What is Problem-solving: Definition and 30 Discussions

Problem solving consists of using generic or ad hoc methods in an orderly manner to find solutions to problems. Some of the problem-solving techniques developed and used in philosophy, artificial intelligence, computer science, engineering, mathematics, medicine and societies in general are related to mental problem-solving techniques studied in psychology and cognitive sciences.

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  1. putongren

    Bees and Trains: A distance problem

    This question is from the MIT Courseware. I’m having difficulty finding the general equation to solve the problem (1). d = vt + ut d = (u + v)t t = d/(u + v) (2). d = vt + ut d - vt = ut sub t with d/(u+v) d - (v*d)/(u+v) = (u*d)/(u+v) I’m done with the...
  2. Mardonio

    Enthalpy derivation differential equation

    Good evening, unfortunately I'm pretty lost in this problem. I tried to use the chain rule $$(\frac {\partial H} {\partial v})_P = (\frac {\partial H} {\partial T})_P (\frac {\partial T} {\partial v})_P$$ and using some Maxwell relations but it doesn't work very well. I know that $$T = (\frac...
  3. R

    Solve this Hamiltonian System in Several Ways

    Good evening, unfortunately I can't get to the solution of my task I wrote for the system: ## \frac{dz}{dt} = \nabla_p H ; \\ \frac{dp}{dt} = - \nabla_z H ## Then the solution would be (as ## \nabla_p H = 0) ##: ## \frac{dz}{dt} = 0 \Rightarrow z = const. ## and ## p = zt + p_0 ##. But...
  4. SvenFromSkyrim

    Studying Chemistry or physics - which one is more suitable for self-studying?

    First of all, I realised that asking this on physics forum might give me answers different than I'd get in chemistry message board, or more "neutral" general science forums for that matter, but this site seems to be particularly helpful and active at the same time, so I'll take my chances. In...
  5. chwala

    Solve the given problem involving: ##\tan^{-1} (2x+1)+ \tan^{-1} (2x-1)##

    I let ##\tan θ = 2x+1## and ##\tan β = 2x-1## ##θ + β = \tan^{-1} \left[\dfrac{(2x+1)+(2x-1)}{1- (2x+1)(2x-1)}\right]## ... ##θ + β = \tan^{-1} \left[\dfrac{4x}{1- 2x^2+1}\right]## ##θ + β = \tan^{-1} \left[\dfrac{4x}{2(1-x^2)}\right]## then ##\tan^{-1} \left[\dfrac{4x}{2(1-x^2)}\right]=...
  6. M

    How Did the Author Derive the Perfect Square from the Algebraic Equation?

    Hello, While following problem solution found this $$ 4a^4 + 8 a^3 + 8 a^2 + 4a + 1 = ( 2a (a+1) + 1 )^2 $$ Trying to figure out how did author do it but failed. Anyone?
  7. S

    Exploring the Pros and Cons of Variable-Based Physics Problem-Solving

    Once students reach Physics, no matter students' major fields, they are forced to (just experience where I attended) handle MOST of the setup and algebraic work using only variables, FOR ALL NUMBERS; and then to solve the whole problem or exercise still all in variables. Then, the last thing...
  8. E

    Classical Suggestions for fun problem-solving type books

    I was just looking to see if anyone knew of a book pitched at the pre-university to undergrad level which contains slightly more unconventional Physics/Maths problems, but is not as formal as some of the old warhorses like Irodov. Something similar to what I'm looking for would be Professor...
  9. Adesh

    How to survive with these kinds of curriculum?

    The institute where I'm studying consists of books, problems and exams which seems to me completely senseless. I have been a self-study guy ( actually this was a compulsion, not a desire) so I read some well renowned books like The Feynman Lectures on Physics, Spivak Calculus , Morrison and...
  10. F

    Is a formal, rigorous math education useful in problem solving?

    I'm very curious as to know how a person who pursued a formal, strict and rigorous education in mathematics would fair in comparison with a person who learned applied math by "intuition" (that is without doing any proofs and relying more on the computational part), when confronted with problem...
  11. Adesh

    What is my problem? (Difficulty solving math and physics questions)

    Hello everyone, Physicsforum has always helped me whenever I get into predicament. So this time again I want the help of experienced people. I did a great deal of hard work for understanding the true nature of calculus. I read Newton's original works and I found that his sole purpose of...
  12. Amlan mihir

    What is the probability? Is it independent?

    Homework Statement The Attempt at a Solution ; [/B] I think it is independent event so , the probability would be 0.5 . correct if me i am wrong please.
  13. W

    Studying Is Struggling with Novel Physics Problems Normal for Undergraduate Students?

    Hi all, I am an undergraduate Physics student. I have recently realized that I am extremely bad at solving "new" problems related to the topics I am working on. Trying to do any question that deviates slightly from the norm will cause me to be stuck on that problem for hours, usually to no...
  14. RoboNerd

    Figuring out how to approach capacitor problem

    Homework Statement Homework Equations C = q / voltage The Attempt at a Solution OK. [/B] By Kirchoff's Voltage Law, we have: EMF - ( q / Capacitance)x - (q/Capacitance)y = 0 Now. I know that having the dielectric increases the capacitance of X, so the voltage drop across it is smaller...
  15. Gopal Mailpalli

    Examples of Creative Problem-Solving

    Can you list few examples.
  16. O

    MHB Linear algebra problem-solving

    Construct a linear system determined by four numbers whose sum is 40, with the first three numbers adding up to 20 and the last three to 30. a) Explain why this system has infinitely many solutions. b) Add another condition on the numbers so that a unique solution can be found and then find...
  17. B

    Other Books for Problem-Solving Skills (i.e. Putnam)

    Dear Physics Forum advisers, My name is Phoenix Kim, a rising junior with major in mathematics and an aspiring applied mathematician & algebraist. I wrote this email to seek your recommendation on great books for problem-solving skills (techniques, strategies, etc.) in the mathematical...
  18. A

    What level of mechanics should go for? | strategies for mastering problems?

    Hi everybody, The question sounds dumb, but I asked it, probably someone had the same experience, and can help me or give advice on it about what I'm going to do next ! I know calculus until the double integrals and I don't know enough about Lagrange multipliers ( Indeed, looking for intuitive...
  19. Q

    LaTeX Latex/Lyx: not just retyping from paper, but live problem-solving?

    Has anyone tried to use software not just for typing math to produce good-looking documents after solving problems/doing research with paper&pencil, but for actually doing research/problem solving with lots of maths directly in electronic form? Has anyone managed to have the same productivity as...
  20. S

    How to Get Good At Problem-Solving ?

    Hey guys I am taking a calculus course that is mainly on computation, no proofs. For the most part the computation is easy, but I struggle to solve "challenging" problems and I don't know how to practice for these problems. An example is I will attempt a solution to the problem but get no...
  21. T

    Solve SAT Physics Test: Problem-Solving Help

    Ok so I'm taking the SAT physics Test soon and I'm woefully unprepared! I've taken physics 2 times already, honors and AP, as well as reteaching it to myself, but i just don't get it. I think my problem is,whenever i see a problem, I panic. I'm ok when learning the material, if i get a few...
  22. Ackbach

    MHB Advanced Problem-Solving Strategies

    I intend for this post to serve as one place to get ideas (the vast majority of which are quite unoriginal with me). Naturally, no one solution method can possibly work for every problem. I would argue that such a solution method does not exist. However, the ideas that so many people have culled...
  23. Ackbach

    MHB Can This Problem-Solving Strategy Save You Hours of Frustration?

    I would highly recommend this to your attention. It can save you hours of frustration in solving problems. Note, however, that not every part necessarily applies to every problem. https://www.physicsforums.com/attachments/8688._xfImport As per the discussion below, it is incumbent upon me to...
  24. Ackbach

    MHB Problem-Solving Strategy for Dynamics Problems

    I would highly recommend this to your attention. It can save you hours of frustration in solving problems. Note, however, that not every part necessarily applies to every problem. As per the discussion below, it is incumbent upon me to cite sources. This pdf was one I created from a...
  25. Andy Resnick

    Pre-Tests for Algebra & Problem-Solving in College Physics

    Doing some end-of-the-semester reflection regarding my course (algebra-based PHYS I & II, non-majors), and a suggestion was made to incorporate 'pre-tests' next term as a way to quickly flag students that may struggle with 1) algebra and 2) problem-solving, and who would then be recommended to...
  26. S

    Calculating Parachute Sizing to Slow Landing Aircraft: A Problem-Solving Scenario

    I'm trying to solve a problem which involves the following scenario. Any help would be great! A landing aircraft (mass 14 tonnes) is to be slowed from 300km/hr to 180km/hr in 3 seconds, by the deployment of two identical parachutes at its rear. Determine the diameter of each parachute. The...
  27. R

    What's Wrong with This Argument? Problem-Solving a Homework Statement

    Homework Statement Our teacher made an unconvincing argument based on this example: If a horizontal force of 15 N were a applied to a 2 kg block, and the work done was 20 J, what distance did the object move? 2. The attempt at a solution Using W=F*d the teacher solved this: 20 J=15 N*x ->...
  28. B

    Drawing Vector Diagrams for Problem-Solving

    Here is the problem i need help with. I run up a down escalator at a speed of 2 m/s while the escalator is moving at a rate of 0.75 m/s. What is the resultant velocity? Of course, I do not need help getting the resultant velocity. I just need help drawing the vector diagram that can help...
  29. A

    Navigating Through Physics Problem-Solving Challenges

    I recently changed my major to Physics (from Computer Engineering) and love the subject. However, there is a problem. Even after doing tons of problems at home to study, there are questions on test that I just can't wrap my head around. The way I try to solve problems is to set them up without...
  30. E

    Problem Solving Techniques: Learn Steps to Solve Problems

    Do you know every step of problem-solving techniques?