Overview of Math 1A Overview of Math 1A May 3 2010 1 7 Overview of Math 1A Functions and Graphs Functions and Graphs Limits Rates of Change Continuity Derivatives and Graphs Integration 2 7 Overview of Math 1A Functions and Graphs I Functions relations tables I Inverting functions I Adding multiplying and composing functions I Examples models 3 7 Overview of Math 1A Limits Limits I Intuitive idea I Precise definition I Limit laws 4 7 Overview of Math 1A Rates of Change Rates of Change I Slope I Derivatives I Tangent line and approximation I Computing derivatives 5 7 Overview of Math 1A Continuity Derivatives and Graphs Continuity Derivatives and Graphs I Intermediate and extreme value theorems I Rolle s theorem and mean value theorem I Applications to graphing I Optimization I Related rates I Newton s method 6 7 Overview of Math 1A Integration Integration I Antiderivatives I Riemann sums and areas I Fundamental theorem of Calculus I Evaluation of integrals I Recognition of integrals volumes averages mass work 7 7
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