Канал: XGAL: David Sobral's Astronomy Outreach & Science

15.5.4 - State-of-the-art Hydrodynamical simulations and examples, summary

15.5.4 - State-of-the-art Hydrodynamical simulations and examples, summary

15.5 - N-body simulations, semi-analytical models and hydro-dynamical simulations

15.5 - N-body simulations, semi-analytical models and hydro-dynamical simulations

15.3-15.4 - How to make a simulation, why is dark matter cold, why we need feedback and how it works

15.3-15.4 - How to make a simulation, why is dark matter cold, why we need feedback and how it works

15.1-15.2 - The basic recipe to make a Universe and the many challenges to simulations

15.1-15.2 - The basic recipe to make a Universe and the many challenges to simulations

15 - Simulating the Universe in super-computers: introduction and overview

15 - Simulating the Universe in super-computers: introduction and overview

14.8 - Summary of Section 14

14.8 - Summary of Section 14

14.6-14.7 - Active Galactic Nuclei (AGN), co-evolution with galaxies and environmental effects

14.6-14.7 - Active Galactic Nuclei (AGN), co-evolution with galaxies and environmental effects

14.4-14.5 - Dark matter and galaxy formation, a galaxy as an almost living thing and SN feedback

14.4-14.5 - Dark matter and galaxy formation, a galaxy as an almost living thing and SN feedback

14.3 - Stellar mass assembly: predicted vs observed

14.3 - Stellar mass assembly: predicted vs observed

14.2 - Star formation rate function and the star formation rate density across time

14.2 - Star formation rate function and the star formation rate density across time

14.1 - What we can measure for distant galaxies and what we have learnt about them so far

14.1 - What we can measure for distant galaxies and what we have learnt about them so far

14 - Galaxy formation and evolution: introduction and overview

14 - Galaxy formation and evolution: introduction and overview

13.6 - Hunting galaxies in the early Universe, techniques, re-ionisation, first stars, CR7 & summary

13.6 - Hunting galaxies in the early Universe, techniques, re-ionisation, first stars, CR7 & summary

13.5 - Galaxy formation and evolution accross time: the very first stages

13.5 - Galaxy formation and evolution accross time: the very first stages

13.4 - The tools II: luminosity functions - counting galaxies and the Schechter function

13.4 - The tools II: luminosity functions - counting galaxies and the Schechter function

13.3 - The tools I: IMF, stars & building blocks + practical examples and applications

13.3 - The tools I: IMF, stars & building blocks + practical examples and applications

13.2 - Stellar spectral types, their lifetimes and consequences for galaxies

13.2 - Stellar spectral types, their lifetimes and consequences for galaxies

13.1 - What do we need to understand a galaxy and its evolution?

13.1 - What do we need to understand a galaxy and its evolution?

13 - Galaxy formation and evolution: tools and the first billion years - introduction and overview

13 - Galaxy formation and evolution: tools and the first billion years - introduction and overview

12.6 - Our local Universe and a summary of Section 12

12.6 - Our local Universe and a summary of Section 12

12.5 - Different types of galaxies according to morphology and mass: Hubble's classification scheme

12.5 - Different types of galaxies according to morphology and mass: Hubble's classification scheme

12.4 - Galaxies and what sets them apart from star clusters

12.4 - Galaxies and what sets them apart from star clusters

12.3 - Other galaxies, determining extra-galactic distances, the Hubble-Lemaitre law and redshift

12.3 - Other galaxies, determining extra-galactic distances, the Hubble-Lemaitre law and redshift

12.2 - Our Galaxy: the Milky Way, where we stand, its components, the galactic centre and the SMBH

12.2 - Our Galaxy: the Milky Way, where we stand, its components, the galactic centre and the SMBH

12-12.1 - Introduction to galaxies, our Galaxy and where are we in the Galaxy

12-12.1 - Introduction to galaxies, our Galaxy and where are we in the Galaxy

11.5 - Drake's equation, reaching out and looking for aliens + Section Summary

11.5 - Drake's equation, reaching out and looking for aliens + Section Summary

11.4 - Results from Extra-solar planet studies in the 2020s

11.4 - Results from Extra-solar planet studies in the 2020s

11.3 - A brief history of extra-solar planet discoveries and main revolutions

11.3 - A brief history of extra-solar planet discoveries and main revolutions

11.2.5-11.2.6 - Transit detections (photometry), how they work, an example and combining w/ Doppler

11.2.5-11.2.6 - Transit detections (photometry), how they work, an example and combining w/ Doppler

11.2.4 - Radial velocities, how it works, an example and the best instruments

11.2.4 - Radial velocities, how it works, an example and the best instruments

11.1-11.2.3 - Introduction, methods to detect extra-solar planets and the first 3 methods

11.1-11.2.3 - Introduction, methods to detect extra-solar planets and the first 3 methods

Section 11 - Extrasolar planets - Introduction and overview

Section 11 - Extrasolar planets - Introduction and overview

10.4 - Definition of planet, dwarf planet, the full extent of the Solar System and Section Summary

10.4 - Definition of planet, dwarf planet, the full extent of the Solar System and Section Summary

10.3 - The Solar system now and its inventory

10.3 - The Solar system now and its inventory

10.2 - The star of the solar system: the Sun

10.2 - The star of the solar system: the Sun

10-10.1 - Formation of the Solar System

10-10.1 - Formation of the Solar System

9.9 - Consequences for element generation, spread and our cosmic origins + Summary of Section 9

9.9 - Consequences for element generation, spread and our cosmic origins + Summary of Section 9

9.8 - Finding and understanding the final evolutionary stages of a star and its destiny: post-MS

9.8 - Finding and understanding the final evolutionary stages of a star and its destiny: post-MS

9.7 - Evolution with HR diagrams: HR diagrams of star clusters

9.7 - Evolution with HR diagrams: HR diagrams of star clusters

9.6 - The Initial Mass Function, general examples and concrete examples + what it means for stars

9.6 - The Initial Mass Function, general examples and concrete examples + what it means for stars

9.5 - High and low limits to stellar mass

9.5 - High and low limits to stellar mass

9.4 - The virial theorem, the condition for a cloud to collapse and the Jeans mass

9.4 - The virial theorem, the condition for a cloud to collapse and the Jeans mass

9.3 - How and where do stars form? How complex is star formation?

9.3 - How and where do stars form? How complex is star formation?

9-9.2 - Star formation, the IMF and stellar evolution, luminosity function, IMF

9-9.2 - Star formation, the IMF and stellar evolution, luminosity function, IMF

8.4.5-8.4.6 - Measuring Stellar Mass with binary star systems and the M-L relation

8.4.5-8.4.6 - Measuring Stellar Mass with binary star systems and the M-L relation

8.6-8.7 - Stellar lifetime: main sequence lifetime (H burning) + Gravity-Radiation pressure

8.6-8.7 - Stellar lifetime: main sequence lifetime (H burning) + Gravity-Radiation pressure

8.4-8.4.4 - HR diagrams, how to construct, interpret and name the locations within them

8.4-8.4.4 - HR diagrams, how to construct, interpret and name the locations within them

8.3.4-8.3.6 - How to classify stars, Balmer lines, the modern Harvard system and how to do it

8.3.4-8.3.6 - How to classify stars, Balmer lines, the modern Harvard system and how to do it

8.3-8.3.3 - How to classify stars, Balmer lines, the modern Harvard system and how to do it

8.3-8.3.3 - How to classify stars, Balmer lines, the modern Harvard system and how to do it

8.2 - Measuring stars without going there: the tools we will need, how they are used and solar units

8.2 - Measuring stars without going there: the tools we will need, how they are used and solar units

8-8.1 - What is a star and what we can use to characterise them

8-8.1 - What is a star and what we can use to characterise them

7.3.5-7.3.6 - Other data-sets in Astronomy, Spectroscopy, fibers, 3D spectroscopy and Summary

7.3.5-7.3.6 - Other data-sets in Astronomy, Spectroscopy, fibers, 3D spectroscopy and Summary

7.3.3-7.3.4 - Towards science-graded quantities, ZPs and a practical example

7.3.3-7.3.4 - Towards science-graded quantities, ZPs and a practical example

7.3-7.3.2- Data reduction: from raw to science-grade data, data reduction & a practical example

7.3-7.3.2- Data reduction: from raw to science-grade data, data reduction & a practical example

7.2.3-7.2.5 - Example of an optical CCD, red-sensitive CCDs, NIR Detectors and examples

7.2.3-7.2.5 - Example of an optical CCD, red-sensitive CCDs, NIR Detectors and examples

7.2-7.2.2 - CCDs, how they work and why are they so good?

7.2-7.2.2 - CCDs, how they work and why are they so good?

7-7.1 - Modern Instrumentation and data in Astronomy: how to go from EM radiation to Science

7-7.1 - Modern Instrumentation and data in Astronomy: how to go from EM radiation to Science

6.7 - Radio telescopes and Summary of Section 6

6.7 - Radio telescopes and Summary of Section 6

6.6 - Improving optics with modern technologies: active and adaptive optics

6.6 - Improving optics with modern technologies: active and adaptive optics

6.5 - A typical Reflecting Telescope

6.5 - A typical Reflecting Telescope

6.5 Extra: Observing experiences from Mauna Kea to La Palma including from your colleagues

6.5 Extra: Observing experiences from Mauna Kea to La Palma including from your colleagues

6.4 - Telescope types, limitations, the Hubble Space Telescope and JWST

6.4 - Telescope types, limitations, the Hubble Space Telescope and JWST

6.3.5 - 6.3.7 - Theoretical Resolution vs real resolution: seeing + focal length

6.3.5 - 6.3.7 - Theoretical Resolution vs real resolution: seeing + focal length

5.3.5 - Blackbodies & stars: how to obtain their luminosity and radius

5.3.5 - Blackbodies & stars: how to obtain their luminosity and radius

6.3.3-6.3.4 - Applications: collecting power and (theoretical) resolution + comparison

6.3.3-6.3.4 - Applications: collecting power and (theoretical) resolution + comparison

6.3.1-6.3.2 - Understanding the resolution of a telescope and why it matters

6.3.1-6.3.2 - Understanding the resolution of a telescope and why it matters

6.3 - Radiation Collecting Power & Resolution + examples for resolution capabilities

6.3 - Radiation Collecting Power & Resolution + examples for resolution capabilities

6.2 - What is a Telescope? A basic (and old-style) telescope: a lens

6.2 - What is a Telescope? A basic (and old-style) telescope: a lens

6.1 - Where on Earth can we find the best telescopes?

6.1 - Where on Earth can we find the best telescopes?

Section 6 - Telescopes: properties, limitations, techniques - introduction and overview

Section 6 - Telescopes: properties, limitations, techniques - introduction and overview

Summary of Section 5 Part II

Summary of Section 5 Part II

5.8 - The widths of lines and the Physics behind them

5.8 - The widths of lines and the Physics behind them

5.7 - Doppler Effect: measuring motions and dynamics + a few examples

5.7 - Doppler Effect: measuring motions and dynamics + a few examples

5.6.5-5.6.6 - Meet our Sun and Kirchoff's three rules of spectroscopic analysis

5.6.5-5.6.6 - Meet our Sun and Kirchoff's three rules of spectroscopic analysis

5.6.4-5.6.5 - Application of the Boltzmann+Saha equations to Hydrogen (Balmer lines) + Helium

5.6.4-5.6.5 - Application of the Boltzmann+Saha equations to Hydrogen (Balmer lines) + Helium

5.6-5.6.3 - Excitation (absorption) and de-excitation, Boltzmann equation & ionisation (Saha)

5.6-5.6.3 - Excitation (absorption) and de-excitation, Boltzmann equation & ionisation (Saha)

5.5.3 - The Bohr Atom: we can define groups of transitions

5.5.3 - The Bohr Atom: we can define groups of transitions

5.5.1 - 5.5.2 - Hydrogen atom and the Bohr Atom model for Hydrogen and other systems

5.5.1 - 5.5.2 - Hydrogen atom and the Bohr Atom model for Hydrogen and other systems

5.5 - Introduction to part II, discrete line spectra & spectroscopy: the basics

5.5 - Introduction to part II, discrete line spectra & spectroscopy: the basics

5.4 - Other types of radiation and Summary of Part I

5.4 - Other types of radiation and Summary of Part I

5.3.7-5.3.8 - We live in an almost perfect blackbody + continuum radio emission

5.3.7-5.3.8 - We live in an almost perfect blackbody + continuum radio emission

5.3.6 - Sirius as an example to apply our Astro super-powers

5.3.6 - Sirius as an example to apply our Astro super-powers

5.3.5 - Blackbodies & stars: how to obtain their luminosity and radius

5.3.5 - Blackbodies & stars: how to obtain their luminosity and radius

5.3.4 - Blackbody radiation in Astrophysics: stars, colours and usefulness

5.3.4 - Blackbody radiation in Astrophysics: stars, colours and usefulness

5.3-5.5.3 - Blackbodies, Wien's law and some examples of application

5.3-5.5.3 - Blackbodies, Wien's law and some examples of application

5.2 - Atmospheric Absorption: what can we see?

5.2 - Atmospheric Absorption: what can we see?

5.1 - What can we detect and how energetic are the different photons?

5.1 - What can we detect and how energetic are the different photons?

Section 5 - Part I: Introduction

Section 5 - Part I: Introduction

4.3.7-4.3.9 - Absolute magnitude, distance modulus and an application example

4.3.7-4.3.9 - Absolute magnitude, distance modulus and an application example

4.3.6 - Colours in Astronomy: magnitude differences

4.3.6 - Colours in Astronomy: magnitude differences

4.3.3-4.3.5 - How to calculate magnitudes, magnitudes in different filters, examples

4.3.3-4.3.5 - How to calculate magnitudes, magnitudes in different filters, examples

4.3.1-4.3.2 - Magnitudes, and the modern unbound definition including the Vega system

4.3.1-4.3.2 - Magnitudes, and the modern unbound definition including the Vega system

4.2 - Energy in Astrophysics: luminosity, flux, flux density and an example

4.2 - Energy in Astrophysics: luminosity, flux, flux density and an example

4.1 - How to map the skies: Right Ascension and Declination

4.1 - How to map the skies: Right Ascension and Declination

Section 4: Introduction and overview

Section 4: Introduction and overview

3.11 - Interplanetary transfers: sending spacecraft up and getting there with some smart moves

3.11 - Interplanetary transfers: sending spacecraft up and getting there with some smart moves

3.10 - Solar day, sidereal day and geostationary satellites

3.10 - Solar day, sidereal day and geostationary satellites

3.9 - Gravity, orbits, escape velocities and physical insight into orbits

3.9 - Gravity, orbits, escape velocities and physical insight into orbits

3.8 - Centre of Mass, generalising Kepler's laws and a practical example

3.8 - Centre of Mass, generalising Kepler's laws and a practical example

3.7 - Newton's law of gravity from Kepler's 3rd law and vice-versa

3.7 - Newton's law of gravity from Kepler's 3rd law and vice-versa

3.5-3.6 - Newton's laws, Connecting position and geometry with Physics and applications

3.5-3.6 - Newton's laws, Connecting position and geometry with Physics and applications

3.4 - Periapsis and apoapsis: highest and lowest speed points - how to calculate them

3.4 - Periapsis and apoapsis: highest and lowest speed points - how to calculate them

3.3 - Kepler's three laws of planetary orbital motion

3.3 - Kepler's three laws of planetary orbital motion

3.2 - Understanding ellipses to understand Elliptical Orbits

3.2 - Understanding ellipses to understand Elliptical Orbits

3.1 - Projectiles in a flat space on Earth (with demonstrations)

3.1 - Projectiles in a flat space on Earth (with demonstrations)

Section 3 - Celestial mechanics, orbits and orbital phenomena: introduction

Section 3 - Celestial mechanics, orbits and orbital phenomena: introduction

2.3.8-2.5 - Cosmic Insignificance update, the Astronomy Distance ladder and test your understanding

2.3.8-2.5 - Cosmic Insignificance update, the Astronomy Distance ladder and test your understanding

2.3.7-2.3.8 - Measuring larger distances: Bessel and Parallax angles + distances

2.3.7-2.3.8 - Measuring larger distances: Bessel and Parallax angles + distances

2.3.5-2.3.6 - Greek Astronomy, the end of the geocentric view and the modern way to calculate 1 AU

2.3.5-2.3.6 - Greek Astronomy, the end of the geocentric view and the modern way to calculate 1 AU

2.3.3-2.3.4 - Moon-Earth relative sizes and Moon-Sun-Earth relative distances: 1 AU

2.3.3-2.3.4 - Moon-Earth relative sizes and Moon-Sun-Earth relative distances: 1 AU

2.2-2.3.2 - What is Astronomy and how large is the (non-flat) Earth: measuring distances

2.2-2.3.2 - What is Astronomy and how large is the (non-flat) Earth: measuring distances

2.1 - Introdution to Astronomy & Astrophysics and why study A&A

2.1 - Introdution to Astronomy & Astrophysics and why study A&A

1.5-1.8 - How will the module work?

1.5-1.8 - How will the module work?

1.10-1.12 - What will come next in other Astro modules and textbooks to learn even more

1.10-1.12 - What will come next in other Astro modules and textbooks to learn even more

1.3 - Course overview & what we will cover

1.3 - Course overview & what we will cover

1.1 - Intro & Meet your lecturer's research

1.1 - Intro & Meet your lecturer's research

1 - Preamble to PHYS263: Welcome to PHYS263

1 - Preamble to PHYS263: Welcome to PHYS263

16.6 - The end of PHYS263 and a final summary/message

16.6 - The end of PHYS263 and a final summary/message

Time to think and answer some quick questions

Time to think and answer some quick questions

16.5 - What are the big unanswered questions?

16.5 - What are the big unanswered questions?

16.3-16.4 - How to make breakthroughs, how science works and what is on the horizon

16.3-16.4 - How to make breakthroughs, how science works and what is on the horizon

16.2 - Unknown unknowns in history: the dark sector and how dark energy came about - observations

16.2 - Unknown unknowns in history: the dark sector and how dark energy came about - observations

16-16.1 - Overview, the Universe and future discoveries: known unknowns

16-16.1 - Overview, the Universe and future discoveries: known unknowns

10.7 - The gradient vector: useful properties & the end of PHYS111

10.7 - The gradient vector: useful properties & the end of PHYS111

10.6 - Directional derivatives: compact notation, the graf vector & applying it

10.6 - Directional derivatives: compact notation, the graf vector & applying it

10.5 - Directional derivatives: examples of how to calculate them

10.5 - Directional derivatives: examples of how to calculate them

10.4 - Directional derivatives and partial derivatives: deriving a simple expression

10.4 - Directional derivatives and partial derivatives: deriving a simple expression

10.3.2 - Directional derivatives: definition

10.3.2 - Directional derivatives: definition

10.3.1 - Directional derivatives: introduction and definition

10.3.1 - Directional derivatives: introduction and definition

10.2 - Application of tangent planes: linear approximation

10.2 - Application of tangent planes: linear approximation

10.1 - Finding tangent planes: a practical example and visualisation

10.1 - Finding tangent planes: a practical example and visualisation

10.1 - Introduction, tangent planes and how to obtain them

10.1 - Introduction, tangent planes and how to obtain them

9.6 - How to transform between 3D Cartesian to 3D Spherical + Ukulele gets spooky for Halloween

9.6 - How to transform between 3D Cartesian to 3D Spherical + Ukulele gets spooky for Halloween

8.9 - Total differential and total differentiation

8.9 - Total differential and total differentiation

9.4-9.5 - 3D Coordinates and coordinate transformations

9.4-9.5 - 3D Coordinates and coordinate transformations

8.8 - Classification of stationary points

8.8 - Classification of stationary points

9.2-9.3 - Coordinate transformations between polar and Cartesian and vice-versa

9.2-9.3 - Coordinate transformations between polar and Cartesian and vice-versa

8.7 - Second order partial derivatives: Examples

8.7 - Second order partial derivatives: Examples

8.7 - Higher order partial derivatives

8.7 - Higher order partial derivatives

9.1 - Polar coordinates and Cartesian coordinates: 2D - the basics

9.1 - Polar coordinates and Cartesian coordinates: 2D - the basics

8.6 - Interpretation and application of partial derivatives: stationary points

8.6 - Interpretation and application of partial derivatives: stationary points

8.4-8.5 - Partial differentiation and chain rule + notation for higher order derivatives

8.4-8.5 - Partial differentiation and chain rule + notation for higher order derivatives

7.4.3-7.4.5 - Cylinders, Hyperboloids and Paraboloids

7.4.3-7.4.5 - Cylinders, Hyperboloids and Paraboloids

8.3 - Partial Implicit Differentiation and examples

8.3 - Partial Implicit Differentiation and examples

8.2 - Partial derivatives: practical examples

8.2 - Partial derivatives: practical examples

7.4.2 - Graphs of functions of two variables: cone and how to use topcat with detailed instructions

7.4.2 - Graphs of functions of two variables: cone and how to use topcat with detailed instructions

8.1 - Partial differentiation: formal definition and notation

8.1 - Partial differentiation: formal definition and notation

8 - Partial Differentiation: introduction

8 - Partial Differentiation: introduction

7.4 - Graphs of functions of two variables: surfaces. 7.4.1 - Ellipsoid and how to plot on topcat

7.4 - Graphs of functions of two variables: surfaces. 7.4.1 - Ellipsoid and how to plot on topcat

6.7-6.8 - Higher order derivatives and practical applications

6.7-6.8 - Higher order derivatives and practical applications

7.3 - Limits for functions of more than one variable: showing they do not exist

7.3 - Limits for functions of more than one variable: showing they do not exist

6.6 - Second order implicit differentiation

6.6 - Second order implicit differentiation

7.2 - Limits of functions that depend on more than one variable

7.2 - Limits of functions that depend on more than one variable

6.5 - Second order parametric differentiation and how to conduct it

6.5 - Second order parametric differentiation and how to conduct it

7-7.1 Functions of more than one variable: notation and definitions

7-7.1 Functions of more than one variable: notation and definitions

6.4 - Sketching functions: the basics and good practices (and famous bad practices)

6.4 - Sketching functions: the basics and good practices (and famous bad practices)

6.2-6.3 - Second order derivative and stationary points + an example

6.2-6.3 - Second order derivative and stationary points + an example

6-6.1 - Extraction of small changes and stationary points

6-6.1 - Extraction of small changes and stationary points

5.10 - Parametric differentiation, how to use it and the final remarks for Section 5

5.10 - Parametric differentiation, how to use it and the final remarks for Section 5

5.9 - Inversion rule and a simple example

5.9 - Inversion rule and a simple example

5.8 - Implicit differentiation: 2 practical solved examples

5.8 - Implicit differentiation: 2 practical solved examples

5.8 - Implicit differentiation: implicit functions and how to carry out implicit differentiation

5.8 - Implicit differentiation: implicit functions and how to carry out implicit differentiation

5.7 - Logarithmic differentiation: how it works and how to apply it

5.7 - Logarithmic differentiation: how it works and how to apply it

5.6.3-5.6.5 - How to use chain rule and a practical example

5.6.3-5.6.5 - How to use chain rule and a practical example

5.6-5.6.2 - Chain rule, functions of functions and identifying composite functions

5.6-5.6.2 - Chain rule, functions of functions and identifying composite functions

5.5.5 - Hyperbolic functions: their interpretation and physical application vs trig. functions

5.5.5 - Hyperbolic functions: their interpretation and physical application vs trig. functions

5.5.2-5.5.4 - Hyperbolic functions: how they look like, how to invert them and differentiate them

5.5.2-5.5.4 - Hyperbolic functions: how they look like, how to invert them and differentiate them

5.5 - Hyperbolic functions: definition, similarities to trig functions and a bit of history

5.5 - Hyperbolic functions: definition, similarities to trig functions and a bit of history

5.4.1 - Differentiating cos(x) from first principles (featuring new PHYS111 magic tricks)

5.4.1 - Differentiating cos(x) from first principles (featuring new PHYS111 magic tricks)

5.4 - Differentiation of trigonometric functions: sin(x) and cos(x)

5.4 - Differentiation of trigonometric functions: sin(x) and cos(x)

5.3.2 - Derivatives of logarithmic functions of base e, 10 and any base

5.3.2 - Derivatives of logarithmic functions of base e, 10 and any base

5.3 and 5.3.1 - The exponential with base e and other bases: how to differentiate them

5.3 and 5.3.1 - The exponential with base e and other bases: how to differentiate them

5.2.7 - The reciprocal rule and how to apply it with a simple example

5.2.7 - The reciprocal rule and how to apply it with a simple example

5.2.6 - Using the quotient rule: 2 different examples

5.2.6 - Using the quotient rule: 2 different examples

5.2.6 - Quotient rule: introduction and full proof/demonstration

5.2.6 - Quotient rule: introduction and full proof/demonstration

5.2.5 - Product rule: proof from first principles

5.2.5 - Product rule: proof from first principles

5.2.5 - The product rule: introduction

5.2.5 - The product rule: introduction

5.2.4: The constant multiple rule: demonstration/proof

5.2.4: The constant multiple rule: demonstration/proof

5.2.3 - Application of the power rule, sum rule and the derivative of lnx

5.2.3 - Application of the power rule, sum rule and the derivative of lnx

5.2.3 - The sum rule and its demonstration from first principles

5.2.3 - The sum rule and its demonstration from first principles

5.2 - Demonstrations of differentiation rules: 5.2.1 - x^n

5.2 - Demonstrations of differentiation rules: 5.2.1 - x^n

5.1 - Derivatives of basic functions you should know/recap: rules of differentiation

5.1 - Derivatives of basic functions you should know/recap: rules of differentiation

4.5 - Differentiating from first principles: another example of how to do it

4.5 - Differentiating from first principles: another example of how to do it

4.4 - Differentiating from first principles: a simple example of how to do it in practice

4.4 - Differentiating from first principles: a simple example of how to do it in practice

4.3 - The definition of derivative from first principles and different notations

4.3 - The definition of derivative from first principles and different notations

3.8 - Special limits: cox-1/x when x tends to 0 and using many methods at the same time

3.8 - Special limits: cox-1/x when x tends to 0 and using many methods at the same time

3.8 - Special limits: sinx/x when x tends to 0 using the squeeze theorem

3.8 - Special limits: sinx/x when x tends to 0 using the squeeze theorem

3.7.6 - The squeeze theorem (#6), definition and a practical example of how to use it

3.7.6 - The squeeze theorem (#6), definition and a practical example of how to use it

Most important tip(s) for solving limits and final remarks for Section 3

Most important tip(s) for solving limits and final remarks for Section 3

3.7.3-3.7.5 - Practical examples of Methods #3 (highest power), #4 (conjugate) and #5 (re-express)

3.7.3-3.7.5 - Practical examples of Methods #3 (highest power), #4 (conjugate) and #5 (re-express)

3.7.1-3.7.2 - Practical examples of Methods #1 (sub-in) and #2 (factorise and cancel) to take limits

3.7.1-3.7.2 - Practical examples of Methods #1 (sub-in) and #2 (factorise and cancel) to take limits

3.6 - How to calculate limits: the basics and limits worth remembering

3.6 - How to calculate limits: the basics and limits worth remembering

3.7 - How to calculate limits: David's list

3.7 - How to calculate limits: David's list

3.5 - Definition of a continuous function and how to find if a function is continuous

3.5 - Definition of a continuous function and how to find if a function is continuous

3.4 - Properties of limits: sum, difference, product and quotient

3.4 - Properties of limits: sum, difference, product and quotient

3.3 - Limits: numerical solutions, interpretation and first analytical solutions

3.3 - Limits: numerical solutions, interpretation and first analytical solutions

3.2 - Definition of limit of a function, including notation

3.2 - Definition of limit of a function, including notation

3.1 - Limits, continuity, functions, values and the concept of limit

3.1 - Limits, continuity, functions, values and the concept of limit

2 - Before you start PHYS111: background material, exponential and log properties

2 - Before you start PHYS111: background material, exponential and log properties

PHYS111: David's handwriting, notation, tips - what you need to know before starting

PHYS111: David's handwriting, notation, tips - what you need to know before starting