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Calculus for Engineers

Курс от The Hong Kong University of Science and Technology
Начальный≈ 31.4 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This course offers a streamlined approach to university-level calculus, tailored for engineers and scientists. We begin with a review of precalculus in the first module, followed by derivatives and integrals in the second and third modules. The fourth module introduces Taylor series, while the fifth and sixth modules cover important applications of calculus. The course features 59 concise lecture videos, each accompanied by practice problems. After each major topic, you will find a short practice quiz to reinforce your understanding. Solutions to problems and practice quizzes are included in the instructor-provided lecture notes. At the end of each module, there is an assessed quiz to evaluate your progress. Score over 80% on these quizzes to earn a course certificate. Download the lecture notes: https://www.math.hkust.edu.hk/~machas/calculus-for-engineers.pdf Watch the promotional video: https://youtu.be/mDuHJos21wo

Навыки, которые вы освоите

CalculusIntegral CalculusNumerical AnalysisDifferential EquationsDerivativesTrigonometryAlgebraMathematical Theory & AnalysisEngineering CalculationsPhysicsApplied Mathematics

Программа курса

6 модулей · 220 учебных материалов

01Foundations41 материалов

Welcome to Calculus for Engineers

Welcome and Course InformationЧтениеCourse OverviewВидеоDiagnostic QuizЗаданиеHow to Write Math in the Discussion Forums using MathJaxЧтение

Учитесь у экспертов

Jeffrey R. Chasnov

Professor

Calculus for Engineers
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≈ 31.4 ч

6 модулей

Язык: Английский

Субтитры: Узбекский, Пушту, Дари, Казахский

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Introduction to Module One

Module One IntroductionВидео

Numbers

Real Numbers | Lecture 1ВидеоRational Numbers are DenseЧтениеSquare Root of Two is IrrationalЧтениеComplex Numbers | Lecture 2ВидеоWrite as a Complex NumberЧтениеSolve a Complex EquationЧтениеDetermine the Square Root of iЧтениеNumbersЗадание

Elementary Functions

Functions and their Inverses | Lecture 3ВидеоInverse of the Linear FunctionЧтениеInverse of the Unit Quarter-Circle FunctionЧтениеLimits and Continuity | Lecture 4ВидеоEvaluate LimitsЧтениеPolynomials and Rational Functions | Lecture 5ВидеоFunction RangesЧтениеFunction Domain and RangeЧтениеElementary FunctionsЗадание

Transcendental Functions

Exponential Function | Lecture 6ВидеоDefinition of e^xЧтениеNatural Logarithm | Lecture 7ВидеоCombine LogarithmsЧтениеAddition and Multiplication of ExponentsЧтениеChange of Base FormulaЧтениеTrigonometric Functions | Lecture 8ВидеоConvert from Degrees to RadiansЧтениеCosine and Sine are Phase-shifted FunctionsЧтениеDouble-angle formulasЧтениеPower reduction formulasЧтениеPythagorean IdentitiesЧтениеPolar CoordinatesЧтениеInverse Trigonometric Functions | Lecture 9ВидеоPlot of ArccosineЧтениеTrigonometric Functions of Inverse Trigonometric FunctionsЧтениеInverse Trigonometric Function IdentityЧтениеTranscendental FunctionsЗадание

Quiz

Module One AssessmentЗадание
02Differentiation48 материалов

Introduction to Module Two

Module Two IntroductionВидео

Differentiation Rules I

Definition of the Derivative | Lecture 10ВидеоAnother Definition of the DerivativeЧтениеLeibnitz’s notationЧтениеDifferentiabilityЧтениеAsymptotic Behavior of the Arctangent FunctionЧтениеPower Rule | Lecture 11ВидеоThe Derivative of 1/xЧтениеThe Derivative of x^{3/2}ЧтениеSum and Constant-Multiple Rules | Lecture 12ВидеоFinite Power SeriesЧтениеDifferentiation Rules IЗадание

Differentiation Rules II

Product Rule | Lecture 13ВидеоProduct Rule for Three FunctionsЧтениеDerivative of x^2ЧтениеQuotient Rule | Lecture 14ВидеоDerive the Quotient Rule from the Product RuleЧтениеDerivative of a Rational FunctionЧтение

Exponential and Logarithm Functions

Exponential Function | Lecture 16ВидеоDerivatives of Exponential FunctionsЧтениеDerivative of the Limit Definition of the Exponential FunctionЧтениеNatural Logarithm | Lecture 17ВидеоDerivatives of Logarithm IdentitiesЧтениеDerivatives of LogarithmsЧтение

Trigonometric Functions

Sine and Cosine | Lecture 19ВидеоAnother Derivation of the Derivative of SineЧтениеDerivatives of ln, sin, cosЧтениеDifferential Equation for Cosine and SineЧтениеDifferential Equation for cos x + i sin xЧтениеTrigonometric Functions | Lecture 20Видео

Quiz

Module Two AssessmentЗадание
03Integration30 материалов

Introduction to Module Three

Module Three IntroductionВидео

Fundamental Theorems

Definite Integral | Lecture 22ВидеоOrthogonal FunctionsЧтениеEven or Odd IntegralsЧтениеFirst Fundamental Theorem of Calculus | Lecture 23ВидеоDerivative of a Constant IntegralЧтениеFirst Fundamental Theorem and the Chain RuleЧтениеDifferentiating the IntegrandЧтениеSecond Fundamental Theorem of Calculus | Lecture 24ВидеоSome Simple IntegralsЧтениеIndefinite Integral | Lecture 25ВидеоPolynomial IntegralЧтениеTrigonometric IntegralЧтениеExponential IntegralЧтениеFundamental TheoremsЗадание

Elementary Techniques of Integration

Integration by Substitution | Lecture 26ВидеоSimple SubstitutionsЧтениеIntegration by SubstitutionЧтениеIntegration by Parts | Lecture 27ВидеоIntegration by PartsЧтениеGamma FunctionЧтениеElementary Techniques of Integration

Advanced Techniques of Integration

Trigonometric Integrals | Lecture 28ВидеоTrigonometric IntegralsЧтениеTrigonometric Substitution | Lecture 29ВидеоTangent and Secant IntegralЧтениеIntegration by Partial Fractions | Lecture 30ВидеоPartial Fraction IntegralЧтение

Quiz

Module Three AssessmentЗадание
04Infinite Series39 материалов

Introduction to Module Four

Module Four IntroductionВидео

Sequences and Series

Sequences and Series | Lecture 31ВидеоSum of the Squares of the Fibonacci NumbersЧтениеSum of the First n NumbersЧтениеSum of the Squares of the First n NumbersЧтениеp-Series | Lecture 32ВидеоSum of the p-SeriesЧтениеHarmonic Series | Lecture 33ВидеоEgyptian FractionsЧтениеRearrangement of the Alternating Harmonic SeriesЧтениеGeometric Series | Lecture 34ВидеоConverting Repeating Decimals into FractionsЧтениеDrug Blood ConcentrationsЧтениеSequences and SeriesЗадание

Power Series

Ratio Test | Lecture 35ВидеоConvergence of a SeriesЧтениеPower Series | Lecture 36ВидеоExponential FunctionЧтениеCosine and Sine FunctionsЧтениеPower Series Equal to ZeroЧтениеPower Series

Taylor Series

Taylor Series | Lecture 37ВидеоLinear ApproximationsЧтениеL’Hospital’s Rule | Lecture 38ВидеоInfinity over InfinityЧтениеCompute LimitsЧтениеExponential Function Grows Faster than any Power LawЧтениеLogarithm Function Grows Slower than any Power Law

Quiz

Module Four AssessmentЗадание
05Applications I33 материалов

Introduction to Module Five

Module Five IntroductionВидео

Complex Exponential Function

Complex Exponential Function | Lecture 41ВидеоAnother derivation of the Complex Exponential FunctionЧтениеIntegration using the Complex Exponential FunctionЧтениеDerivation of the Pythagorean IdentityЧтениеHyperbolic Trigonometric Functions and the Complex Exponential FunctionЧтениеPolar Form of Complex Numbers | Lecture 42ВидеоSimplifying Complex ExpressionsЧтениеRoots of Complex NumbersЧтениеTrigonometric Identities | Lecture 43ВидеоOrthogonality Relations for Cosine and SineЧтениеAdditional and Double Angle Formulas for Hyperbolic Trigonometric FunctionsЧтениеComplex Exponential FunctionЗадание

Areas and Volumes

Circumference of a Circle | Lecture 44ВидеоCircumference of a Circle in Cartesian CoordinatesЧтениеArea of a Circle | Lecture 45ВидеоArea of an EllipseЧтениеCircumference from AreaЧтениеSurface Area of a Sphere | Lecture 46Видео

Numerical Methods

Newton’s Method | Lecture 48ВидеоCompute sqrt(3)ЧтениеTrapezoidal Rule | Lecture 49ВидеоEstimate ln 2ЧтениеTrapezoidal Rule for Unevenly Spaced PointsЧтениеCentered Differences | Lecture 50ВидеоCentered Difference Approximation for a Differential Equation

Quiz

Module Five AssessmentЗадание
06Applications II29 материалов

Introduction to Module Six

Module Six IntroductionВидео

Local Extrema

Maxima and Minima | Lecture 51ВидеоCubic Polynomials with no Local ExtremaЧтениеCubic Polynomial with Three Distinct Real RootsЧтениеMaximum Area of a Rectangle | Lecture 52ВидеоThree-sided FenceЧтениеShortest Path | Lecture 53ВидеоPipe around a CornerЧтениеLifeguard Problem | Lecture 54ВидеоSeated Lifeguard ProblemЧтениеLocal ExtremaЗадание

Newton's Second Law

Position, Velocity, and Acceleration | Lecture 55ВидеоPosition, Velocity, and AccelerationЧтениеGravity of Earth | Lecture 56ВидеоTrajectory of a Cannon BallЧтениеNewton’s Second LawЗадание

Growth, Decay and Oscillations

Growth, Decay, and Oscillations | Lecture 57ВидеоDifferential Equation for the Complex Exponential FunctionЧтениеCompound Interest | Lecture 58ВидеоRule of 72ЧтениеNewton’s Law of CoolingЧтениеPendulum | Lecture 59Видео

Quiz

Module Six AssessmentЗадание

Farewell

Concluding RemarksВидеоPlease Rate this CourseЧтениеAcknowledgementsЧтение
Derivative of Negative Exponent Power LawsЧтение
Chain Rule | Lecture 15Видео
Derivative using the Power Rule and Chain RuleЧтение
Derivative using the Power Rule, Product Rule and Chain RuleЧтение
Derivative using the Power Rule, Quotient Rule and Chain RuleЧтение
The Chain Rule for the Composition of Three FunctionsЧтение
Differentiation Rules IIЗадание
Power Rule Redux | Lecture 18Видео
Derivative of a to the x powerЧтение
Derivative of log base aЧтение
Derivative of x to the xЧтение
Exponential and Logarithm FunctionsЗадание
Derivative of a Complicated Trigonometric ExpressionЧтение
Inverse Trigonometric Functions | Lecture 21Видео
Another Derivation of the Derivative of arccosЧтение
Derivative of an arcsineЧтение
Trigonometric FunctionsЗадание
Задание
Advanced Techniques of IntegrationЗадание
Задание
Чтение
Taylor Series of Elementary Functions I | Lecture 39Видео
Taylor Series DerivativesЧтение
Taylor Series LimitsЧтение
Trigonometric Addition FormulasЧтение
Hyperbolic Trigonometric FunctionsЧтение
Taylor Series of Elementary Functions II | Lecture 40Видео
Binomial TheoremЧтение
Taylor Series for TangentЧтение
Integrating using Taylor SeriesЧтение
Taylor SeriesЗадание
Surface Area of a ConeЧтение
Volume of a Sphere | Lecture 47Видео
Surface Area from VolumeЧтение
Volume of a ConeЧтение
Areas and VolumesЗадание
Чтение
Numerical MethodsЗадание
Pendulum Starting at the BottomЧтение
Pendulum with Friction and a Driving ForceЧтение
Growth, Decay, and OscillationsЗадание