Course Details
Country:
Netherlands
Institution:
Free University of Amsterdam
Course Title:
Mathematical Analysis
Course Number:
XB_0009
Course Description:
This course treats the rigorous mathematical theory behind single-variable Calculus: completeness of R, limits, continuity, differentiability, integrability, and the mutual relation between these concepts. The mathematical theory is presented in such a way that everything can later be generalised to the context of metric spaces. The space C^0[a,b] of real-valued continuous functions on an interval [a,b] will appear as the main example of such metric spaces for which the theory can be applied to solve differential equations via the Banach contraction principle. Topics: Suprema, infima and completeness of real numbers; Limit of real sequences; The Bolzano-Weierstrass Theorem and the Cauchy Criterion; Applications of convergence to infinite series and to the Banach contraction principle; Basic topology of R Functional limits and (uniform) continuity; Differentiable functions: linear approximation and the Mean Value Theorems; The Riemann integral: construction, properties and the Fundamental Theorem of Calculus Pointwise and uniform convergence of sequences of functions
Language:
English
Approved Equivalent:
Pending For Approval
Attachment Files:
Studyguide (14)_3.pdf
