Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology chemistry physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables such as temperature chemical and biochemical concentrations and cell densities as a function of space and time (spatiotemporal distributions). For a complete PDE model initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries must also be included for a well-posed PDE model. In this book PDE models are considered for which the physical boundaries move with time. For example as a tumor grows its boundary moves outward. In atherosclerosis the plaque formation on the arterial wall moves inward thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R a quality open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming. | Moving Boundary PDE Analysis Biomedical Applications in R
Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology chemistry physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables such as temperature chemical and biochemical concentrations and cell densities as a function of space and time (spatiotemporal distributions). For a complete PDE model initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries must also be included for a well-posed PDE model. In this book PDE models are considered for which the physical boundaries move with time. For example as a tumor grows its boundary moves outward. In atherosclerosis the plaque formation on the arterial wall moves inward thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R a quality open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming. | Moving Boundary PDE Analysis Biomedical Applications in R
Sellers offer a range of delivery options, so you can choose the one that’s most convenient for you. Many sellers offer free delivery. You can always find the postage cost and estimated delivery date in a seller’s listing. You'll then be able to see a full list of delivery options during checkout. These can include: Express delivery, Standard delivery, Economy delivery, Click & Collect, Free local collection from seller.
Your options for returning an item vary depending on what you want to return, why you want to return it, and the seller's return policy. If the item is damaged or doesn't match the listing description, you can return it even if the seller's returns policy says they don't accept returns. If you've changed your mind and no longer want an item, you can still request a return, but the seller doesn't have to accept it. If the buyer changes their mind about a purchase and wants to return an item, they may need to pay return postage costs, depending on the seller's return policy. Sellers can provide a return postage address and additional return postage information for the buyer. Sellers pay for return postage if there's a problem with the item. For example, if the item doesn't match the listing description, is damaged or defective or is counterfeit. By law, customers in the European Union also have the right to cancel the purchase of an item within 14 days beginning from the day you receive, or a third party indicated by you (other than the carrier) receives, the last good ordered by you (if delivered separately). This applies to all products except for digital items (e.g. Digital Music) that are provided immediately to you with your acknowledgement, and other items such as video, DVD, audio, video games, Sex and Sensuality products and software products where the item has been unsealed.
Sellers have to offer a refund for certain items only if they are faulty, such as: Personalised items and custom-made items, Perishable items, Newspapers and magazines, Unwrapped CDs DVDs and computer software. If you used your PayPal balance or bank account to fund the original payment, the refunded money will go back to your PayPal account balance. If you used a credit or debit card to fund the original payment, the refunded money will go back to your card. The seller will effect the refund within three working days but it may take up to 30 days for Paypal to process the transfer. For payments funded partially by a card and partially by your balance/bank, the money taken from your card will go back to your card and the remainder will return to your PayPal balance.