In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures.Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard-Lindelöf and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm-Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows.Our introduction to the calculus of variations includes a discussion of the Euler-Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton-Jacobi theory. Related first order partial differential equations are treated in more detail.The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.

Course In Analysis, A - Vol. Iv: Fourier Analysis, Ordinary Differential Equations, Calculus Of Variations

Special offer terms

Zookal Study - 14-day Premium trial

Free trial

By clicking the checkbox "Add 14-day FREE trial" you are enrolling in a 2-week (14 day) free trial of Zookal Study Premium Plan, and if you do not cancel within those 14 days, you will be enrolled in an auto-renewing monthly subscription for Zookal Study Premium Plan at the end of the trial. Unused trial period benefits have no cash value, are not transferable, and expire at the end of the trial period.

Auto-Renewal

Following the expiration of any free trial period, your Zookal Study subscription will be renewed each month until you cancel. You consent to Zookal automatically charging your payment method on file $14.95 each month after any free trial period until you cancel.

How to Cancel

You can cancel your subscription anytime by visiting "My Account" on homework.zookal.com, clicking "Cancel" and completing the steps to cancel. Cancellations take effect at the end of the free trial period (if applicable) or at the end of the billing month in which your request to cancel was received. Subscription fees are not refundable.

Zookal Study Premium Monthly Subscription Includes:

Ability to post up to twenty (20) questions per month.

0% off your textbooks order and free standard shipping whenever you shop online at
textbooks.zookal.com.au

Unused monthly subscription benefits have no cash value, are not transferable, and expire at the end of each month. This means that subscription benefits do not roll over to or accumulate for use in subsequent months.

Payment Methods

Afterpay and Zip Pay will not be available for purchases with Zookal Study Premium Plan and/or Free Trial additions.

$1 preauthorisation

You may see a $1 preauthorisation by your bank which will disappear from your statement in a few business days..

Email communications

By adding Zookal Study Premium or Premium Free Trial, you agree to receive email communications from Zookal.

In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures.Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard-Lindelöf and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm-Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows.Our introduction to the calculus of variations includes a discussion of the Euler-Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton-Jacobi theory. Related first order partial differential equations are treated in more detail.The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.