Here is a tentative schedule for what material we'll cover. Adjustments will be made whenever they seem advisable. Two copies of each text book are on one-day reserve in the math library.
Text: Introduction to Analysis, by Arthur Mattuck.
The plan is to
cover Chapter 21 Improper integrals, Chapter 26 Integrals
with a parameter, and Chapter 27 Differentiating Improper
Integrals.
In class we'll do the Questions in each
section and the Exercises at the end of each chapter. The
Problems at the end of the Chapter are homework, to be written
up and handed in at the date noted in the schedule below.
Wed, Aug 6, 10am-noon: Introduction and Sect. 21.1 Improper Integrals: Basic Definitions.
Fri, Aug 8, 10am-noon: Sect. 21.2 Comparison Theorems.
Mon, Aug 11, 10am-noon: Sect. 21.3 The gamma function.
Wed, Aug 13, 10am-noon: Sect. 21.4 Absolute and conditional convergence.
Fri, Aug 15, 10am-noon: Sect. 26.1
Integrals depending on a parameter.
Sect. 26.2 Differentiation under the integral
sign.
Mon, Aug 18, 10am-noon: Sect. 26.2 continued, Sect. 26.3 Fubini's Theorem.
Wed, Aug 20, 10am-noon: Sect. 27.1 Introduction and Sect. 27.2 Pointwise vs. uniform
convergence of integrals.
Sect. 27.3 Continuity theorem for improper
integrals and
Sect. 27.4 Integrating and differentiating
improper integrals.
Fri, Aug 22, 3pm: Problems at end of Chapter 27 are due.
Text: Linear Algebra, 2nd ed., by Kenneth Hoffman and Ray Kunze. The
plan is to cover Chapter 8 and the first three sections of
Chapter 9.
Do the exercises at the end of each section. Some exercises will be
collected.
Wed, Aug 6, 1pm-3pm: Sect. 8.1 Inner Products.
Fri, Aug 8, 1pm-3pm: Sect. 8.2 Inner Product Spaces.
Mon, Aug 11, 1pm-3pm: Sect. 8.3 Linear Functionals and Adjoints.
Wed, Aug 13, 1pm-3pm: Sect. 8.4 Unitary Operators.
Fri, Aug 15, 1pm-3pm: Sect. 8.5 Normal Operators.
Mon, Aug 18, 3pm-5pm: Sect. 9.1 & 9.2 Forms on Inner Product Spaces.
Wed, Aug 20, 3pm-5pm: Sect. 9.3 Positive Forms.
Fri, Aug 22, 3pm: Hand in designated exercises from Section 9.3.