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thinkBS 202 Advanced Calculus

  • Level: Intermediate
  • Status: Ready
  • Offered by: Kadir Has University
Academic Institution offering the course Kadir Has University
Mode of Delivery
(in class / online / blended)
Blended
Prerequisites by topic Calculus of one and several variables.
Language of Instruction English
Course Objectives To give a basic understanding of elementrary methods of mathematical analysis beyond first year 's calculus courses.
Course Contents Number systems, Basics of mathematical reasoning, Topology of metric spaces, Sequences and series, Continuity, Derivatives, Riemann integral, Function spaces.
Learning Outcomes of the Course Unit 1. To solve the engineering problems using mathematical tools.
2. To construct models for real world problems under certain measures of accuracy.
3. To be able to approach to the applied mathematics problems in a logical systematic way.


WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES


Week Subjects
1 Rational, Real and Complex numbers
2 A quick introduction to logic and reasoning
3 Introduction to point-set topology and metric spaces
4 Compactness, Connectedness, Completeness
5 Sequences of real and complex numbers
6 Numerical series and power series
7 Topologicsl properties under continuity
8 Derivative as linear transformation
9 The Riemann-Stieltjes integral
10 Sequence of functions and uniform convergence
11 Taylor and Weierstrass approximation theorems
12 Fourier Series
13 Special functions: Exponentials and Logarithms