Series
AY 2004
Arts and Sciences

Math IB (Differential and Integral Calculus)

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#Arts and Sciences
Math I is a mandatory course for students specializing in natural sciences in Junior Divisions (1st & 2nd years) of the College of Arts and Sciences. Math I is offered in “Math IA” and “Math IB”. Both classes cover almost the same content although Math IA focuses on theoretical aspects while Math IB emphasizes in practical computation. In Math I, students learn differential and integral calculus to acquire basic knowledge on differential and integral required for university-level study. Thus, differential and integral of high-school mathematics are prerequisite for taking this course.

Content List

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#1 Real numbers, limits, series and continuity

Lecturer | Takeshi Saito
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Resources
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#2 Real numbers, limits, series and continuity

Lecturer | Takeshi Saito
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#3 Inverse trigonometric functions

Lecturer | Takeshi Saito
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Resources
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#4 Intermediate value theorem, theorem of maximum number and transformation of real function continuity

Lecturer | Takeshi Saito
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Resources
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#5 Differential: first-order approximation and Taylor expansion

Lecturer | Takeshi Saito
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Resources
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#6 Taylor’s theorem

Lecturer | Takeshi Saito
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Resources
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#7 Power series expansion

Lecturer | Takeshi Saito
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#8 Calculation of convergence radius and differential and integral of power series

Lecturer | Takeshi Saito
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#9 Differential and integral of power series and power series expansion

Lecturer | Takeshi Saito
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Resources
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#10 Alternating series convergence, power series expansion of other functions, and differential equations

Lecturer | Takeshi Saito
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#11 Improper definite integral

Lecturer | Takeshi Saito
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#12 Improper integral calculus

Lecturer | Takeshi Saito
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#13 Two variable functions and the visualization of two variable functions

Lecturer | Takeshi Saito
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#14 Differential of two variable functions

Lecturer | Takeshi Saito
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#15 Partial differential and total differential

Lecturer | Takeshi Saito
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#16 Differential of composite functions and high derivative

Lecturer | Takeshi Saito
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#17 Change of order and extreme value in two variable functions

Lecturer | Takeshi Saito
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#18 Extreme value in two variable functions

Lecturer | Takeshi Saito
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#19 Integral and definition in multivariable functions, multiple integral and iterated integral

Lecturer | Takeshi Saito
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#20 Iterated integral

Lecturer | Takeshi Saito
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#21 Variable transformation and polar coordinate

Lecturer | Takeshi Saito
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Resources
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#22 Variable transformation, change of coordinate and Jacobian

Lecturer | Takeshi Saito
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Resources
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#23 Integral of rational functions

Lecturer | Takeshi Saito
Resources
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練習問題

Lecturer | Takeshi Saito
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