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Calculus DrOfEng Videos
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Absolute convergence, rearranging series
Absolute, conditional, convergence
Accumulation functions, example
Accumulation functions, interpret behaviour
Accumulation of change using the derivative
Alternating series test, convergence
Alternating series, error bound
Arc length, parametric curves
Arc length, parametric curves, example
Arc length, smooth planar curve, distance, definite integrals
Arc length, smooth planar curve, example
Area between curves, definite integrals over x
Area between curves, definite integrals over y
Area between curves, definite integrals, example
Area between two polar curves, definite integrals
Area between two polar curves, definite integrals, example
Basic differentiation rules
Behaviour of implicit relations
Behaviour of implicit relations, worked example 1
Behaviour of implicit relations, worked example 2
Behaviour of implicit relations, worked example 3
Candidates test
Chain Rule of Differentiation, Composite Functions, Example
Comparison test, convergence
Comparison tests, examples
Connecting position, velocity, acceleration, definite integrals
Connecting position, velocity, acceleration, example
Construct Maclaurin series, prove Euler's formula, example
Continuity, Functions, Three Conditions, Examples
Critical points: DrOfEng
Defining parametric equations
Definite integral, definition
Definite integrals, applying properties
Definite integrals, area between curves, piecewise integrals
Definite integrals, area between curves, with intersects
Definition of the derivative: DrOfEng
Derivative as a rate of change
Derivative of arccos(x)
Derivative of arccosec(x), inverse trig functions
Derivative of arccot(x), inverse trig functions
Derivative of arcsec(x), inverse trig functions
Derivative of arcsin(x)
Derivative of arctan(x)
Derivatives of composite exponential functions, a^x [u(x)]
Derivatives of composite logarithms, log_ax [u(x)]
Derivatives of e^x and ln(x), definition of the derivative
Derivatives of exponential functions, a^x
Derivatives of exponential functions, examples
Derivatives of inverse functions, examples
Derivatives of inverse functions: DrOfEng
Derivatives of logarithms, examples
Derivatives of logarithms, log_a(x)
Derivatives, inverse trig functions, examples
Determine if function increasing on interval
Differentiability, continuity, smooth function
Differential Equations, Verifying Solutions
Differentiating parametric equations
Differentiating parametric equations, example
Differentiation using the chain rule, examples
Differentiation, definition of the derivative, examples
Differentiation, examples
Discontinuities, removable, jump, essential
Error approximation
Euler's method, approximating solutions to ODEs
Euler's method, approximating solutions to ODEs, example
Exponential decay and growth, modelling using ODEs
Exponential decay, radioactive, example
Exponential decay, reaction, differential equation, example
Exponential growth, differential equations, example 1
Exponential growth, differential equations, example 2
Extreme value theorem: DrOfEng
First and second derivative tests
Fundamental theorems of calculus
Geometric series, convergence
Global and local extrema
Harmonic series, p-series, convergence
Implicit differentiation, examples
Implicit differentiation: DrOfEng
Implicit second order derivative, example
Improper integrals, example 1
Improper integrals, example 2
Improper integrals, example 3
Improper integrals, example 4
Improper integrals: DrOfEng
Indefinite integrals, basic rules
Indefinite integrals, definition, power rule
Indefinite integrals, trig functions from their derivatives 1)
Indefinite integrals, trig functions from their derivatives 2)
Infinite series, partial sums
Integral test for convergence
Integrals in applied contexts, accumulation, definite integrals
Integrals in applied contexts, example 1
Integrals in applied contexts, example 2
Integrals in applied contexts, example 3
Integrals in applied contexts, example 4
Integrating functions with removable and jump discontinuities
Integration by parts, examples 1
Integration by parts, examples 2
Integration by parts: DrOfEng
Integration by substitution, integrals of e^u and 1/u
Integration by substitution, u-substitution
Integration by substitution, u-substitution, examples 1
Integration by substitution, u-substitution, examples 2
Integration by u-substitution, a^x [u(x)]
Integration by u-substitution, cosec(x), example
Integration by u-substitution, cot(x), example
Integration by u-substitution, definite integrals
Integration by u-substitution, examples 1
Integration by u-substitution, examples 2
Integration by u-substitution, inverse trig functions
Integration by u-substitution, sec(x), example
Integration, completing the square
Integration, inverse trig, completing the square, examples
Integration, partial fractions, distinct linear factors
Integration, partial fractions, example 1
Integration, partial fractions, example 2
Integration, partial fractions, irreducible quadratic factors
Integration, partial fractions, repeated linear factors
Integration, polynomial long division
Integration, polynomial long division, example 1
Integration, polynomial long division, example 2
Integration, polynomial long division, example 3
Integration, power rule, examples
Integration, trig functions, examples
Introduction to Differential Equations, Modelling
Introduction to limits: DrOfEng
Introduction to related rates problems
L'hopital's rule, indeterminate limits
L'hopital's rule, indeterminate limits (0/0)
Lagrange error bound, example 1
Lagrange error bound, example 2
Lagrange error bound, taylor polynomial approximations
Left Riemann sum, approx area under a curve
Left Riemann sum, right Riemann sum, example
Limit comparison test, first rule, convergence and divergence, with proof
Limit comparison test, second rule, convergence, with proof
Limit comparison test, third rule, divergence, with proof
Limits and continuity, examples
Limits and Continuity, Revision, Calculus, with Worked Examples
Limits and Continuity, Test, 15 Worked Examples
Limits, addition rules, multiplication rules
Limits, logarithms and exponential functions, x [(x-3)/x]^(1/x)
Limits, logarithms and exponential functions, x^(1/x)
Limits, rational polynomial functions
Limits, reciprocal functions
Limits, trigonometric functions, sin(x)/x
Limits, trigonometric functions, x [1-cos(x)]/x
Local linearity and approximation
Logistic model, analysing the solution, limiting value
Logistic model, ODE, alternate solution method
Logistic model, ODE, population growth, qualitative analysis
Logistic model, solution to the ODE, differential equation
Logistic Model, Solution, Time at Maximum Growth Rate
Mean value theorem, derivatives
Midpoint Riemann sum, approx area under a curve
Midpoint Riemann sum, example
Motion problems, differentation, vector-valued, parametric
Motion problems, integration, vector-valued, parametric
Motion problems, vector-valued, parametric, example
n-th term test for divergence
Optimisation
Polar coordinates, definition, intro to polar curves
Polar coordinates, differentiation
Polar curves, area of polar region, definite integrals
Polar curves, area of polar region, example
Polar curves, plotting, differentiation, with example, cardioid
Polar curves, plotting, with example, lemniscate
Polar curves, second derivative, example
Power series, convergence, example
Power series, definition
Power series, radius of convergence, interval of convergence
Product rule, differentiation
Proving the quotient rule using chain rule
Quotient rule, differentiation
Ratio test, infinite series
Relating position, velocity, acceleration
Representing power series as functions, with example
Right Riemann sum, approx area under a curve
Second derivative, parametric equations
Selecting convergence tests, power series, example
Selecting integration techniques, example
Selecting Integration Techniques, Summary, Methods
Selecting Integration Techniques, Worked Example
Separation of variables, general solution, example
Separation of variables, general solution, separable ODE
Separation of variables, particular solution, example
Separation of variables, particular solution, separable ODE
Sequences, convergence
Sequences, convergence, limits, examples
Series, convergence, partial sums
Slope fields, differential equations
Slope fields, differential equations, example
Taylor Polynomials, Approximation of Functions
Taylor series, example
Telescoping series, convergence, example
Term-by-term differentiation, power series
Term-by-term integration, power series
Trapezoid method, approx area under a curve
Trapezoid method, example
Vector valued functions, integration, example
Vector-valued functions, definition
Vector-valued functions, differentiation
Vector-valued functions, differentiation, example
Vector-valued functions, integration
Verifying solutions to differential equations, example
Volume with cylindrical shell method, revolve around x-axis
Volume with cylindrical shell method, revolve around y-axis
Volume with disc method, revolving around the x-axis
Volume with disc method, revolving around the y-axis
Volume, cylindrical shell, revolving around other horizontal axes
Volume, revolved solid, definite integral, example: DrOfEng
Volume, washer, revolving around other horizontal axes
Volumes with cross sections, equilateral triangles
Volumes with cross sections, example
Volumes with Cross Sections, Isosceles Right Triangles
Volumes with cross sections, perpendicular to y-axis
Volumes with cross sections, semi-circles
Volumes with cross sections, squares, rectangles
Volumes, cylindrical shell, revolving around other vertical axes
Volumes, disc, revolving around other horizontal axes
Volumes, washer, revolving around other vertical axes
Washer method, volume, revolving around the x-axis
Washer method, volume, revolving around the y-axis
Worked example, derivative as rate of change
Worked example, error approximation
Worked example, function, oblique asymptote
Worked example, linearisation
Worked example, local linearity
Worked example, motion
Worked example, non motion problem
Worked example, optimisation, closest point
Worked example, optimisation, maximise area
Worked example, optimisation, projectile
Worked example, optimisation, surface area
Worked example, reading motion from a graph
Worked example, related rates
Worked example, related rates, cone problem
Worked example, related rates, ladder
Worked example, sketch function with cusp
Worked example, sketch function, asymptote
Worked example, sketch polynomial function
Worked examples, L'hopital's rule
Worked examples, mean value theorem
Jumps
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