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2019　Calculus II O(21～30)

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Academic unit or major
Basic science and technology courses
Instructor(s)
-
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(H101)  Thr1-2(H101)  
Group
O(21～30)
Course number
LAS.M105
Credits
2
Academic year
2019
Offered quarter
4Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

Based on "Calculus I", this course focuses on more rigorous mathematical analysis of the limit of sequences of numbers and functions, applications of differentiation of functions of a single variable and partial differentiation of multivariate functions, series of numbers and sequences of functions.

The aim of this course is to provide knowledge about analysis which will be important for
science and engineering.

Student learning outcomes

Following "Calculus I", this course aims for a deeper understanding and development of the theory of calculus.

Keywords

Limit, continuity, Taylor's theorem, series, sequence of functions

Competencies that will be developed

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

Class flow

Besides lectures, a recitation class is held every week in accordance with the progress of the lectures.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Limit of a sequence of numbers, supremum, infimum Understand sequences of numbers and related notions.
Class 2 Continuity of real numbers, monotone sequences, Cauchy sequences Understand the continuity of real numbers and related notions.
Class 3 Limits of functions of a single variable, continuity, maximum, intermediate value theorem Understand the properties of continuous functions.
Class 4 Differentiation, Rolle's theorem, mean value theorem Understand the properties of differentiable functions.
Class 5 Limits of indeterminate forms, l'Hospital's rule Understand how to find limits of indeterminate forms.
Class 6 Taylor's theorem, extremal values Understand Taylor's theorem.
Class 7 Definite integral Understand the definition of the definite integral.
Class 8 Point sets on a plane, sequences of points Understand point sets and their properties.
Class 9 Limits of multivariate functions, continuity Understand the limit and continuity of multivariate functions.
Class 10 Partial derivative, total differentiation Understand the partial differentiation of multivariate functions.
Class 11 Taylor's theorem for multivariate functions, extremal values Understand Taylor's theorem and extremal values.
Class 12 Series, absolute convergence, conditional convergence Understand series of numbers and their convergence.
Class 13 Criteria for the convergence of series, power series Understand criteria for the convergence of series.
Class 14 Sequences of functions, series of functions Understand sequences and series of functions.
Class 15 Advanced topics Understand some advanced topics in analysis.

Textbook(s)

Basic Calculus, Toshitsune Miyake, Baifukan

Reference books, course materials, etc.

None in particular.

Assessment criteria and methods

Based on overall evaluation on the results of quizzes, reports, mid-term and final examinations. Details will be announced in class.

Related courses

  • LAS.M101 ： Calculus I / Recitation
  • LAS.M107 ： Calculus Recitation II

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

Students are supposed to have completed Calculus I / Recitation (LAS.M101).
Students are required to complete Calculus Recitation II (LAS.M107) at the same time.

Other

None in particular.

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