Question: I am an assistant professor preparing a 5 lecture series 'introduction to programming'. The target audience are first year engineering undergrads - from a mix of mechanical, electrical, electronic, telecomms and civil engineering majors. Some of these students will never have programmed before. We will use Matlab.

I am expecting that many of these students will never have coded before and almost all will not have seen Matlab before. They will need Matlab in all subsequent years of their degree.

Given the extremely limited time for this course, how can I give best bang for their buck, without it being too dry?

Is there something cool we could work towards creating over the 5 weeks?

More info: There are 5 x 4 hours sessions. Classroom cannot be flipped as there will be 50+ students.

Editing here to thank everyone who has taken the time and effort to give extremely helpful detailed replies. I appreciate it guys.

Answer: 
I studied and TA'd electrical engineering and computer science in college and graduate school. You have a unique opportunity versus most introductory programming languages that use general languages like java or python because Matlab, which is a portmanteau for "Matrix Laboratory", is a language that is meant to be very interactive, intuitive to mathematically-savvy students, and easy to pick up and includes the constructs of 1-d vectors, 2-d matrices, and n-dimensional tensors as first-order data structures (I know you know all this, but I'm stating it for other readers who may be less familiar with this language). 

Most of your students will have a background in linear algebra and matrix notation and use in mathematics from their courses in all of the state engineering disciplines. Therefore, you can focus less on teaching fundamental of data types, data structure, control flow logic, hierarchy and namespaces, and instead build up from intuitive Matrix-like mathematical operations that naturally have sequences of repeating steps with exit conditions.

* 1st-week of introduction to typical matrix problems in the engineering sciences, and walking them through building the simple scripts to execute those.
* 2nd-week add Matlab function wrapper per file concept as an introduction to hierarchy and namespace (informally, this is how it works, not focusing on the deeper theoretical aspects) of scoping local variables in input/return values.
* 3rd-week show how there are lots of the simple operations (like matrix multiples, inverting matrices, DFT and FFT, that are prebuilt library functions, and study some tradeoffs on choosing them and how they deal with padding, non-invertible data sets, etc.)
* 4th and 5th-week focus on a large programming project that does something interesting with larger data and doing something iterative like gradient descent on a simple pattern match like regression, or simple cases of convex cost function search, or even backpropagation in a 3-layer neural network. 

Pre-build much of the base and helper code and have them learn how to use what they learned so far to code the inner loop of the iterations. Definitely give them the code that they can easily tweek so they get some experience generating graphics to demonstrate (and debug) the optimization iteration sequence.
I don't know Matlab, so this answer is mostly about generic programming concepts.

The core of programming is problem solving, so I would think the best use of the limited time you have available would be to focus on computational thinking and providing them with the techniques they will need to be able to think their way around a problem sufficiently to be able to express a solution in code.

Matlab is of course designed specifically for solving problems rooted in various Scientific, Mathematical and Engineering domains, so ideally, any example programs you use for demonstration and explaining the concepts should be as close as possible to the types of problems that the students will be solving by themselves. 

One of the pre-requisites for being able to write the code to solve a problem is to have gained a clear understanding of the problem being solved, so it would be useful to stick to problems which the learners would already be able to understand on-paper.

It could be useful to look at the Harvard CS50 syllabus as a starting point, it places a heavy emphasis on developing computational thinking skills by challenging learners to solve typical programming problems: <https://cs50.harvard.edu/ap/syllabus/>

Many of the concepts covered in the first 3-4 lessons of the CS50 syllabus are universally applicable to programming in any language, and David J Malan's delivery of these concepts in his lectures seems to go down very well with his students. 

A number of other specific techniques which I believe would be useful:

* Problem decomposition, illustrated by describing a complex problem, analysing it and dividing into sub-problems.
* Steps to solving a problem by starting with example/test inputs, describing the steps, and reaching a result 'by-hand'.
* Pattern recognition and using generalisation to describe a solution using pseudocode, then translation into a runnable program
* Using the debugger to set breakpoints, inspect variables and step through code to find/fix errors.

Terminology, as well as the 'grammar' of the language is of course important too - there's a lot of jargon to to absorb in a very limited space of time. 

Newcomers frequently find themselves spending a great deal of time attempting to decypher syntax errors, so some of the most important terminology for them to understand will be the words/phrases which frequently appear in the Matlab error frame - for example, misuse of particular symbols/operators, or incorrect use of particular data types. 

Perhaps finally, make sure to include frequent reminders that they can (and should) be making extensive use of Google and StackOverflow to find out what the syntax errors and other jargon means as well.