MATH 441 — Advanced Calculus-Prerequisite MATH 351 or MATH 353
Mathematics · University of Ghana
Here we think of differentiation as a process of approximating the function f near a, by a linear map. This linear map is called the Frèchet derivative of f at a. The main aim of this course is to understand two of the most important theorems for modern analysis: the Inverse Map Theorem and the Implicit Function Theorem. Other ideas include: linear and affine maps between normed vector spaces. Limits, continuity, tangency of maps and the derivative as a linear map. Component-wise differentiation, partial derivatives, the Jacobian as the matrix of the linear map. Generalized mean value theorem.
- Credits
- 3
- Level
- Level 400
- Semester
- Semester One
Other courses on this programme
- MATH 440 — Abstract Algebra II-Prerequisite MATH 354
- MATH 442 — Integration Theory and Measure –Prerequisite MATH 356
- MATH 443 — Differential Geometry-Prerequisite MATH 355
- MATH 444 — Calculus on Manifolds-Prerequisite MATH 441
- MATH 445 — Introductory Functional Analysis-Prerequisite MATH 356
- MATH 446 — Module Theory-Prerequisite MATH 440
- MATH 447 — Complex Analysis-Prerequisite MATH 223
- MATH 448 — Special Relativity- Prerequisite MATH 362
- MATH 449 — Electromagnetic Theory II-Prerequisite MATH 366
- MATH 450 — Differential Equations II-Prerequisite MATH 350
- MATH 451 — Introduction to Algebraic Field Theory-Prerequisite MATH 354
- MATH 452 — Introduction to Lie Groups and Lie Algebras- Prerequisite MATH 354
Practising MATH 441 with Questora
Upload your own slides, notes and past papers for MATH 441 and Questora builds mock exams, practice questions and a revision plan from them.
Start freeCourse details from University of Ghana Volume 3 Handbook for the Bachelor's Degree: Course Descriptions for Programmes in the Sciences (2017).