Pre-college Mathematics *Optional subject
| Lecturer | Yukio ISHIDA, Professor |
|---|---|
| Department | G30, 2015 Fall |
| Recommended for: | G30 (2・1.5 hours / session One session / week 15 weeks / semester) |
Course Overview
This course is a companion course to Calculus I. It aims to help students with little or no precalculus knowledge to master the basic calculus material in preparation for the more advanced course of Calculus I. This is done by reviewing high school mathematics.
Course Prerequisites
There are no particular prerequisites for this course. Basic algebraic computation capabilities will ease the learning.
Course Content
Notice for Students
This course is an optional subject which does not count towards the number of credits required for graduation in any program at Nagoya University. This course will be more or less demanding depending on the initial level in mathematics. In case of difficulties, it is recommended to study in e-learning lecture introduced in the first lesson.
Textbook
Handouts are delivered.
Reference Book
E-learning in the Nagoya University website (This is introduced in the first lecture).
Lecture Videos
| Session | Lectures | Video | Notes |
|---|---|---|---|
| Course I Functions and Equations | |||
| 1 | Polynomials and Factoring |
Video (19:45) |
Note |
| 2 | Algebraic Equations and Functions |
Video (18:35) |
Note |
| 3 | Linear and Quadratic Inequalities |
Video (16:08) |
Note |
| 4 | Trigonometric Functions Video(I) |
Video (14:09) |
Note |
| 5 | Trigonometric Functions Video(II) |
Video (17:25) |
Note |
| 6 | Trigonometric Functions Video(III) |
Video (15:01) |
Note |
| 7 | Complex Numbers |
Video (23:10) |
Note |
| 8 | Exponential Functions |
Video (22:42) |
Note |
| 9 | Fractional Functions and Irrational Functions |
Video (15:33) |
Note |
| 10 | Inverse Functions |
Video (14:42) |
Note |
| 11 | Common Logarithms |
Video (30:14) |
Note |
| 12 | Law of Sines and Law of Cosines |
Video (16:41) |
Note |
| 13 | Applications of Trigonometric Functions |
Video (14:25) |
Note |
| 14 | Graphs and Equations Video(I) |
Video (22:20) |
Note |
| 15 | Graphs and Equations Video(II) |
Video (25:10) |
Note |
| Course II Calculus | |||
| 1 | Limit of Functions and Derivatives |
Video (26:28) |
Note |
| 2 | Derivative and Graphs |
Video (22:07) |
Note |
| 3 | Differentiation Formulas |
Video (16:55) |
Note |
| 4 | Derivatives of Trigonometric Functions |
Video (18:01) |
Note |
| 5 | Derivatives of Logarithmic Functions and Exponential Functions |
Video (19:33) |
Note |
| 6 | Applications of Derivatives to Equations and Inequality |
Video (19:54) |
Note |
| 7 | Application to Physics |
Video (22:52) |
Note |
| 8 | Approximation of a Function |
Video (20:04) |
Note |
| 9 | Antiderivatives |
Video (30:03) |
Note |
| 10 | Definite Integrals |
Video (20:58) |
Note |
| 11 | Estimating Area by Rectangles |
Video (14:41) |
Note |
| 12 | Application of Integrals Video(1) |
Video (22:24) |
Note |
| 13 | Application of Integrals Video(2) |
Video (27:03) |
Note |
| 14 | Differential Equations Video(1) |
Video (21:20) |
Note |
| 15 | Differential Equations Video(2) |
Video (19:07) |
Note |
| Course III Linear Algebra | |||
| 1 | Basic Rules of Vectors |
Video (23:58) |
Note |
| 2 | Inner Product |
Video (22:06) |
Note |
| 3 | Vector Equations |
Video (15:16) |
Note |
| 4 | Basic Rules of Matrices |
Video (16:09) |
Note |
| 5 | Multiplication of Matrices |
Video (16:53) |
Note |
| 6 | Inverse Matrix and Simultaneous Equations |
Video (18:08) |
Note |
| 7 | Linear Transformation |
Video (14:20) |
Note |
Grading
There will be two main exams: midterm (40%) and final (40%). In addition, there will be homework each week (20%). The final grade will be determined by the total amount of points obtained according to the following scale: S: 90-100, A: 80-89, B: 70-79, C: 60-69, F: 0-59. In case a student wants to drop off, a course withdrawal request should be submitted before the midterm exam.
Last updated
January 20, 2016