2003 Spring Term
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This course is an introduction to calculus.
Its primary goal is a grasp of the basic notions related with functions
of one variable.
Its secondary goal is a grasp of the very basic notions related with
functions of two variables.
After successfully learning basics from this course,
students will have the ability to actively study calculus
for geometrically formulated problems.
Plan
04/14 (**) Graph and Function
04/21 (**) Derivative of Function
04/28 (**) Composition of Function
05/12 (**) Differential Equation
05/19 Definite Integral and Primitive Function (Indefinite
Integral)
05/26 -- No Lecture because of International Conference --
06/02 Infinitesimal Analysis and its Interpretation in the Finite
06/09 Method of Calculation
06/16 First Approximation, Second Approximation and Power Series
06/23 Reconstruction and Calculation of Function with Power Series
06/30 Maximum and Minimum of Function and Shape of Graph
07/07 Planar Curve --- Parametrized Curve and Local Coordinates
07/14 (***) Function of Two Variables and Singularity
07/15 (***) Directional Derivative and Partial Derivative
07/16 Double Integral and Successive Integral
A ruler is required
and
color pens are recommended
for
the lectures marked with (**),
when exercises of planar graph are scheduled.
A pair of scissors, a ruler and a calculator
are required
for
the lectures marked with (***),
when handcrafts of solid graph are scheduled.
Evaluation
Assignments 100%
Students can touch the basic notions of calculus through working
on planar graphs and making solid graph.
Assignments should be completed and submitted by in the specified time
during the exercise.
Assignments are exercise of planar graph, handcraft of solid graph,
drill of calculation and writing.
Exersise and handcraft of graphs have more weight.
How to Study
In the Classroom
Students are requested to discuss everything for assignments
(planar graph, solid graph, calculation and writing).
They can also consult the staff.
Talking on the subjects of the lecture while I am writing on the blackboard
is allowed.
However, making a qeustion is strongly recommended.
Outside the Classroom
Students are not requested to study the subject before the
lecture.
Indeed, I expect the plan of lectures to depend heavily on their prior
responses.
It is a good habit to review the subject in a group after the
classroom.
It is good to acquire the habit of using lecture notes as your drill.
Mathematics is an accumulation of ideas of greatly many people.
That is why it is important to study mathematics by exchanging opinions
in a group.
Some serious students repeated taking a mathematical lecture course
to discuss subjects in different groups.
I saw the corresponding outcome.