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MATH 150 – CALCULUS AND ANALYTIC GEOMETRY I (Shannon) Course Description: This course is the first in a three-semester calculus sequence designed for mathematics, science, and engineering majors. Topics include limits and- continuity; differentiation of algebraic, trigonometric, and exponential functions and their inverses; integration and the fundamental theorem of calculus; and applications of differentiation and integration. Concepts are covered with the expectation that students are preparing to take Calculus II and beyond. This course requires memorization of the differentiation and anti-differentiation formulas covered in this course to insure success in future courses. A graphing calculator is ics CoveredI. Limits and continuityA. Definition of a limit and computation of limits using numerical, graphical and algebraic approachesB. Theorems about limitsC. Continuity of a function at a point and on an intervalD. Intermediate Value Theorem.II. DerivativesA. Derivative as a limit and differentiability of a functionB. Interpretation of derivative as a slope of a tangent line and as a rate of changeC. Differentiation formulas: power rule, product rule, quotient ruleD. Chain ruleE. Derivatives of trigonometric functionsE. Higher order derivativesF. Implicit differentiationG. Related ratesH. Tangent line approximation and differential.III. Applications of derivativesA. Maximum and minimum? optimizationB. Mean Value TheoremC. Concavity and inflection pointsD. Graphing functions using first and second derivatives, concavity, and asymptotes.IV. IntegralsA. Indefinite integrals and their propertiesB. Definite integrals as Riemann sumsC. Special properties of definite integralsD. Fundamental Theorem of CalculusE. Integration by substitutionG. Application of integration to areas and volumes.V. Inverse functionsA. Differentiation of inverse functionsB. Exponential and logarithmic functionsC. Inverse trigonometric functions.What to expect;5 hours per week inside and at least 10 hours outside class. HW could be online, on paper, or both. Graphing technology is used.Students who earn a grade of C or higher in Math 150 will pass this course and can take the next Math class that they need for their major. Who should enroll: This Calculus course is recommended for any student who majors in STEM. Students who are eligible to enroll in MATH 150, Calculus and Analytic Geometry I can enroll in this class.5. Concepts/skills needed prior to enrolling: * Solving Equations – quadratic, rational, radical, exponential, logarithmic, polynomial, trigonometric* Inequalities and Interval Notation * Rational Expressions – factoring, simplifying, long division, completing the square, rationalizing numerators* Relations and Functions- definitions, evaluating, domain and range * Trigonometric Identities – the ability to rewrite and algebraically manipulate trigonometric expressions ................
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