3-5: Inequalities Involving Quadratic Functions

Chapter 4: Polynomial and Rational Functions
4-1: Polynomial Functions and Models
4-2: Properties of Rational Functions
4-3: The Graph of a Rational Function
4-4: Polynomial and Rational Inequalities
4-5: The Real Zeroes of a Polynomial Function
4-6: Complex Zeroes: Fundamental Theorem of Algebra

Chapter 5: Exponential and Logarithmic Functions
5-1: Composite Functions
5-2: One-to-One Functions; Inverse Functions
5-3: Exponential Functions
5-4: Logarithmic Functions
5-5: Properties of Logarithms
5-6: Logarithmic and Exponential Equations
5-7: Financial Models
5-8: Exponential Growth and Decay Models
5-9: Building Exponential, Logarithmic and Logistic Models from Data

Chapter 6: Trigonometric Functions
6-1: Angles and Their Measures
6-2: Trigonometric Functions: Unit Circle Approach
6-3: Properties of Trigonometric Functions
6-4: Graphs of the Sine and Cosine Functions
6-5: Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions
6-6: Phase Shift; Sinusoidal Curve Fitting 

Chapter 7: Analytic Trigonometry
7-1: The Inverse Sine, Cosine, and Tangent Functions
7-2: The Inverse Trigonometric Functions
7-3: Trigonometric Equations
7-4: Trigonometric Identities
7-5: Sum and Difference Formulas
7-6: Double-angle and Half-angle Formulas
7-7: Product-to-Sum and Sum-to-Product Formulas

Chapters 8-14 will be covered in my "Pre-Calculus Semester 2: Chapters 8-14 (Flexible Schedule)" class. If you'd like to take both classes over one semester, you can sign up for both and just work through the material twice as fast. 

Thank you so much for considering my class! I hope to see you in the classroom!