AY2015 NIT Ibaraki College
Shinzo BANNAI
Exercises of Mathematics
Email: sbannai@ge.ibaraki-ct.ac.jp
Basic Information
Course
Regular Course
Compulsory / Elective
Elective
Grade
4th
Number of Credits
1
Semester
2nd Semester
Credit Type
Normal
Class Type
Common Technical Subject
Course Objectives
This course is designed so that the students can deepen their understanding of mathematics that they
learned in first to third grade through exercises. The goals are:
1. To sort out and understand the concepts related to Calculus and Linear Algebra learned up to now by
solving composite multidisciplinary problems.
2. To newly grasp the concepts of vector spaces and linear maps.
Topic Outline / Schedule
Week
Topic
Outline
1
Functions and limits
Various functions, limits of functions, continuity of
functions
2
Differentiation and applications
Calculation of derivatives and applications
3
Integration and applications
Calculation of integrals and applications
4
Partial Derivatives
Calculation of partial derivatives
5
Multiple integrals
Calculation of multiple integrals
6
Differential equations
First order differential equations, Second order
differential equations
7
Mid-term exam of 1st semester
8
Elementary row operations and
applications
Elementary row operations, rank, calculation of inverse
matrices, solving linear systems.
9
2 and 3 dimensional vectors
Linear independence, linear dependence, equations of
lines and planes
10
Determinants
Calculation of determinants, inverse matrices, Cramer’s
rule
11
Vector spaces
The definition of a vector space, subspaces, basis and
dimension
12
Linear maps
Linear maps and their associated matrices
13
Vectors and metrics
Inner product, norm, orthonormal set of vectors
14
Eigen values and applications
Eigenvalues and eigenvectors of linear operators,
diagonalization
15
Final Exam on 1st semester
16
Review of 1st semester
2
AY2015 NIT Ibaraki College
Textbooks and Other Readings
Text Book:
F. Terada, S. Hirabuki and I. Kasahara, “Seminar text Calculus”, Saiensu-sya, (in Japanese)
F. Terada and S. Hirabuki, “Seminar text Linear Algebra”, Saiensu-sya, (in Japanese)
Relevant Online Resources
KHAN ACADEMY:
https://www.khanacademy.org/math
MIT Open Courseware: “Single Variable Calculus “, Professor David Jerison
http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/
MIT Open Courseware: “Linear Algebra“, Professor Gilbert Strang
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
Grading Policy
Grading will be based on the mid-term exam and the final exam and also homework assignments. The
exams will account for 80% of the grades and the assignments will account for 20%. You will need a score
of 60 or higher to earn credits.
Course Description
The students are expected to prepare for and to review each class on their own. Also, they are expected to
solve as many problems as possible on their own. If there are any questions concerning the course, please
actively ask questions during class or utilize the Office Hours effectively.
3