Course title
M20010001
Pre-calculus

ikegami daisuke
Course description
This is a preliminary course for the calculus courses. Starting with functions and graphs, you will learn how to play with basic functions such as trigonometric functions, exponentials, and logarithms. You will also learn how to solve quadratic equations, how to draw the graph of quadratic functions as well as how to use polar coordinates to express complex numbers and solve basic equations with De Moivre's Theorem. People with enough background and understanding of the mathematics at the IB higher level do not need to take this course.
Purpose of class
Through this course, you are expected to obtain basic knowledge & understanding of mathematics required to take the course "Calculus I" afterwards.
Goals and objectives

Goals and objectives Course Outcomes
1. The students can compute the values of basic functions such as linear functions, quadratic functions, and polynomial functions and their combinations & inverses. You can also draw the graphs of those functions.
A-1
2. The students can solve quadratic equations. You can use division of polynomials to solve basic polynomial equations.
A-1
3. The students can compute the values of exponential functions & logarithms as well as solve basic equations with those functions. You can also draw the graphs of exponential functions & logarithms.
A-1
4. The students can compute the values of trigonometric functions & their inverses using laws of sines & cosines and trigonometric identities. You can also draw the graphs of those functions.
A-1
5. The students can express complex numbers using poloar coordinates and solve basic equations using De Moivre's Theorem.
A-1
Language
English
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Real numbers
Exponents and radicals
Algebraic expressions
Rational expressions
Read 1.1-1.4 in the textbook 100分
Work on exercises 90分
2. Equations
Modeling with equations
Inequalities
Coordinate geometry
Read 1.5, 1.7-1.9 in the textbook 100分
Work on exercises 90分
3. Functions
Graphs
Average rate of change
Linear functions
Read 2.1-2.5 in the textbook 100分
Work on exercises 90分
4. Transformations of functions
Combining functions
Read 2.6-2.7 in the textbook 60分
Work on exercises 130分
5. One-to-one functions and inverses
Quadratic functions
Polynomial functions
Read 2.8, 3.1-3.2 in the textbook 80分
Work on exercises 110分
6. Dividing polynomials and real roots
Complex numbers and fundamental theorem of algebra
Rational functions
Read 1.6, 3.3-3.6 in the textbook 100分
Work on exercises 90分
7. Mid-term exam and discussions on the solutions afterwards Preparation for mid-term 190分
8. Exponential functions and logarithms
Properties of logarithms
Equations with exponents and logs
Read 4.4-4.6 in the textbook 100分
Work on exercises 90分
9. Trigonometric functions via the unit circle
Graphs of trigonometric functions
Read 5.1-5.4 in the textbook 80分
Work on exercises 110分
10. Inverse trig functions and their graphs
Trigonometric functions via right angles
Read 5.5-5.6, 6.1-6.3 in the textbook 100分
Work on exercises 90分
11. Inverse trig functions and right triangles
Laws of sines and cosines
Trigonometric identities
Read 6.4-6.6, 7.1-7.2 in the textbook 80分
Work on exercises 110分
12. More identities
Working with equations involving trig functions
More equations with trig functions
Read 7.3-7.5 in the textbook 60分
Work on exercises 130分
13. Polar coordinates Read 8.1-8.3 in the textbook 60分
Work on exercises 130分
14. Final exam and discussions on the solutions afterwards Preparation for final 190分
Total. - - 2660分
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Mid-term etc. Final Total.
1. 15% 10% 25%
2. 15% 10% 25%
3. 5% 15% 20%
4. 5% 20% 25%
5. 0% 5% 5%
Total. 40% 60% -
Evaluation method and criteria
Mid-term exam, presentation on exercises etc. will contribute 40% of your grade.
Final exam will contribute 60% of your grade.
Those who get at least 60% of the full score will pass this course.
Textbooks and reference materials
Precalculus: Mathematics for Calculus, 7th edition, James Stewart, Lothar Redlin, Saleem Watson
Prerequisites
There are no prerequisites.
Office hours and How to contact professors for questions
  • Monday, 17:00-18:00 in the lecturer's office. Contact e-mail address: ikegami@shibaura-it.ac.jp
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic problem-solving skills
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicatable
N/A N/A
Education related SDGs:the Sustainable Development Goals
    Last modified : Sat Mar 21 11:42:36 JST 2020