After a very long hiatus, a new section is up in the linear algebra course covering vector combinations and span. There is about a 5 year gap between the publishing dates of video #25 and #26, whoops. Oh well, I'm back at it again with linear algebra and hope to finish off the set this month. Here are the new videos:

• How to determine if one vector is a linear combination of a set of vectors 
• How to determine if one vector in the span of a set of vectors 
• Write a vector as a linear combination of a set of vectors 
• How to determine if a set of vectors are linearly dependent or independent 
• Write a dependence equation for a set of vectors 
• Does a set of vectors span R^n
• What is a subspace
• Find a basis for the span of a set of vectors (either a subspace or a vector space)
• Some thoughts on linear combinations and span​​

The final section in the Structural Analysis course is now complete, it's on the force method. This is a great method for solving one degree statically indeterminate structures. It's an awful way to solve structures that are 2+ degrees indeterminate. This is pretty evident by the one degree example taking under 10 minutes to solve, and the two degree example taking 40 minutes (split into 3 parts). Unfortunately, at some point in your life, you are probably going to be asked to solve a two degree statically indeterminate structure with the force method, and because of that, I slogged my way through example #2.

Force method explained
Force method example #1: one degree indeterminate
Force method example #2: two deg indeterminate (pt 1/3)
Force method example #2: two deg indeterminate (pt 2/3)
Force method example #2: two deg indeterminate (pt 3/3)

A new section of the Structural Analysis course is done! It covers the explanation of the 3 moment equation and three comprehensive example problems:
3 moment equation explained
3 moment equation example #1 (pt 1/3)
3 moment equation example #1 (pt 2/3)
3 moment equation example #1 (pt 3/3) - alternate method
3 moment equation example #2: three span beam (pt 1/3)
3 moment equation example #2: three span beam (pt (2/3)
3 moment equation example #2: three span beam (pt (3/3)
3 moment equation example #3: rigid connection (pt 1/2)
3 moment equation example #3: rigid connection (pt (2/2)

Learn how to solve statically and kinematically indeterminate beams with the slope deflection method with these structural analysis tutorials. These problems are typically pretty long, so the examples are split into 3 parts each:

• Slope deflection method explained
• Slope deflection method example #1 (part 1/3)
  
• Slope deflection method example #1 (part 2/3)
  
• Slope deflection method example #1 (part 3/3)
• Slope deflection method example #2 (part 1/3)
  
• Slope deflection method example #2 (part 2/3)
• Slope deflection method example #2 (part 3/3)​

New structural analysis tutorials are up on the moment area method! Hope you like geometry, because there's lots in this method. Check out the 10 new videos:

• Moment area method explained
• Moment area method example #1
• Moment area method example #2
• Moment area method example #3
• Moment area method example #4
• Moment area method by parts explained
• Moment area method by parts example #1
• Moment area method by parts example #2
• Non-symmetrical moment area method example
• Find location & magnitude of max deflection

We've got 4 new tutorials up in our structural analysis course on the method of superposition! These lessons go over some statically determinate beam problems, and show how to use the method of superposition while looking up common table values for slope and deflection:

• Method of superposition for beam slope and deflection explained
• Method of superposition example #1: a simply supported beam
• Method of superposition example #2: a cantilever beam
• Method of superposition example #3: with an applied moment

We recently created 53 free Mechanics of Materials tutorials that together form a whole course. The course begins with introducing stress and strain, and then goes on to cover torsion, pure bending, composite materials, beam deflection, energy methods, and columns! There are tons of detailed explanations and worked examples to help you better understand and grasp Mechanics of Materials.

The Mechanics of Materials course section on Column Buckling is now complete! 7 new tutorials that cover buckling of centrically  loaded columns with various end conditions are covered:​

• Columns and buckling introduced
• Effective length of columns with different end conditions
• Column buckling example #1: both ends pinned
• Column buckling example #2: both ends fixed 
• Column buckling example #3: one fixed end, one free end
• Column buckling example #4:  one fixed end, one pinned end
• Column buckling example #5: with bracing