Advanced Calculus University of Tsukuba
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.
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.
Related to 1. Mathematical logic and calculation skills.
* 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.
Class performance 20% Midterm 40% Final 40%
Parametric Equations and Polar CoordinatesConic SectionsConic Sections in Polar CoordinatesVectors and Geometry of SpaceVector Functions: dot product and cross productVector Functions: tangent vector, curves, derivatives, integralsSummary and RecitationPartial Derivatives: geometric interpretationPartial Derivatives: implicit differentiationPartial Derivatives: steepest decent, Lagrange multiplierMid-term ExamMultiple Integrals: double integralsMultiple Integrals: double integrals with general RMultiple Integrals: triple integralsMultiple Integrals: change of variablesVector Calculus: line integralsVector Calculus: Green's theorem, vector operationsVector Calculus: parametric surfacesVector Calculus: Gauss theorem and Stokes theoremSummary and Recitation
Lectures and Class Exercises
Online Course Requirement
* 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