![]() ![]() Can't see how you can work with PDEs if you don't have undergrad familiarity with ODEs as many problems are solved by converting a PDE to an ODE.Afghanistan, Albania, Algeria, American Samoa, Andorra, Angola, Anguilla, Antigua and Barbuda, Armenia, Aruba, Australia, Austria, Azerbaijan Republic, Bahamas, Bahrain, Bangladesh, Belarus, Belgium, Belize, Benin, Bermuda, Bhutan, Bolivia, Bosnia and Herzegovina, Botswana, British Virgin Islands, Brunei Darussalam, Bulgaria, Burkina Faso, Burundi, Cambodia, Cameroon, Canada, Cape Verde Islands, Cayman Islands, Central African Republic, Chad, Chile, Colombia, Comoros, Cook Islands, Costa Rica, Cyprus, Czech Republic, Côte d'Ivoire (Ivory Coast), Democratic Republic of the Congo, Denmark, Djibouti, Dominica, Dominican Republic, Ecuador, Egypt, El Salvador, Equatorial Guinea, Eritrea, Estonia, Ethiopia, Falkland Islands (Islas Malvinas), Fiji, Finland, France, Gabon Republic, Gambia, Georgia, Germany, Ghana, Gibraltar, Greece, Greenland, Grenada, Guam, Guatemala, Guernsey, Guinea, Guinea-Bissau, Guyana, Haiti, Honduras, Hong Kong, Hungary, Iceland, India, Indonesia, Iraq, Israel, Italy, Jamaica, Japan, Jersey, Jordan, Kazakhstan, Kenya, Kiribati, Kuwait, Kyrgyzstan, Laos, Latvia, Lebanon, Lesotho, Liberia, Liechtenstein, Lithuania, Luxembourg, Macau, Macedonia, Madagascar, Malawi, Malaysia, Maldives, Mali, Malta, Marshall Islands, Mauritania, Mauritius, Mayotte, Micronesia, Moldova, Monaco, Mongolia, Montenegro, Montserrat, Morocco, Mozambique, Namibia, Nauru, Nepal, Netherlands, Netherlands Antilles, New Zealand, Nicaragua, Niger, Nigeria, Niue, Norway, Oman, Pakistan, Palau, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Poland, Portugal, Puerto Rico, Qatar, Republic of Croatia, Republic of the Congo, Romania, Rwanda, Saint Helena, Saint Kitts-Nevis, Saint Lucia, Saint Pierre and Miquelon, Saint Vincent and the Grenadines, San Marino, Saudi Arabia, Senegal, Serbia, Seychelles, Sierra Leone, Singapore, Slovakia, Slovenia, Solomon Islands, Somalia, South Korea, Spain, Sri Lanka, Suriname, Svalbard and Jan Mayen, Swaziland, Sweden, Switzerland, Taiwan, Tajikistan, Tanzania, Thailand, Togo, Tonga, Trinidad and Tobago, Tunisia, Turkey, Turkmenistan, Turks and Caicos Islands, Tuvalu, Uganda, United Arab Emirates, Uzbekistan, Vanuatu, Vatican City State, Vietnam, Virgin Islands (U.S. I'm curious if you have a gap in PDEs also. ![]() And even has a lot of non rigorous proofs. This is why you can't teach a young gymnast a double back when they start.Ī good, cheap book for self study is Tenanbaum and Pollard. The human brain is not a computer, it learns from imitation and repetition. It's actually more efficient and you will learn more and deeper by learning the content first in terms of problem solving manipulation and later in terms of all the fancy stuff. And it's not just about how books are constructed and how people typically learn. Then after that, go grab some fancy book with all the grad school emphasis on proofs and Sobolev spaces and the like.īecause 90%+ of those books assume exposure to diffyQs first (in the way that "real analysis" typically assumes "calculus" exposure first). Institutiones calculi differentialis (Foundations of differential calculus) is a mathematical work written in 1748 by Leonhard Euler and published in 1755. But one emphasizing manipulation and problem solving and applications. Not one with all the fancy connections to other fields of math that you know. Work through a standard undergrad text on DiffyQs first. It is very classical, but it really does cover all the essential theory. It sounds like you have a strong geometry/topology background, so maybe this disqualifies this text for you.įor a more classical treatment of ODEs, in particular the treatment of ODEs as linear operators (Sturm-Liouville theory), I might go for Coddington's Theory of Ordinary Differential Equations. There are some tools missing, in particular from geometry/topology, that could make the presentation a bit cleaner. The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Some flaws: The book really only presupposes mastery of analysis. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications. However, I think the emphasis of this text on geometry, and on using some more modern results, makes the book a decent choice. I would not call this a standard introduction to ODE - it does not cover some of the absolute basics. The focus of this book is on qualitative behavior - existence of fixed points, limit cycles, blow-up solutions, etc. In differential calculus basics, you may have learned about differential equations, derivatives, and applications of derivatives. I occasionally use a book called Differential Equations and Dynamical Systems, by Lawrence Perko. There are way too many approaches to ODEs to have any one book cover them all. ![]()
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