### 2020　Calculus II W

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Basic science and technology courses
Instructor(s)
Purkait Soma
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Tue3-4(H112)  Thr1-2(H115)
Group
W
Course number
LAS.M105
Credits
2
2020
Offered quarter
4Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
English
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 Continuity of the real numbers, supremum, infimum Understand basic properties of real numbers.
Class 2 Limits of sequences, monotone sequences, Cauchy sequences Understand basic facts related to sequences.
Class 3 Limits of functions of a single variable, continuity, maximum, intermediate value theorem Understand the properties of continuous functions.
Class 4 Differentiation, mean value theorem, limits of indeterminate forms Understand the properties of differentiable functions.
Class 5 Taylor's theorem, extremal values Understand Taylor's theorem.
Class 6 Definite integral Understand the definition of the definite integral.
Class 7 Point sets on a plane, sequences of points Understand point sets and their properties.
Class 8 Limits of multivariate functions, continuity Understand the limit and continuity of multivariate functions.
Class 9 Differentiation of multivariate functions, total derivative and partial derivative Understand the differentiation of multivariate functions.
Class 10 Taylor's theorem for multivariate functions, extremal values Understand Taylor's theorem and extremal values.
Class 11 Series, absolute convergence, conditional convergence Understand series of numbers and their convergence.
Class 12 Sequences of functions Understand sequences of functions.
Class 13 Series of functions, power series Understand series of functions and, as a special case of them, power series.

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

### Textbook(s)

Instructions are given in class

### Reference books, course materials, etc.

Instructions are given in class

### 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).

### Other

None in particular.