### 2019　Exercises in Analysis A I

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Mathematics
Instructor(s)
Kagei Yoshiyuki  Miura Tatsuya
Course component(s)
Exercise
Day/Period(Room No.)
Mon5-8(H103)
Group
-
Course number
ZUA.C202
Credits
2
2019
Offered quarter
1-2Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
Japanese
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### Course description and aims

This course is a complementary recitation for "Advanced Calculus I (ZUA.C201)". We will have problem solving sessions about the materials taught in that course.

### Student learning outcomes

At the end of this course, students are expected to:
-- Understand the construction of irrational numbers
-- Be familiar with limits superior and limits inferior
-- Be able to state and prove propositions about limits of sequences and functions by using "epsilons and deltas".
-- Understand some important properties of continuous functions, such as the intermediate value theorem, and the existence of the maximum/minimum.
-- Be able to calculate polynomial approximations of a given function by using the Taylor expansion or asymptotic expansion.
-- Understand the difference between pointwise and uniform convergences
-- Be familiar with calculus of power series in the disk of convergence
-- Understand the differentiability of multivariable functions as linear approximations
-- Understand the relation between gradient vectors and partial derivatives
-- Be able to calculate partial derivatives of composed functions
-- Understand the principle of the method of Lagrange multiplier

### Keywords

Continuity of real numbers, infimum, supremum, limit superior, limit inferior,
Cauchy sequence, continuous function, derivative, Taylor expansion
Uniform convergence, power series, total derivative, partial derivative, Taylor expansion of multivariable functions, inverse function theorem, implicit function theorem, the method of Lagrange multiplier

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

This is a standard lecture course with recitation sessions. Homework will be assigned every week. There will be occasional quizzes.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Recitation for the 1st class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 2 Recitation for the 2nd class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 3 Recitation for the 3rd class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 4 Recitation for the 4th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 5 Recitation for the 5th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 6 Recitation for the 6th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 7 Recitation for the 7th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 8 Recitation for the 8th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 9 Recitation for the 9th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 10 Recitation for the 10th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 11 Recitation for the 11th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 12 Recitation for the 12th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 13 Recitation for the 13th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 14 Recitation for the 14th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.
Class 15 Recitation for the 15th class of Advanced Calculus I (ZUA.C201) Details will be provided in class.

None required

None required

### Assessment criteria and methods

Based on the problem solving situation in the recitation sessions. Details will be provided in the class.

### Related courses

• ZUA.C201 ： Advanced Calculus I
• MTH.C201 ： Introduction to Analysis I
• MTH.C202 ： Introduction to Analysis II

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are expected to have passed Calculus (I/II), Linear Algebra (I/II), and their recitations.