Lecture Mathematical Analysis 2

5. Uniform convergence

• 5.1 Pointwise and uniform convergence

• 5.2 The Weierstrass Test

• 5.3 Integration and differentiation of series of functions

• 5.4 The space of continuous functions and the Arzela-Ascoli Theorem

• 5.5 Dini's Theorem and the Approximation Theorems of Stone and Weierstrass

• Section 5 additional examples

6. Some special functions

• 6.1 Power series

• 6.2 The complex exponential function and trigonometric functions

• 6.3 Fourier series I

• 6.4 Improper integrals and the Gamma function

7. The Lebesgue integral

• 7.1 Construction of the Lebesgue measure

• 7.2 Measure spaces and measurable functions

• 7.3 Integration

• 7.4 L2-spaces, inner product spaces and Fourier series II

• 7.5 Integrals depending on a parameter

• 7.6 Some fundamental inequalities and the Lp-spaces

• 7.7 Fourier integrals