Канал: Chris Odden

The radius of curvature and the circle of best fit

The radius of curvature and the circle of best fit

Rules for integrating linear combinations of functions

Rules for integrating linear combinations of functions

The quotient rule for differentiation

The quotient rule for differentiation

Velocity, speed, and acceleration

Velocity, speed, and acceleration

Introduction to rectilinear motion

Introduction to rectilinear motion

Why is Simpson's rule so effective?

Why is Simpson's rule so effective?

The trapezoid rule and Simpson's rule as weighted averages of Riemann sums

The trapezoid rule and Simpson's rule as weighted averages of Riemann sums

Related rates: three worked examples

Related rates: three worked examples

Regular Riemann sums: left-hand sums, right-hand sums, and midpoint sums

Regular Riemann sums: left-hand sums, right-hand sums, and midpoint sums

Linear approximations to differentiable functions

Linear approximations to differentiable functions

The law of cosines

The law of cosines

Power rule, part 2: rational exponents

Power rule, part 2: rational exponents

Areas between graphs

Areas between graphs

Areas between graphs: using technology to calculate absolute area

Areas between graphs: using technology to calculate absolute area

Polynomial approximations of functions (Introduction to the Taylor recipe)

Polynomial approximations of functions (Introduction to the Taylor recipe)

The p-test for improper integrals

The p-test for improper integrals

Improper integrals: decomposing compound improper integrals into a sum of simple improper integrals

Improper integrals: decomposing compound improper integrals into a sum of simple improper integrals

Improper integrals: integration on a finite interval with a problem endpoint

Improper integrals: integration on a finite interval with a problem endpoint

Improper integrals: integration on a semi-infinite interval

Improper integrals: integration on a semi-infinite interval

The Fundamental Theorem of Calculus (Part 2)

The Fundamental Theorem of Calculus (Part 2)

Finding the area under the curve y=x^2

Finding the area under the curve y=x^2

Rates of change, net change, and signed areas under graphs

Rates of change, net change, and signed areas under graphs

Optimization

Optimization

The definition of inflection point

The definition of inflection point

A test for monotonicity: Using the derivative to understand the monotonicity of a function

A test for monotonicity: Using the derivative to understand the monotonicity of a function

Monotonicity (What it means for a function to be increasing or decreasing)

Monotonicity (What it means for a function to be increasing or decreasing)

The Mean Value Theorem

The Mean Value Theorem

Derivatives of scalar multiples, sums, and differences of functions

Derivatives of scalar multiples, sums, and differences of functions

The alternating series test (also known as the Leibniz Test)

The alternating series test (also known as the Leibniz Test)

The alternating harmonic series

The alternating harmonic series

The p-series

The p-series

The divergence test (also known as the nth term test)

The divergence test (also known as the nth term test)

The harmonic series

The harmonic series

Using a spreadsheet and desmos to plot sequences of partial sums

Using a spreadsheet and desmos to plot sequences of partial sums

On scaling series

On scaling series

The general geometric series a+ax+ax^2+...

The general geometric series a+ax+ax^2+...

Using desmos to plot sequences

Using desmos to plot sequences

The geometric series 1+x+x^2+x^3+...

The geometric series 1+x+x^2+x^3+...

Introduction to sequences

Introduction to sequences

The Basel Problem: finding the sum of the reciprocals of the squares

The Basel Problem: finding the sum of the reciprocals of the squares

Introduction to implicit differentiation

Introduction to implicit differentiation

Newton's law of cooling

Newton's law of cooling

The derivative of a linear function

The derivative of a linear function

Concavity and the second derivative

Concavity and the second derivative

About the non-uniqueness of antiderivatives

About the non-uniqueness of antiderivatives

The chain rule in action: Leibniz notation versus explicit composition

The chain rule in action: Leibniz notation versus explicit composition

The derivative of an exponential function

The derivative of an exponential function

Introduction to l'Hospital's Rule

Introduction to l'Hospital's Rule

Tangent slopes of parametric curves

Tangent slopes of parametric curves

Accumulation functions

Accumulation functions

The "1-4-1" rule

The "1-4-1" rule

Average value of a function

Average value of a function

Discontinuities

Discontinuities

Introduction to polar coordinates

Introduction to polar coordinates

Interval laws for definite integrals

Interval laws for definite integrals

The Fundamental Theorem of Calculus (Evaluation Theorem)

The Fundamental Theorem of Calculus (Evaluation Theorem)

Indefinite integrals and antiderivatives

Indefinite integrals and antiderivatives

Introduction to the derivative function

Introduction to the derivative function

Introduction to arc length

Introduction to arc length

The product rule for differentiation

The product rule for differentiation

Definite and indefinite integrals of cos^2x and sin^2x

Definite and indefinite integrals of cos^2x and sin^2x

Introduction to series

Introduction to series

Position vectors, velocity and speed

Position vectors, velocity and speed

The algebraic properties of the dot product

The algebraic properties of the dot product

The dot product of two vectors in the plane

The dot product of two vectors in the plane

Introduction to vectors, Part 2

Introduction to vectors, Part 2

Introduction to vectors, Part 1

Introduction to vectors, Part 1

Simpson's Rule

Simpson's Rule

Integration by parts (Introduction)

Integration by parts (Introduction)

QuickVid: Basic curve sketching principles

QuickVid: Basic curve sketching principles

QuickVid: Analyzing relative extrema

QuickVid: Analyzing relative extrema

QuickVid: Summary of limit laws for quotients

QuickVid: Summary of limit laws for quotients

QuickVid: Minimizing the surface area of a soda can

QuickVid: Minimizing the surface area of a soda can

QuickVid: Examples of substitution

QuickVid: Examples of substitution

Definite integrals and signed area

Definite integrals and signed area

Riemann sums and the definite integral

Riemann sums and the definite integral

Extreme values of continuous functions on closed intervals

Extreme values of continuous functions on closed intervals

Relative extrema, critical numbers, and Fermat's Theorem

Relative extrema, critical numbers, and Fermat's Theorem

Introduction to relative and absolute extrema of functions

Introduction to relative and absolute extrema of functions

Cylindrical shells and the volume of a solid of revolution

Cylindrical shells and the volume of a solid of revolution

Cross-sectional area, volume, and integration

Cross-sectional area, volume, and integration

Related rates, part 2: A few more tips

Related rates, part 2: A few more tips

Introduction to related rates

Introduction to related rates

Functions defined by power series

Functions defined by power series

Euler's method

Euler's method

Plotting families of solutions of differential equations

Plotting families of solutions of differential equations

Notation for derivatives

Notation for derivatives

The derivative of a polynomial function

The derivative of a polynomial function

Continuity, Part 2 (One-sided continuity)

Continuity, Part 2 (One-sided continuity)

About intervals

About intervals

The power rule, Part 1

The power rule, Part 1

The derivative of sine and cosine

The derivative of sine and cosine

Tangent slopes of y = x^2

Tangent slopes of y = x^2

A special trigonometric limit (limit of sin x / x as x goes to zero)

A special trigonometric limit (limit of sin x / x as x goes to zero)

What is a radian?

What is a radian?

Introduction to the chain rule

Introduction to the chain rule

Algebra and limits

Algebra and limits

Continuity, Part 1

Continuity, Part 1

Limit laws, Part 4

Limit laws, Part 4

Limit laws, Part 3

Limit laws, Part 3

Limit laws, Part 2

Limit laws, Part 2

Limit laws, Part 1

Limit laws, Part 1

Secant slope, tangent slope, and instantaneous rates of change

Secant slope, tangent slope, and instantaneous rates of change

Introduction to limits, Part 2

Introduction to limits, Part 2

Introduction to limits

Introduction to limits

Average rates of change

Average rates of change

Introduction to polar coordinates

Introduction to polar coordinates

Area enclosed by a polar curve

Area enclosed by a polar curve

Separation of variables

Separation of variables

Introduction to differential equations

Introduction to differential equations

Tangent slopes of polar curves

Tangent slopes of polar curves

Arc length of polar curves

Arc length of polar curves

When polar graphs cross the origin

When polar graphs cross the origin

Natural growth and decay

Natural growth and decay

Slope fields

Slope fields

Initial value problems

Initial value problems

Simple harmonic motion

Simple harmonic motion

Introduction to the Ellipse

Introduction to the Ellipse