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Graduate School
Precollege Mathematics *Optional subject
Yukio ISHIDA Professor
Department: G30
Class Time:  2015 Fall Wednesday 
Recommended for:  G30 
Course Overview
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.
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Syllabus
Course Prerequisites
There are no particular prerequisites for this course. Basic algebraic computation capabilities will ease the learning.
Course Content
CONTENTS (PDF, 28KB)
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 elearning lecture introduced in the first lesson.
Textbook
Handouts are delivered.
Reference Book
Elearning in the Nagoya University website (This is introduced in the first lecture).
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: 90100, A: 8089, B: 7079, C: 6069, F: 059. In case a student wants to drop off, a course withdrawal request should be submitted before the midterm exam.
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Class Materials
Lecture Videos
Session  Lectures  Video  Notes 

Course I Functions and Equations  
1  Polynomials and Factoring  Video (FlashVideo, 19:45)  Note (PDF, 1456KB) 
2  Algebraic Equations and Functions  Video (FlashVideo, 18:35)  Note (PDF, 2011KB) 
3  Linear and Quadratic Inequalities  Video (FlashVideo, 16:08)  Note (PDF, 1846KB) 
4  Trigonometric Functions Video(I)  Video (FlashVideo, 14:09)  Note (PDF, 1815KB) 
5  Trigonometric Functions Video(II)  Video (FlashVideo, 17:25)  Note (PDF, 2407KB) 
6  Trigonometric Functions Video(III)  Video (FlashVideo, 15:01)  Note (PDF, 1357KB) 
7  Complex Numbers  Video (FlashVideo, 23:10)  Note (PDF, 1678KB) 
8  Exponential Functions  Video (FlashVideo, 22:42)  Note (PDF, 1781KB) 
9  Fractional Functions and Irrational Functions  Video (FlashVideo, 15:33)  Note (PDF, 1779KB) 
10  Inverse Functions  Video (FlashVideo, 14:42)  Note (PDF, 1659KB) 
11  Common Logarithms  Video (FlashVideo, 30:14)  Note (PDF, 3451KB) 
12  Law of Sines and Law of Cosines  Video (FlashVideo, 16:41)  Note (PDF, 1598KB) 
13  Applications of Trigonometric Functions  Video (FlashVideo, 14:25)  Note (PDF, 1338KB) 
14  Graphs and Equations Video(I)  Video (FlashVideo, 22:20)  Note (PDF, 2223KB) 
15  Graphs and Equations Video(II)  Video (FlashVideo, 25:10)  Note (PDF, 2197KB) 
Course II Calculus  
1  Limit of Functions and Derivatives  Video (FlashVideo, 26:28)  Note (PDF, 2287KB) 
2  Derivative and Graphs  Video (FlashVideo, 22:07)  Note (PDF, 3216KB) 
3  Differentiation Formulas  Video (FlashVideo, 16:55)  Note (PDF, 1876KB) 
4  Derivatives of Trigonometric Functions  Video (FlashVideo, 18:01)  Note (PDF, 1861KB) 
5  Derivatives of Logarithmic Functions and Exponential Functions  Video (FlashVideo, 19:33)  Note (PDF, 1375KB) 
6  Applications of Derivatives to Equations and Inequality  Video (FlashVideo, 19:54)  Note (PDF, 2746KB) 
7  Application to Physics  Video (FlashVideo, 22:52)  Note (PDF, 1627KB) 
8  Approximation of a Function  Video (FlashVideo, 20:04)  Note (PDF, 1863KB) 
9  Antiderivatives  Video (FlashVideo, 30:03)  Note (PDF, 2638KB) 
10  Definite Integrals  Video (FlashVideo, 20:58)  Note (PDF, 1528KB) 
11  Estimating Area by Rectangles  Video (FlashVideo, 14:41)  Note (PDF, 1270KB) 
12  Application of Integrals Video(1)  Video (FlashVideo, 22:24)  Note (PDF, 1862KB) 
13  Application of Integrals Video(2)  Video (FlashVideo, 27:03)  Note (PDF, 1697KB) 
14  Differential Equations Video(1)  Video (FlashVideo, 21:20)  Note (PDF, 1563KB) 
15  Differential Equations Video(2)  Video (FlashVideo, 19:07)  Note (PDF, 1328KB) 
Course III Linear Algebra  
1  Basic Rules of Vectors  Video (FlashVideo, 23:58)  Note (PDF, 1330KB) 
2  Inner Product  Video (FlashVideo, 22:06)  Note (PDF, 1544KB) 
3  Vector Equations  Video (FlashVideo, 15:16)  Note (PDF, 1132KB) 
4  Basic Rules of Matrices  Video (FlashVideo, 16:09)  Note (PDF, 1256KB) 
5  Multiplication of Matrices  Video (FlashVideo, 16:53)  Note (PDF, 1379KB) 
6  Inverse Matrix and Simultaneous Equations  Video (FlashVideo, 18:08)  Note (PDF, 1131KB) 
7  Linear Transformation  Video (FlashVideo, 14:20)  Note (PDF, 1201KB) 
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Page last updated November 10, 2015
The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.