Pre-college Mathematics *Optional subject

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LecturerYukio ISHIDA, Professor
DepartmentG30, 2015 Fall
Recommended for:G30 (21.5 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 CONTENTS

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.


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
2 Algebraic Equations and Functions Video
3 Linear and Quadratic Inequalities Video
4 Trigonometric Functions Video(I) Video
5 Trigonometric Functions Video(II) Video
6 Trigonometric Functions Video(III) Video
7 Complex Numbers Video
8 Exponential Functions Video
9 Fractional Functions and Irrational Functions Video
10 Inverse Functions Video
11 Common Logarithms Video
12 Law of Sines and Law of Cosines Video
13 Applications of Trigonometric Functions Video
14 Graphs and Equations Video(I) Video
15 Graphs and Equations Video(II) Video
Course II Calculus
1 Limit of Functions and Derivatives Video
2 Derivative and Graphs Video
3 Differentiation Formulas Video
4 Derivatives of Trigonometric Functions Video
5 Derivatives of Logarithmic Functions and Exponential Functions Video
6 Applications of Derivatives to Equations and Inequality Video
7 Application to Physics Video
8 Approximation of a Function Video
9 Antiderivatives Video
10 Definite Integrals Video
11 Estimating Area by Rectangles Video
12 Application of Integrals Video(1) Video
13 Application of Integrals Video(2) Video
14 Differential Equations Video(1) Video
15 Differential Equations Video(2) Video
Course III Linear Algebra
1 Basic Rules of Vectors Video
2 Inner Product Video
3 Vector Equations Video
4 Basic Rules of Matrices Video
5 Multiplication of Matrices Video
6 Inverse Matrix and Simultaneous Equations Video
7 Linear Transformation Video


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