### Advanced Calculus University of Tsukuba

#### Course Overview

Following“Introduction to Single-Variable Calculus I & II," this course introduces the basic tools of calculus and develops their technical competence, namely, differential equations, infinite series, vector calculus, curvilinear coordinate systems, and partial derivatives, etc. This is achieved by visualization, numerical and graphical experimentations and, thus, students are required to be acquainted with Mathematica (or similar ones) during the course as working exercises and homework problems. This course as well as “Introduction to Single-Variable Calculus I & II” provides a core and practical knowledge required for many courses in both natural and social sciences.

#### Learning Achievement

1. The students are able to express lines and planes in high dimensions in terms pf parameters.

2. The students are able to describe the conic sections by cartesian and polar coordinates.

3. The students are able to describe the geometry with vectors and vector functions.

4. The students are able to carry out partial derivatives of multi-variable functions.

5. The students are able to evaluate areas and volumes by multiple integrals.

6. The students are able to carry out derivatives and integrals of vector functions.

#### Competence

Related to 1. Mathematical logic and calculation skills.

#### Course prerequisites

* Students are required to have taken "Introduction to Single-Variable Calculus I and II" or equivalent courses.

If not, they are asked to discuss with the instructor before registering this course.

* Those who already earned the credit of Calculus II (FJ20114) are not allowed to earn the credit of this course.

#### Grading Philosophy

Class performance 20%

Midterm 40%

Final 40%

#### Course schedule

Parametric Equations and Polar Coordinates

Conic Sections

Conic Sections in Polar Coordinates

Vectors and Geometry of Space

Vector Functions: dot product and cross product

Vector Functions: tangent vector, curves, derivatives, integrals

Summary and Recitation

Partial Derivatives: geometric interpretation

Partial Derivatives: implicit differentiation

Partial Derivatives: steepest decent, Lagrange multiplier

Mid-term Exam

Multiple Integrals: double integrals

Multiple Integrals: double integrals with general R

Multiple Integrals: triple integrals

Multiple Integrals: change of variables

Vector Calculus: line integrals

Vector Calculus: Green's theorem, vector operations

Vector Calculus: parametric surfaces

Vector Calculus: Gauss theorem and Stokes theorem

Summary and Recitation

#### Course type

Lectures and Class Exercises

#### Online Course Requirement

#### Instructor

Sano Nobuyuki

#### Other information

* You may discuss with other students for preparing the homework. Yet, just “a copy-and-paste” will not be accepted. No late homework is accepted.

* All exams are closed book for in-class lecture. In the case of hybrid lecture, all exams are open book.

#### Site for Inquiry

Link to the syllabus provided by the university