कोर्स · College
Calculus
Limits, derivatives, integrals and series: the single-variable calculus of a first university course.
A complete first course in single-variable calculus, in the order it is taught at university: limits and continuity, the derivative and its rules, the chain rule and implicit differentiation, what derivatives are for (rates, optimisation, curve sketching, the mean value theorem), the integral and the fundamental theorem, the techniques of integration, the applications of integration, and finally sequences, series and Taylor expansions.
It is for anyone who is comfortable with algebra, functions and trigonometry. Each unit ends with a quiz that mixes computation, concepts and short proofs; the final exam covers the whole course.
के बाद आता है: Precalculus, Trigonometry
कोर्स
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Limits and continuity
20 सबकLimitsCalculusA Preview of CalculusIntroduction to CalculusReview of FunctionsBasic Classes of FunctionsTrigonometric FunctionsInverse FunctionsExponential and Logarithmic FunctionsThe notion of limitThe Limit of a FunctionFinding Limits: Numerical and Graphical ApproachesThe Limit LawsFinding Limits: Properties of LimitsThe Precise Definition of a LimitLimit (mathematics)ContinuityContinuous functionLimits, continuity, and differentiabilityLimits at Infinity and Asymptotes -
Derivatives: the definition and the rules
18 सबकDerivativesHow do we measure velocity?The derivative of a function at a pointDefining the DerivativeDerivativeThe derivative functionThe Derivative as a FunctionInterpreting, estimating, and using the derivativeDerivatives as Rates of ChangeThe second derivativeElementary derivative rulesDifferentiation rulesThe product and quotient rulesProduct ruleQuotient ruleThe sine and cosine functionsDerivatives of Trigonometric FunctionsDerivatives of other trigonometric functions -
The chain rule and implicit differentiation
6 सबक -
Applications of derivatives
20 सबकMaxima and minimaRelated rates and optimisationRelated ratesThe tangent line approximationLinear Approximations and DifferentialsLinear approximationUsing derivatives to identify extreme valuesMaxima and MinimaGlobal optimizationThe Mean Value TheoremMean value theoremDerivatives and the Shape of a GraphUsing derivatives to describe families of functionsCurve sketchingApplied optimizationApplied Optimization ProblemsOptimization (mathematics)Using derivatives to evaluate limitsL'Hôpital's ruleNewton’s Method -
Integrals and the fundamental theorem
19 सबकIntegralsDefinite integralsAntiderivativesAntiderivativeApproximating AreasRiemann sumsRiemann sumThe Definite IntegralIntegralDetermining distance traveled from velocityThe Fundamental Theorem of CalculusFundamental theorem of calculusThe Second Fundamental Theorem of CalculusConstructing accurate graphs of antiderivativesIntegration Formulas and the Net Change TheoremSubstitutionIntegration by substitutionIntegrals Involving Exponential and Logarithmic FunctionsIntegrals Resulting in Inverse Trigonometric Functions -
Techniques of integration
11 सबकIntegration techniques: substitution, parts, partial fractionsIntegration by partsTrigonometric IntegralsTrigonometric substitutionPartial FractionsPartial fraction decompositionOther Strategies for IntegrationOther options for finding algebraic antiderivativesNumerical IntegrationImproper IntegralsImproper integral -
Applications of integration
18 सबकApplications of integration: area, volume, arc lengthAreas between CurvesUsing definite integrals to find area and lengthDetermining Volumes by SlicingUsing definite integrals to find volumeVolumes of Revolution: Cylindrical ShellsSolid of revolutionArc Length of a Curve and Surface AreaArc lengthPhysical ApplicationsPhysics applications: work, force, and pressureMoments and Centers of MassDensity, mass, and center of massIntegrals, Exponential Functions, and LogarithmsCalculus of the Hyperbolic FunctionsExponential Growth and DecayExponential growthLogistic function -
Sequences and series
21 सबकInfinite series and convergence testsSeries and sumsTaylor seriesSequencesInfinite SeriesGeometric sumsThe Divergence and Integral TestsComparison TestsAlternating SeriesRatio and Root TestsConvergence testsPower Series and FunctionsPower seriesProperties of Power SeriesExtending local linearizationTaylor polynomialsTaylor and Maclaurin SeriesMaclaurin seriesWorking with Taylor SeriesFinding and using Taylor seriesQuantifying the accuracy of approximations
अंतिम परीक्षा
हर इकाई से सवाल, पिछले. टाइप करने वाले जवाब कुल शक्ति प्रणाली से चिह्नित हैं; सबूतों और फोटो कार्य मॉडल द्वारा पढ़ा जाता है, फिर एक व्यक्ति आपके परिणाम के बाद पूरे कागज पर पुनर्विचार करता है. अब आप अपने लिंक के साथ एक प्रमाणपत्र प्राप्त कर सकते हैं. पास चिह्न: 70%.
इसमें हस्ताक्षर करेंमूल्य
कोर्स पास
$39
हर इकाई के प्रश्न, अंतिम परीक्षा एक पुनः लेने के साथ, और एक कोर्स के लिए, आपके अपने काम की 20 जांच करती है.
एक अंतिम परीक्षा
$15
एक पाठ्यक्रम के अंतिम, चिह्नित और समीक्षा किया. किसी के लिए जो पहले से ही भौतिक जानता है और यह परीक्षण करना चाहता है.
प्रत्येक मार्ग
$19/मो.
सभी प्रश्नों और अंतिम हर कोर्स में (दो अंतिम एक माह) और १०० काम करते हैं । अपने खाते से रद्द करें.
कार्यशील जांच
$9
दस जांच: किसी भी काम की तस्वीर अपलोड करें या टाइप करें, और देखें कि यह कहाँ गलत हो गया था.
खरीद के लिए कोर्स जल्द ही खुला है ।