Канал: Calculus is pictures.

Vibrating membranes on a disk.

Vibrating membranes on a disk.

Vibrating membranes on a rectangle.

Vibrating membranes on a rectangle.

Differential inclusions and the Aviles Giga functional

Differential inclusions and the Aviles Giga functional

Regularity of differential inclusions in subspaces without rank-1 connections.

Regularity of differential inclusions in subspaces without rank-1 connections.

Sverak's regularity theorem part 2.

Sverak's regularity theorem part 2.

Sverak's regularity theorem for differential inclusions

Sverak's regularity theorem for differential inclusions

Sobolev Poincare inequality

Sobolev Poincare inequality

Sketch of Elliptic regularity

Sketch of Elliptic regularity

The three gradient problem

The three gradient problem

Intro to the finite gradient problem

Intro to the finite gradient problem

The Tartar square

The Tartar square

Introduction to the Tartar square

Introduction to the Tartar square

Quasiregular mappings in higher dimension and generalizations of Liouville's theorem

Quasiregular mappings in higher dimension and generalizations of Liouville's theorem

Intro to quasiregular mappings in higher dimensions and more on Liouville's theorem.

Intro to quasiregular mappings in higher dimensions and more on Liouville's theorem.

L^p bounds on the Hilbert transform part 2, and intro to L^p boundness of the Beurling transform.

L^p bounds on the Hilbert transform part 2, and intro to L^p boundness of the Beurling transform.

L^p bounds on the Hilbert transform. Part 1

L^p bounds on the Hilbert transform. Part 1

Intro to the Hilbert transform and the Plememlj formula

Intro to the Hilbert transform and the Plememlj formula

More on the Beltrami equation

More on the Beltrami equation

Solving Betrami's equation

Solving Betrami's equation

More estimates for a Cauchy type operator and weak Wirtinger derivatives.

More estimates for a Cauchy type operator and weak Wirtinger derivatives.

L^p estimates on a Cauchy type transform

L^p estimates on a Cauchy type transform

More on the Beurling transform.

More on the Beurling transform.

Introduction to the Beurling transform

Introduction to the Beurling transform

Intro to the Cauchy transform

Intro to the Cauchy transform

A generalized Cauchy integral formula

A generalized Cauchy integral formula

Stoilow decomposition reduces to solving Beltrami equation

Stoilow decomposition reduces to solving Beltrami equation

Conformal and anticonformal matrices, Wirtinger derivatives, the Beltrami equation and Stoilow.

Conformal and anticonformal matrices, Wirtinger derivatives, the Beltrami equation and Stoilow.

Quasiregular mappings, the Beltrami coefficient and introduction to the Stoilow decomposition.

Quasiregular mappings, the Beltrami coefficient and introduction to the Stoilow decomposition.

Regularity of Sobolev differential inclusions and introduction to Quasiregular mappings.

Regularity of Sobolev differential inclusions and introduction to Quasiregular mappings.

A weak quantitative Liouville theorem and introduction to Sobolev differential inclusions.

A weak quantitative Liouville theorem and introduction to Sobolev differential inclusions.

More introduction to weak convergence

More introduction to weak convergence

More introduction to Sobolev space and introduction to weak convergence

More introduction to Sobolev space and introduction to weak convergence

Korn's inequality and intro to Sobolev space

Korn's inequality and intro to Sobolev space

Sketch of background for Korn's inequality's via Fourier transform

Sketch of background for Korn's inequality's via Fourier transform

Quantitative Liouville Theorem for rotations. Part 2

Quantitative Liouville Theorem for rotations. Part 2

Quantitative Liouville Theorem for rotations. Part 1

Quantitative Liouville Theorem for rotations. Part 1

Differential inclusions into rotations and intro to rigidity

Differential inclusions into rotations and intro to rigidity

Liouville's theorem and special cases

Liouville's theorem and special cases

Riemann mapping theorem part 2

Riemann mapping theorem part 2

Riemann mapping theorem part 1

Riemann mapping theorem part 1

Sequences of injective holomorphic mappings

Sequences of injective holomorphic mappings

Normal familes

Normal familes

Differential Inclusions and the Aviles Giga functional. Short research talk.

Differential Inclusions and the Aviles Giga functional. Short research talk.

Another example of using symmetry to understand a Mobius transform.

Another example of using symmetry to understand a Mobius transform.

Yet another example of using symmetry to understand a Mobius mapping

Yet another example of using symmetry to understand a Mobius mapping

Mobius transforms preserve symmetries

Mobius transforms preserve symmetries

An example of using symmetry to understand a Mobius mapping

An example of using symmetry to understand a Mobius mapping

Defining symmetry across line or circles via the cross ratio.

Defining symmetry across line or circles via the cross ratio.

Cross ratios and introductions to symmetry across a circle.

Cross ratios and introductions to symmetry across a circle.

Mobius transformations maps circles to lines.

Mobius transformations maps circles to lines.

The principle log on simply connected domains.

The principle log on simply connected domains.

Schwartz lemma

Schwartz lemma

An example of a conformal mapping

An example of a conformal mapping

Introduction to conformal mappings.

Introduction to conformal mappings.

Examples of Laurent series

Examples of Laurent series

Laurent series

Laurent series

Simply connected domains

Simply connected domains

The maximum modulus principle

The maximum modulus principle

The open mapping theorem

The open mapping theorem

Rouche's theorem

Rouche's theorem

The argument principle

The argument principle

The winding number

The winding number

Classification of singularities

Classification of singularities

An integral of function with a pole on the real line via the residue theorem

An integral of function with a pole on the real line via the residue theorem

Riemann's theorem on removeable singularities

Riemann's theorem on removeable singularities

Integration with a pole on the real line via the residue theorem

Integration with a pole on the real line via the residue theorem

Integration of functions that are a product of trig and rational functions.

Integration of functions that are a product of trig and rational functions.

Integration of rational function via the residue theorem

Integration of rational function via the residue theorem

Calculating trig integrals via the residue theorem.

Calculating trig integrals via the residue theorem.

A simple example of calculating a real integral via the residue theorem

A simple example of calculating a real integral via the residue theorem

Calculating residues

Calculating residues

The residue theorem

The residue theorem

Zeros, poles and singularities

Zeros, poles and singularities

Morera's theorem

Morera's theorem

Liouville's Theorem for bounded holomorphic functions on the complex plane

Liouville's Theorem for bounded holomorphic functions on the complex plane

Taylor's theorem for holomorphic functions

Taylor's theorem for holomorphic functions

Cauchy integral formula

Cauchy integral formula

Integration on complex curves

Integration on complex curves

Introduction to the Laplacian

Introduction to the Laplacian

Introduction to Cauchy integral formula

Introduction to Cauchy integral formula

Complex primitives on a ball

Complex primitives on a ball

Complex curves and parametrizations

Complex curves and parametrizations

Complex Log and exponential functions.

Complex Log and exponential functions.

Complex differentiation

Complex differentiation

The field of complex numbers

The field of complex numbers

The algebra of complex numbers

The algebra of complex numbers

Lecture 38: Review of methods for testing convergence of series.

Lecture 38: Review of methods for testing convergence of series.

Lecture 26: Mobius symmetries and automorphisms

Lecture 26: Mobius symmetries and automorphisms

Lecture 37: Review of arclength, surface area, sequences and series.

Lecture 37: Review of arclength, surface area, sequences and series.

Lecture 36: Review of integration methods

Lecture 36: Review of integration methods

Lecture 25: More Mobius mappings

Lecture 25: More Mobius mappings

Lecture 24: Mobius transforms

Lecture 24: Mobius transforms

Lecture 35: Arclength of polar curves and review problems

Lecture 35: Arclength of polar curves and review problems

Lecture 23: Schwarz lemma and introduction to Mobius transformations

Lecture 23: Schwarz lemma and introduction to Mobius transformations

Lecture 34: Area swept out by polar curves.

Lecture 34: Area swept out by polar curves.

Lecture 22: Introduction to conformal mappings

Lecture 22: Introduction to conformal mappings

Lecture 33: Polar curves.

Lecture 33: Polar curves.

Lecture 32: Calculus on parametric curves.

Lecture 32: Calculus on parametric curves.

Lecture 21: Laurent series

Lecture 21: Laurent series

Lecture 31: Introduction to parametric curves.

Lecture 31: Introduction to parametric curves.

Lecture 30: Applications of Taylor Polynomials.

Lecture 30: Applications of Taylor Polynomials.

Lecture 29: Taylor and Maclaurin series

Lecture 29: Taylor and Maclaurin series

Lecture 20: Complex log on simply connected domains and complex powers

Lecture 20: Complex log on simply connected domains and complex powers

Lecture 19: The open mapping theorem, max modulus principle and homotopic curves.

Lecture 19: The open mapping theorem, max modulus principle and homotopic curves.

Lecture 28: Representation of functions and integration and differentiation of power series.

Lecture 28: Representation of functions and integration and differentiation of power series.

Lecture 27: More power series

Lecture 27: More power series

Lecture 18: Winding number, the argument principle and Rouche's theorem

Lecture 18: Winding number, the argument principle and Rouche's theorem

Lecture 26: Intro to power series.

Lecture 26: Intro to power series.

Lecture 17: Meromorphic functions and stereographic projection.

Lecture 17: Meromorphic functions and stereographic projection.

Lecture 25: More problems from the practice exam for midterm 3

Lecture 25: More problems from the practice exam for midterm 3

Lecture 24: Problems from the practice exam for midterm 3.

Lecture 24: Problems from the practice exam for midterm 3.

Lecture 16: Classification of singularities and Casorati–Weierstrass theorem

Lecture 16: Classification of singularities and Casorati–Weierstrass theorem

Lecture 23: Review problems on convergence of series.

Lecture 23: Review problems on convergence of series.

Lecture 15: More evaluation of real integrals via Cauchy's residue formula

Lecture 15: More evaluation of real integrals via Cauchy's residue formula

Lecture 22: More examples of testing series for convergence.

Lecture 22: More examples of testing series for convergence.

Lecture 21: Strategy for testing convergence of series

Lecture 21: Strategy for testing convergence of series

Lecture 14: Evaluating real integrals via Cauchy residue formula

Lecture 14: Evaluating real integrals via Cauchy residue formula

Lecture 20: Root and ratio test, absolute and conditional convergence.

Lecture 20: Root and ratio test, absolute and conditional convergence.

Lecture 13: The residue theorem

Lecture 13: The residue theorem

Lecture 19: Alternating series

Lecture 19: Alternating series

Lecture 18: The Limit comparison test

Lecture 18: The Limit comparison test

Lecture 17: The integral test for series and integral test remainder estimate.

Lecture 17: The integral test for series and integral test remainder estimate.

Lecture 12: Sequences of holomorphic functions and introduction to zeros and singularities.

Lecture 12: Sequences of holomorphic functions and introduction to zeros and singularities.

Lecture 16: Question from the practice exam for midterm 2.

Lecture 16: Question from the practice exam for midterm 2.

Questions from the practice exam for midterm 2.

Questions from the practice exam for midterm 2.

Lecture 15: More on series

Lecture 15: More on series

Lecture 11: Morera's theorem

Lecture 11: Morera's theorem

Lecture 14: Introduction to series.

Lecture 14: Introduction to series.

Lecture 13: More on sequences.

Lecture 13: More on sequences.

Lecture 12: Introduction to sequences

Lecture 12: Introduction to sequences

Lecture 10: Liouville's Theorem and the fundamental theorem of algebra.

Lecture 10: Liouville's Theorem and the fundamental theorem of algebra.

Lecture 11: Area of Surface of Revolution

Lecture 11: Area of Surface of Revolution

Lecture 9: Harmonic functions and Taylor series

Lecture 9: Harmonic functions and Taylor series

Lecture 10: Arclength of a graph

Lecture 10: Arclength of a graph

Lecture 9: Improper integrals part 2.

Lecture 9: Improper integrals part 2.

Lecture 8: Cauchy integral formula for derivatives.

Lecture 8: Cauchy integral formula for derivatives.

Lecture 8: Introduction to improper integrals.

Lecture 8: Introduction to improper integrals.

Lecture 7: Complex primitives and Cauchy integral formula

Lecture 7: Complex primitives and Cauchy integral formula

Lecture 7: Review of integration methods

Lecture 7: Review of integration methods

Lecture 6: Practice exam for midterm 1

Lecture 6: Practice exam for midterm 1

Lecture 6: Goursat's theorem and closed curves in the complex plane.

Lecture 6: Goursat's theorem and closed curves in the complex plane.

Lecture 5: Strategy for integration.

Lecture 5: Strategy for integration.

Lecture 5: Integration on curves in the complex plane.

Lecture 5: Integration on curves in the complex plane.

Lecture 4: Integration of rational functions continued.

Lecture 4: Integration of rational functions continued.

Lecture 3: Introduction to integration of rational functions

Lecture 3: Introduction to integration of rational functions

Lecture 4: Complex exponential and trig functions.

Lecture 4: Complex exponential and trig functions.

Lecture 3: Examples of holomorphic functions and intro to complex power series.

Lecture 3: Examples of holomorphic functions and intro to complex power series.

Lecture 2: More trig integrals

Lecture 2: More trig integrals

Lecture 2: Complex differentiability, the Cauchy Riemann questions and Liouville's theorem.

Lecture 2: Complex differentiability, the Cauchy Riemann questions and Liouville's theorem.

Lecture 1: Trig integrals part 1

Lecture 1: Trig integrals part 1

Lecture 1: Intro to the complex numbers.

Lecture 1: Intro to the complex numbers.

Introduction to Calc 2.

Introduction to Calc 2.

Lecture 39: Review problems.

Lecture 39: Review problems.

Lecture 38: Volumes by cylindrical shells

Lecture 38: Volumes by cylindrical shells

Lecture 37: The practice exam for midterm 3

Lecture 37: The practice exam for midterm 3

Lecture 36: More on volumes by slicing

Lecture 36: More on volumes by slicing

Lecture 35: Volumes of revolution

Lecture 35: Volumes of revolution

Lecture 34: Introduction to volumes.

Lecture 34: Introduction to volumes.

Lecture 33: Area between curves.

Lecture 33: Area between curves.

Lecture 32: U-substitution method

Lecture 32: U-substitution method

Lecture 31: Applications of the fundamental theorem of calculus and indefinite integrals.

Lecture 31: Applications of the fundamental theorem of calculus and indefinite integrals.

Lecture 30: The fundamental theorem of Calculus

Lecture 30: The fundamental theorem of Calculus

Lecture 29: The definite integral.

Lecture 29: The definite integral.

Lecture 28: Area under a graph and distance travelled.

Lecture 28: Area under a graph and distance travelled.

Lecture 27: Antiderivatives.

Lecture 27: Antiderivatives.

Lecture 26: Introduction to optimization

Lecture 26: Introduction to optimization

Lecture 25: Curve Sketching.

Lecture 25: Curve Sketching.

Lecture 24: The practice exam for midterm 2.

Lecture 24: The practice exam for midterm 2.

Lecture 23: L’Hopitals rule

Lecture 23: L’Hopitals rule

Lecture 15: Introduction to related rates and differentiation of inverse trig functions

Lecture 15: Introduction to related rates and differentiation of inverse trig functions

Lecture 22: Second derivatives and graphs

Lecture 22: Second derivatives and graphs

Lecture 17: Linearization and the conclusion of related rates.

Lecture 17: Linearization and the conclusion of related rates.

Lecture 21: Concavity and the second derivative.

Lecture 21: Concavity and the second derivative.

Lecture 19: The closed interval method and introduction to the mean value theorem

Lecture 19: The closed interval method and introduction to the mean value theorem

Intro to power series

Intro to power series

Lecture 20: Conclusion of Mean Value Theorem and how the derivative affects the shape of the graph.

Lecture 20: Conclusion of Mean Value Theorem and how the derivative affects the shape of the graph.

Lecture 18: Introduction to absolute and local max and mins.

Lecture 18: Introduction to absolute and local max and mins.

Lecture 16: More related rates.

Lecture 16: More related rates.

Lecture 14: Differentiation of log and log differentiation

Lecture 14: Differentiation of log and log differentiation

Lecture 13: Implicit differentiation.

Lecture 13: Implicit differentiation.

Lecture 12: The chain rule

Lecture 12: The chain rule

Lecture 11: The practice exam

Lecture 11: The practice exam

Lecture 10: Trigonometric functions, differentiation, limits and their applications.

Lecture 10: Trigonometric functions, differentiation, limits and their applications.

Lecture 9: Product and quotient rule, and differentiation of trig functions

Lecture 9: Product and quotient rule, and differentiation of trig functions

Lecture 8: Differentiation of polynomials and introduction to the exponential function

Lecture 8: Differentiation of polynomials and introduction to the exponential function

Lecture 7: More on derivatives.

Lecture 7: More on derivatives.

Lecture 6: Introduction to derivatives.

Lecture 6: Introduction to derivatives.

Lecture 5: Limits at infinity and horizontal asymptotes

Lecture 5: Limits at infinity and horizontal asymptotes

Lecture 4: Continuity and the intermediate value theorem

Lecture 4: Continuity and the intermediate value theorem

Lecture 3: Limit laws and squeeze them

Lecture 3: Limit laws and squeeze them

Lecture 2: Limits, one sided limits and vertical asymptotes

Lecture 2: Limits, one sided limits and vertical asymptotes

Lecture 1: Tangents and velocities.

Lecture 1: Tangents and velocities.

Introduction and welcome to Math 1061/1060.

Introduction and welcome to Math 1061/1060.

Summary and review of Calc 2 course

Summary and review of Calc 2 course

Area under polar curves, arc length of polar curve

Area under polar curves, arc length of polar curve

Area swept out by a Polar curve

Area swept out by a Polar curve

Tangents to polar curves, area under polar curves

Tangents to polar curves, area under polar curves

Sketching the polar curve r(t)=2cos(t)

Sketching the polar curve r(t)=2cos(t)

Sketching the polar curve r(t)=cos(2t)

Sketching the polar curve r(t)=cos(2t)

More polar curves and the slope of a polar curve

More polar curves and the slope of a polar curve