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14 Pages

### Lecture1

Course: MTH MTH122, Spring 2009
School: SUNY Buffalo
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Word Count: 438

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to Math Welcome 122 Survey of Calculus and its Applications I1 Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009 Instructor contact Information Text Grading In-class work/ Hw / Tests Make-up policy Special needs Come to lectures regularly Do homework regularly Go to recitations regularly Prepare for the quizzes / tests Mark the test dates Make friends and help each other...

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to Math Welcome 122 Survey of Calculus and its Applications I1 Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009 Instructor contact Information Text Grading In-class work/ Hw / Tests Make-up policy Special needs Come to lectures regularly Do homework regularly Go to recitations regularly Prepare for the quizzes / tests Mark the test dates Make friends and help each other Calculus is the study of change. In particular, it looks at the rates in which quantities change (i.e., areas, volumes, distances, etc.). It was developed in the later part of the 17th century by Gottfried Leibnitz and Isaac Newton. The two key areas of Calculus are Differential Calculus (having a quantity and finding the rate of change) and Integral Calculus. (knowing the rate of change and finding the quantity) The big surprise is that these two seemingly unrelated areas are actually connected via the Fundamental Theorem of Calculus. If you choose a career path that requires any level of mathematical sophistication, you will need Calculus. To succeed in Calculus (and Mathematics in general) you must be able to: solve problems, reason logically and understand abstract concepts.. Function a set of ordered pairs (x, y) such that for each x-value there is one and only one y-value. y = f Domain (x) of a function the set of all xs that we can input into the function. Range of a function all images y of all of the xs. Vertical line test Is it a function a not? If any vertical line intersects the graph more than once, then the graph is not a function. Polynomial y = x 5 , y = ( x + 10) 4 x 7 Algebraic y = x + 4, y = x , y = (x + 1) e 2 5 Rational y= x+6 2 , y= x2 + 5 x+4 Exponential and Logarithmic x x x +4 y = e , y = 2 , y = 2e y = ln(4 x 2 + 5) Piecewise y= x Trigonometric* Inverse Trigonometric* Linear function Quadratic function Cubic Function Absolute Value Function y= x Rational Exp & Log Differential Calculus 15 y 10 5 x -6 -4 -2 2 4 6 8 -5 Based on the rate of change of one variable in comparison to another. For example if y=x3 , we talk about the rate of change of y in comparison to x. Another example: if t=time and s= the distance travelled and s and t are related by the equation s=2t2+5. We then talk about the rate of change of the distance with respect to time. Derivative Limit as slope formula definition of derivative f '( x) = lim h 0 f (x + h) f ( x) h How to compute derivatives Applications About Office hrs: Please write down your preferred time spots. For example, one spot could be: Monday 11:00am-11:50am
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SUNY Buffalo - MTH - MTH122
Welcome toMath 122 Lecture 2 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009MTH 121 ReviewMore about Derivative Applications of differential calculusDerivativeDefinition Ex
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Welcome toMath 122 Lecture 3 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009MTH 121 ReviewIntegral calculusIntegrationDefinite Integralx = (b a)/n, x1, x2, ., xn are se
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Welcome toMath 122 Lecture 4 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Group workYou will have 4 problems based on MTH 121. Form a group (no more than 3 for each group) a
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Welcome toMath 122 Lecture 5 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Chapter 7 Functions of Several VariablesLast timeExamples of Functions of Several Variables 7.2
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Welcome toMath 122 Lecture 6 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Last timePartial derivativesDefinition ExamplePartial Derivative of f (x, y) If f ( x, y ) = 2 x
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Welcome toMath 122 Lecture 7 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Last timeFinding Relative Maxima and Minima 7.4Lagrange Multipliers and Constrained Optimizatio
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Welcome toMath 122 Lecture 8 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009! ! !Partial Derivatives Finding Relative Maxima and Minima Lagrange Multipliers and Constrained O
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Welcome toMath 122 Lecture 9 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009! ! !Functions of Several Variables Partial Derivatives Finding Relative Maxima and Minima Lagrang
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Welcome toMath 122 Lecture 10 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009!Integration by SubstitutionIf u = g(x), then 9.2Integration by Parts!Integration by Part
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Welcome toMath 122 Lecture 11 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009! !Integration by Substitution Integration by Parts 9.3Evaluation of Definite Integrals!Th
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Welcome toMath 122 Lecture 12 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009 9.3 (Contd)Evaluation of Definite Integrals!The Definite Integral Evaluating Definite Integra
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SUNY Buffalo - MTH - MTH122
MATH 122 (Section C)Survey of Calculus &amp; its Applications 2Spring 2009TIME: INSTRUCTOR: OFFICE: PHONE: E-MAIL: WEB (course):Course HandoutMWF 10:00-10:50am Quanlei Fang 106 Mathematics Building 645-6284 x159 qfang2@buffalo.edu http:/www.acsu.
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