This volume aims to bridge between elementary textbooks on calculus and established books on advanced analysis. It provides elucidation of the reversible process of differentiation and integration through two featured principles: the chain rule and its inverse - the change of variable - as well as the Leibniz rule and its inverse - the integration by parts. The chain rule or differentiation of composite functions is ubiquitous since almost all (a.a.) functions are composite functions of (elementary) functions and with the change of variable method as its reverse process. The Leibniz rule or differentiation of the product of two functions is essential since it makes differentiation nonlinear and with the method of integration by parts as its reverse process.Readers will find numerous worked-out examples and exercises in this volume. Detailed solutions are provided for most of the common exercises so that readers remain enthusiastically motivated in solving and understanding the concepts better.The intention of this volume is to lead the reader into the rich fields of advanced analysis and to obtain a much better view of useful mathematics. show more
{"bd_js_shop":"Shop","bd_js_too_long_for_shipping_label":"Sorry, that's too long for our shipping labels","bd_omnibus_ph1_price_statement_suffix":"vs RRP","bd_js_too_long":"Sorry, that's too long","bd_js_could_not_find_address_try_again":"Sorry, we couldn't find the address. Please try again","bd_saving_percent_off":"{0}%<br>off","bd_js_total_basket_count":"{0, plural, one {You have <b><span class='item-count'>1</span> <span class='item-text'>item</span></b> in your basket} other {You have <b><span class='item-count'>#</span> <span class='item-text'>items</span></b> in your basket}}","bd_js_total_cost":"Total cost: <b class='pink-text big total'>{0}</b>","bd_js_show_less":"show less","bd_js_item_added_to_your_basket":"Item added to your basket","bd_rrp":"RRP","bd_link_prefix":"","bd_js_unable_get_address_enter_manually":"Sorry, we are unable to get the address. Please enter manually:","bd_js_keep_typing_to_refine_search_results":"Keep typing to refine the search results","bd_js_top_categories":"Top Categories","bd_price_save":"Save {0}","bd_js_name_only_letters":"Sorry, full name can only contain letters","bd_js_show_more":"show more","bd_js_enter_valid_email_address":"Please enter a valid email address","bd_js_enter_address_manually":"Enter address manually","bd_js_more_categories":"More Categories","bd_30_day_low_price_carousel":"30-day low price","bd_js_continue_shopping":"Continue Shopping","bd_js_account_and_help":"Account & Help","bd_js_basket_checkout":"Basket / Checkout","bd_add_to_basket":"Add to basket","bd_js_enter_first_last_name":"Please enter a first and last name","bd_js_please_enter_your":"Please enter your"}
