About Engineer4Free
Engineer4Free is a tutorial site where anyone can learn university level engineering for free. Engineer4Free has made hundreds of YouTube tutorials and organized them into several courses ranging from Calculus to Project Management to Structural Analysis. Whether you're cramming at 3AM, reviewing for the FE exam, or just life-long-learning, you've come to the right place.
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What People Are Saying
IT'S SO OBVIOUS NOW. This must be what an epiphany feels like.
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Great video, I got the same kind of question in my examination and I nailed it.
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Thank You Patreon Supporters
Thank you to ALL of my Patreon supporters. Your contributions enable me to keep focusing on making new tutorials that all engineering students around the word can benefit from. Big shout out to the following individuals:
Aaron Barraso, Abasifreke David, Abeeralthani Nasser, Adity Adity, Adnan Bonsu, Adriaan Badenhorst, Afnan Asif, Ahmad Shah, AJ Durnil, Al Alshahrani, Alejandro Gallardo, Alex Brindle, Alexander Marsh, Am Tjabadi, Amine Sidi-Boumedine, Anabel Jacques, Andrew Edman, Andrew Scholes, Angel Rodriguez, Angel Rojas, Anon, Anthony, Anton Kröss, Anvar Kunanbayev, Arian Davis, Arianna Vazquez, Armando, Áron Milyen, Ashley Richley, Audrey Afrifa, August Engelke, Augustine Uyah, Autumn Moos, Austin, Avery Hodell, Barbara Charalambidi, Bas, Bemmy Hai, Ben Carr, Benjamin Seow, Berta, Bhav Chatha, Bishesh Malla, Boba the Fish, Bonner Feller, Brady Christensen, Brendan Beall, Brendan Courtney, Brendan Lamothe, Brian Geary, Bomber24, Caden Graphman, Cameron Wayne Huff, Carter Nolan, Casey Ellyson, Celeste Ramseyer, Cesar Perez, Charlie, Charles Harres, Charles Ondoy, Charlie F, Chaza Kazem, Chimeka, Chloe, Chris Patel, Claire Arnold, Clint C Ross, Clinton, Colin Goegle, Cyndy Y Zhu, Dagmawi Berhane, Dakota Streck, Dan G, Daniel Cerrada, Daniel Georgioff, Daniel Ribero, Daniga, Darryn Medhurst, David Bowles, David G Allsebrook, David Keith, DD, Denzel, Devon, Dominic Myrin-O'Dell, Doris Wagner, Dresser MTB, Dylan Keats, Dylan Mic, Eb, Edgar Berges, Eileen Hammer, Elizabeth Shepard, Elona Ganchenko, Emelia Boyer, Emily Lane, Emily Stamos, Emrah, Enache, Erixs Reyes, Ethan Coorey, Ethan Prescott, Evan Haukaas, Evan Thapa, Fahad Albanna, Farhan Majid, Fernando Axel Pascacio Cruz, G, Gabriel Alin, Garrett Romanzin, Gavin Lingefelt, George Hutson, Giovanni Arevalo, Greg Peterson, Gustav Pedersen, Gustavo Toolis, Haisem Said, Hannah, hằng khánh, Harrys Jackson, Hayden Claire McCombs, Hayden Feschuk, Haiyley Lutjelusche, Hedi, Henry Hunt, Hijiri, gomathishankarprabhakaran, Huda Kabbani, Huda Zainab, Hunter Soulie, Ian Grant, Ilgar Aziz, Isaac Washington, Isabel Bunn_25, Isabellaa, Isabelll, Isha Huft, Izet Zekiroski, Jaco, Jack Boreham, Jack Boland, Jackson Monroe, James I Countryman, Jakob, Jared Bowen, Jared Gumula, Jarom Foster, Jasmine, Jacob Shuman, Jason, Jason Kim, Jay Venca, Jaxx Brown, Jeaux, Jeremy Bozzo, Jerry, Jesner Pereira, Jess Wood, Jessica Reilly, Jesus Garcia, JJJ, Jimmy Konekeo, Joe Sefchik, Joel Harris, Joey, Joey Moriarity, John Carney, John Burkus, John K, John Moors, John S, John Zambarano, Johnna Verry, Jonah Simminger, Jonas Hanssen, Jonathan Aparicio, Jonathon Rama, Jones Llabres Inso, Jordan, Jordan Vantatenhove, Jorge Cortes, Jorge Guevara, Joseph Marks, Joshua Bernabe, Joshua Keller, Jsnake333, Julian Osario, Jullian Phan, Justin Schwarz, Juvenal Marin Sanchez, Ka C.h, Kade Hagerson, Kaif Rizvi, Katyria Cruz, Kayla S, Keara Kerr, Keltan Kemp, Kevin R, Kevin Roupec, Kevin Parra, Kiowa Campbell, KO, Krishna A, Kuliwa Syakwasia, Kyle, Kyle Haynes, Kyley Fijalkowski, L, Laaiqka Sukaih, Lamar Eastland, LambdaScotch, Lance Wytko, Laszlo, Laura Cardenas, Laura Nicholson, Lauren M, Lauryn Grant, Leah Puchalsky, Leanna Carr, Lee Rodrigue, Lemuel, Liam, Lillie Gillespie, Lindsay, Liz Kelly, LLJMMOOSE, Logan S, Lostingravity.xx, Mackenzie Henderson, Madusanka Thilakarathne, Malcom, Mals Boehle, Manahil Irshad, Marc Martin, Marcus Vela, Mark Zagumennyy, Maria Lessis, Matara Jonathan, Mateusz Garnys, Matúš Kuba-Danaj, Matt, Max Ruane, Melinda Xu, Melody Dan, Max Eiszele, Mia Desouza, Miro Tapio Repo, Michael Jin, Michael Hartman, Miguel Alvarez, Mike Perez, Mit, Mitch Hewitt, Mohammed, Mohamed Awale, Morten Leth, Mouad Sheredi, Nabin Bhattarai, Naome Mash, Nareg Shirajian, Nathalia Peregrino, Nawath Aljaberi, Ness L, Niamh Donohue, Nick Sprague, Nick Wallace-Beach, Nikolaj Munk, Nikoloz Babajanashvili, Noah, Noor, Nyteceya Lewis, Ola Ayeko, Olivia Owens, Ookami, Orren, Otto Nemesvari, Owen Chen Parker Spurlin, Pascal Chitho, Patrick Long, Patrick Riche, Paul Fieldwick, Peter, Poppy Calder, Portera Gian Alfonso Q., Pouya Samandi, Providence Uwimana Rukundo, R, Rachel Thomas, Radu, Raines09k, Rashad, Raymond Cronin, rcan, Renne Eustaquio, Regina ZC, Rezwan Mashid, Rigo Marulanda, Riley Giwoo Jin, Risen Benjamin Perez, Robert, Robert Licup, Roger Bjarke Andersen, Roman Jackson, Ruhie Pareek, Russell Erocido, Ryan Stashko, 少卿 倪, Saisanjith Kakkireni, Salvador Gil, Sam Brooks, Sampson Tandoh, Sarah Mbayi, Saran, Sarah Norberg, Sauce, Sayed Ghalleby, Scott S., Scarlet Dixon, Scott Walker, Se Jun Kim, Sebastian Kenley, Shahram Omary, Shalamar Clarke, Shaun Riach, Shirin Ibesh, Simon Roper, Skar, Stefan Henry, Stephen Pimentel, Steven, Steven Arreola, Steven W., Sulabh Gupta, Sya, Syed Amir Haikal, Syed Musawi, Tasi, Taiwo Babalola, Tawny Denzer, Terrell Jackson, TheKingsReaper, Thomas Andrew Francis, Thomas Schumacher, Timothy Rogers, Tobias V, Trinity Ijoma, Truman Spring, Turiya Moka, Varsha, Vassilis Bakalas, Vaughn Patrick, Veronica McRae, Ranma, Walker Young, Wes Dubroc, Will Hornung, Will Schreiber, William Evans, Xander De Kock, Xander Zhang, Yasir Ali, Yusuke Morita, Zac Davidson, Zack Martin, Zaid Alhawari, Zane King-Williamson, Zoba Don, 7aro Al-Saleh
Aaron Barraso, Abasifreke David, Abeeralthani Nasser, Adity Adity, Adnan Bonsu, Adriaan Badenhorst, Afnan Asif, Ahmad Shah, AJ Durnil, Al Alshahrani, Alejandro Gallardo, Alex Brindle, Alexander Marsh, Am Tjabadi, Amine Sidi-Boumedine, Anabel Jacques, Andrew Edman, Andrew Scholes, Angel Rodriguez, Angel Rojas, Anon, Anthony, Anton Kröss, Anvar Kunanbayev, Arian Davis, Arianna Vazquez, Armando, Áron Milyen, Ashley Richley, Audrey Afrifa, August Engelke, Augustine Uyah, Autumn Moos, Austin, Avery Hodell, Barbara Charalambidi, Bas, Bemmy Hai, Ben Carr, Benjamin Seow, Berta, Bhav Chatha, Bishesh Malla, Boba the Fish, Bonner Feller, Brady Christensen, Brendan Beall, Brendan Courtney, Brendan Lamothe, Brian Geary, Bomber24, Caden Graphman, Cameron Wayne Huff, Carter Nolan, Casey Ellyson, Celeste Ramseyer, Cesar Perez, Charlie, Charles Harres, Charles Ondoy, Charlie F, Chaza Kazem, Chimeka, Chloe, Chris Patel, Claire Arnold, Clint C Ross, Clinton, Colin Goegle, Cyndy Y Zhu, Dagmawi Berhane, Dakota Streck, Dan G, Daniel Cerrada, Daniel Georgioff, Daniel Ribero, Daniga, Darryn Medhurst, David Bowles, David G Allsebrook, David Keith, DD, Denzel, Devon, Dominic Myrin-O'Dell, Doris Wagner, Dresser MTB, Dylan Keats, Dylan Mic, Eb, Edgar Berges, Eileen Hammer, Elizabeth Shepard, Elona Ganchenko, Emelia Boyer, Emily Lane, Emily Stamos, Emrah, Enache, Erixs Reyes, Ethan Coorey, Ethan Prescott, Evan Haukaas, Evan Thapa, Fahad Albanna, Farhan Majid, Fernando Axel Pascacio Cruz, G, Gabriel Alin, Garrett Romanzin, Gavin Lingefelt, George Hutson, Giovanni Arevalo, Greg Peterson, Gustav Pedersen, Gustavo Toolis, Haisem Said, Hannah, hằng khánh, Harrys Jackson, Hayden Claire McCombs, Hayden Feschuk, Haiyley Lutjelusche, Hedi, Henry Hunt, Hijiri, gomathishankarprabhakaran, Huda Kabbani, Huda Zainab, Hunter Soulie, Ian Grant, Ilgar Aziz, Isaac Washington, Isabel Bunn_25, Isabellaa, Isabelll, Isha Huft, Izet Zekiroski, Jaco, Jack Boreham, Jack Boland, Jackson Monroe, James I Countryman, Jakob, Jared Bowen, Jared Gumula, Jarom Foster, Jasmine, Jacob Shuman, Jason, Jason Kim, Jay Venca, Jaxx Brown, Jeaux, Jeremy Bozzo, Jerry, Jesner Pereira, Jess Wood, Jessica Reilly, Jesus Garcia, JJJ, Jimmy Konekeo, Joe Sefchik, Joel Harris, Joey, Joey Moriarity, John Carney, John Burkus, John K, John Moors, John S, John Zambarano, Johnna Verry, Jonah Simminger, Jonas Hanssen, Jonathan Aparicio, Jonathon Rama, Jones Llabres Inso, Jordan, Jordan Vantatenhove, Jorge Cortes, Jorge Guevara, Joseph Marks, Joshua Bernabe, Joshua Keller, Jsnake333, Julian Osario, Jullian Phan, Justin Schwarz, Juvenal Marin Sanchez, Ka C.h, Kade Hagerson, Kaif Rizvi, Katyria Cruz, Kayla S, Keara Kerr, Keltan Kemp, Kevin R, Kevin Roupec, Kevin Parra, Kiowa Campbell, KO, Krishna A, Kuliwa Syakwasia, Kyle, Kyle Haynes, Kyley Fijalkowski, L, Laaiqka Sukaih, Lamar Eastland, LambdaScotch, Lance Wytko, Laszlo, Laura Cardenas, Laura Nicholson, Lauren M, Lauryn Grant, Leah Puchalsky, Leanna Carr, Lee Rodrigue, Lemuel, Liam, Lillie Gillespie, Lindsay, Liz Kelly, LLJMMOOSE, Logan S, Lostingravity.xx, Mackenzie Henderson, Madusanka Thilakarathne, Malcom, Mals Boehle, Manahil Irshad, Marc Martin, Marcus Vela, Mark Zagumennyy, Maria Lessis, Matara Jonathan, Mateusz Garnys, Matúš Kuba-Danaj, Matt, Max Ruane, Melinda Xu, Melody Dan, Max Eiszele, Mia Desouza, Miro Tapio Repo, Michael Jin, Michael Hartman, Miguel Alvarez, Mike Perez, Mit, Mitch Hewitt, Mohammed, Mohamed Awale, Morten Leth, Mouad Sheredi, Nabin Bhattarai, Naome Mash, Nareg Shirajian, Nathalia Peregrino, Nawath Aljaberi, Ness L, Niamh Donohue, Nick Sprague, Nick Wallace-Beach, Nikolaj Munk, Nikoloz Babajanashvili, Noah, Noor, Nyteceya Lewis, Ola Ayeko, Olivia Owens, Ookami, Orren, Otto Nemesvari, Owen Chen Parker Spurlin, Pascal Chitho, Patrick Long, Patrick Riche, Paul Fieldwick, Peter, Poppy Calder, Portera Gian Alfonso Q., Pouya Samandi, Providence Uwimana Rukundo, R, Rachel Thomas, Radu, Raines09k, Rashad, Raymond Cronin, rcan, Renne Eustaquio, Regina ZC, Rezwan Mashid, Rigo Marulanda, Riley Giwoo Jin, Risen Benjamin Perez, Robert, Robert Licup, Roger Bjarke Andersen, Roman Jackson, Ruhie Pareek, Russell Erocido, Ryan Stashko, 少卿 倪, Saisanjith Kakkireni, Salvador Gil, Sam Brooks, Sampson Tandoh, Sarah Mbayi, Saran, Sarah Norberg, Sauce, Sayed Ghalleby, Scott S., Scarlet Dixon, Scott Walker, Se Jun Kim, Sebastian Kenley, Shahram Omary, Shalamar Clarke, Shaun Riach, Shirin Ibesh, Simon Roper, Skar, Stefan Henry, Stephen Pimentel, Steven, Steven Arreola, Steven W., Sulabh Gupta, Sya, Syed Amir Haikal, Syed Musawi, Tasi, Taiwo Babalola, Tawny Denzer, Terrell Jackson, TheKingsReaper, Thomas Andrew Francis, Thomas Schumacher, Timothy Rogers, Tobias V, Trinity Ijoma, Truman Spring, Turiya Moka, Varsha, Vassilis Bakalas, Vaughn Patrick, Veronica McRae, Ranma, Walker Young, Wes Dubroc, Will Hornung, Will Schreiber, William Evans, Xander De Kock, Xander Zhang, Yasir Ali, Yusuke Morita, Zac Davidson, Zack Martin, Zaid Alhawari, Zane King-Williamson, Zoba Don, 7aro Al-Saleh