Past Lecture Notes : 1997 Fall
Additional lecture notes will be posted in this homepage in order to provide more
information on the subjects covered in the class, but they may not be clearly explained in
the textbook of this course. You can read notes by using Adobe Acrobat 3.0 Reader. If you
do not have this software, please down load this.
Couese notes were originally prepared in 1997 Fall, but I am planning to edit these in
this term, while other additional notes will be prepared with many examples and exercise
problems. Please check these, too.
- Lecture Note #1 : Computational Linear Algebra (1) :
9/18/97, Revised on 9/19/97. Now I put a MATLAB example of symbolics for PC Version 5.0
Student Edition. You will notice script commands are significantly different from Version
4.
- Additional Note #1 : Linear Space and Subspace : 9/21/97. This
additional note should provide additional material for Homework #1 in which linear
subspaces of a linear space are asked.
- Lecture Note #2 : Computational Linear Algebra (2) :
9/22/97, Revised on 9/23/97 to add examples of curve fitting method. This is a second
lecture note on computational linear algebra, especially for Singular Value Decomposition
and Generalized Inverse of a Rectangular Matrix. This note may be helpful to finish up
Homework #1.
- Lecture Note #3 : Computational Linear Algebra (3) :
9/24/97. This explains determinant, eigenvalues and eigenvectors with their application in
vibration of a rod, QR/QL algorithms with Housholder Transformation, Inverse Iteration
Methods, and also Singular Value Decomposition.
- MATLAB Example #4 : Curve Fitting and Newton's Method : 10/7/97.
This is a MATLAB .m file in the text format so that you can use directly in your exercise.
- Additional Note #2 : Householder Transformation and
Tridiagonalization : 10/7/97. For solving Homework #2, this note should be helpful.
- Lecture Note #4 : Orthogonal Polynomials and Approximation
Theory : 11/03/97. This note describes inner product, Lagarange interpolation, Hermite
interpolation, Bzier pline and B-spline to approximate curves and surfaces in the
three-dimensional space, Quadrature, and Orthogonal polynomials.
- Lecture Note #5 : Variational Calculus and Minimum Principle
: 11/13/97. This is for Variational Calculus, Minimum Principle, Constrained Minimization,
Variational Inequality, and Finite Difference Approximation.
- Lecture Note #6 : Function Approximations and the Ritz Method
: 11/13/97. This note explains the least squares approximation of a function by
polynomials and trigonometric functions, i.e., Fourier series, and also explains the Ritz
method to solve the minimization problem of a functional derived in mechanics.
- MATHEMATICA Note #1 : Introduction to MATHEMATICA :
11/13/97. This is a note for introduction to MATHEMATICA that I prepared for MEAM 305,
311, and 501 few years ago. I suppose this is still fine to make quick exercise by using
MATHEMATICA for symbolic manipulation. For function approximation and the Ritz method,
MATHEMATICA is very useful. Similar can be performed by MAPLE too.
These can be used as examples and exercises for the course of 1998 Fall Term. In order
to solve the homework problems assigned in this term, these should be very useful.
Homework #1 : Solutions by Kikuchi Posted on 10/14/97
Homework #2 : Solutions by Kikuchi Posted on 11/13/97
Homework #3 : Solutions by Kikuchi Posted on 11/15/97
Homework #4 : Solutions by Kikuchi Posted on 11/26/97
Homework #5 : Solutions by Kikuchi Posted on 12/08/97
Homework #5 : Problems Posted on 11/25/97
Review Problem #1 : Exercises for Mid-Term Examination on
October 28 (T), 1997 / This is the problems in the mid-term examination in 1995 Fall
semester : Posted on 10/14/97
Review Problem #2 : Exercises for Final Examination on
December 9 (T), 1997 / This review problems cover most of the subjects we have studied
after the midterm examination. Please review these to prepare for the final examination. :
Posted on 11/17/97
Solutions of Review Problem #2 : Solutions of Review #2 :
I may have mistakes in my solutions. I did not have time to check them once more. Posted
on 12/04/97