PPT-AP Problems Involving the Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus If then 1 2 One of the hardest calculus topics to teach in the old days was Riemann sums They were hard to draw hard to compute and many felt totally unnecessary. adding it all up. Integral Calculus. 1. Goal. Compute the . signed. area . under some portion of an arbitrary curve. Integral Calculus. 2. Divide and Conquer. Integral Calculus. 3. Animatedly. Integral Calculus. A Service Learning Experience. Melinda Rudibaugh. Mathematics Faculty,. Chandler-Gilbert Community College. What is Service Learning?. Not volunteerism. Tied to the curriculum. Requires meaningful reflection and self-growth. Casey Parsons. What is impact calculus?. You might remember on the first . powerpoint. that something called “impact calculus” was referenced a couple of times. It’s how we determine who wins the round . Deloitte. Festival. Community . s. inging. h. ttps://. www.youtube.com/watch?v=a3krrLc4Oc8. Involving workshop artists in school . based projects. Family Sundays and workshops. ‘Insight’ Programme. 8. Newton & Leibniz. History & Philosophy of Calculus, Session . 8. The invention of the calculus. Newton and Leibniz in 17. th. Century invented the algorithmic procedures underlying the calculus. There are negative issues involving science and accidents do happen.. However in general the worst issues are because society makes unwise decisions on how scientific advances should be used in for instance armed conflicts.. BARROW AND LEIBNIZ ON THE FUNDAMENTAL THEOREM . OF CALCULUS. In . 1693, . Leibniz . published . a geometrical . proof of the fundamental theorem of the calculus. During his notorious . dispute with . Fundamental theorem of calculus. Deriving the Theorem. Let. Apply the definition of the derivative:. Rule for Integrals!. Deriving the Theorem. This is average value of . f. from. x. to . x. + . h. The Return of the Infinitesimal?. So far on this course we’ve stayed close to mainstream mathematics.. In this final session we look at some more “fancy” material, much of it very recent.. These aren’t just techniques for doing complicated calculations – they represent new ways to think about geometry and continuity, and so they promise to raise some old philosophical questions. . The mathematics of continuous change. Instead of looking at average or overall results, calculus looks at how things change from second to second.. Calculus. The mathematics of continuous change. Instead of looking at average or overall results, calculus looks at how things change from second to second.. Divergence. In calculus, the divergence is used to measure the magnitude of a vector field’s source or sink at a given point. Thus it represents the volume density of the outward flux of a vector field . As the number of rectangles increased, the approximation of the area under the curve approaches a value.. Copyright .  2010 Pearson Education, Inc.. Section 5.3 – The Definite Integral. Definition. Books ordered. Stewart. . Calculus: Early . Transcendentals. 7e. Ocean. Ngl.cengage.com. Stewart. . Calculus: Early . Transcendentals. 7e. Middlesex. Ngl.cengage.com. Larson:. Calculus of a Single Variable: Early . Complex Numbers. Standard form of a complex number is: . a bi.. Every complex polynomial function of degree 1 or larger (no negative integers as exponents) has at least one complex zero.. a . and. b .