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Calculus I

by: Mitchell Skiles

Calculus I MAT 295

Mitchell Skiles
GPA 3.52


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Class Notes
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This 2 page Class Notes was uploaded by Mitchell Skiles on Tuesday October 20, 2015. The Class Notes belongs to MAT 295 at Syracuse University taught by Staff in Fall. Since its upload, it has received 34 views. For similar materials see /class/225558/mat-295-syracuse-university in Mathematics (M) at Syracuse University.


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Date Created: 10/20/15
PROJECT ADVANCE Faculty Uday BanerjeePhD Associate Professor Department of Mathematics Terry McConnellPhD Professor Department of Mathematics Administrative Contact William R Newell Associate Director PROJECT ADVANCE 400 Ostrom Avenue Syracuse NY 152443250 3154452404 FAX 5154431626 bllpMJllpaJyl lll Math 295 Calculus 4 credits MAT 295296 is the rstyear calculus sequence required of all science and engineering majors at Syracuse University MAT 295 comprises the rst four credits of this eight credit sequence The development of scienti c calculators with graphics capability has made possible some signi cant changes in the way this material is taught and many colleges and universities are now incorporating them in their calculus sequence In sections of calculus offered off campus through Project Advance and in selected campus sections design changes have been made to integrate these calculators into the learning process The course design allows for some variations in pacing as determined by site instructors and the supervising faculty Students who elect to enroll in the course sequence should have completed four years of high school mathematics Course Content The mathematical content of this program is typical of most traditional rstyear calculus courses The concepts of limit continuity derivative and antiderivative and de nite integral are developed in the usual way and are then applied to the traditional collection of functions polynomial rational trigonometric and exponential together with their inverses compositions and algebraic combinations The results are then applied to a wide variety of problems from geometry physics and other sciences These include maximum and minimum problems related rates areas volumes and surfaces of revolution arc length work uid pressure velocity and acceleration and exponential growth and decay Curve sketching is introduced at the very beginning and emphasized throughout as we believe strongly that this is an important skill for any calculus student to acquire Graphing calculators are a help here since they contribute substantially to an understanding of the functions being sketched They are only a help however the calculators are not used as a substitute for the skill itself During the course students are introduced to progressively more sophisticated program ming techniques for the calculator They are shown how to write programs rst for the evaluation and tabulation of functions and then for numerical evaluation of limits derivatives and roots the last by Newton39s Method Students then learn to do nite sums Riemann sums and nally numerical integration by Simpson39s Rule Programs are stored in the calculator as they are written and are used throughout the course OVER N 50 Outline of MAT 295 Review of Pre Calculus a trigonometry b graphing of functions c special functions including sgn X and X Limits including one sided and at 00 a definitions intuitive and formal b techniques of evaluation Continuity a de nitions at a point and on an interval b the Intermediate Value Theorem c use of IVT for numerical approximation of roots Derivatives a de nition b geometric and physical interpretation c formulas for X sin X and cos X d product quotient and chain rules e implicit di erentiation f higher derivatives g Rolle39s Theorem and the Mean Value Theorem for derivatives h di erentials i anti derivatives Applications of Derivatives a increasing and decreasing functions b critical points and eXtreme values c maX min problems d related rate problems e concavity and in ection points f linear appr0Ximation g error estimates h Newton39s Method Brief Review of Conic Sections De nite Integral a definition area under a curve Riemann sum b average value of a function c Mean Value Theorem for integrals d Fundamental Theorem of Calculus two versions e integrals of X1 sin X and cos X f substitution in an integral Applications of the Definite Integral a areas between curves b volumes and surface areas of solids of revolution c arc lengths of curves d work done by a force e force due to uid pressure Calculator Programs a numerical appr0Ximation of limits and derivatives b Newton39s Method c finite sums d Riemann sums e numerical appr0Ximation of integrals by Midpoint Rule Trapezoid Rule Simpson s Rule Instructional Materials The teXt for the course is Edwards and Penney Calculus anal Analytic Geometry with Early Transcendentals Prentice Hall 63911 Edition A class set of grang calculators is needed as well We recommend the TeXas Instruments TI 83 but other calculators may also be used updated 0105


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