Study guide for exam 1, math 20d, Fall 2010 Hint: Best way to study is to go over as many problems as you can in the book. Both my notes (L) and Boyce-DiPrima (BD). Correspondence is: L 0.2 is BD chapter 1 L chapter 1 (1.1,1.2,1.3,1.4,1.6) is BD chapter 2 L chapter 2 (2.1,2.2,2.3,2.4) is BD chapter 3 Here’s the summary. L 0.2: What is a diﬀerential equation and what is a mathematical model. Key terms: diﬀerential equation , initial value problem , initial condition(s) , the general solution , particular solution . L 1.1: Solution by integration, i.e. y0 = f ( x ) or y0 = f ( y ). L 1.2: Slope ﬁelds and Solution curves. Be able to sketch slope ﬁelds, solution curves. Note the existence and uniqueness theorem. L 1.3: Separable equations: y0 = f ( x ) g ( y ). New key terms: implicit solution . L 1.4: Linear ﬁrst order ODE. Know how to solve using the integrating factor . Study the mixture problem. L 1.6: Autonomous equations. Long term behaviour of solutions to autonomous equations. Key terms:
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This note was uploaded on 09/07/2011 for the course MATH 20D taught by Professor Mohanty during the Spring '06 term at UCSD.