Free cheat sheets + practice sets for engineering students

Thermo, Circuits, Fluid Mechanics, and Calculus IV cheat sheets (incl. Calc IV Mid-2 & Final quick sheets). Circuits DC, Statics, Fluid Mechanics & Calculus II–IV practice. Ads help keep everything free.

One-page summaries Exam-style drills Printable A4 100% Free
📚

Download free cheat sheets

One-page references you can print and bring to exams

Thermo

Thermodynamics — Brayton & Rankine

PDF • formulas + worked examples
  • Key relations & state-point diagrams
  • Quick example flow with units
Circuits

Intro to Circuits — AC Basics & Phasors

PDF • quick tables + examples
  • Impedance, phasors, complex power
  • Two-wattmeter method summary
Calculus IV

Calculus IV — Vector Calculus Quick Ref

PDF • grad/div/curl • line/surface integrals • theorems
  • Green, Gauss, Stokes — statements + hints
  • Mini examples for set-up recognition
Calculus IV

Calculus IV — Midterm 2 Quick Sheet

PDF • line integrals • Green's Theorem • vector fields
  • Conservative tests, potentials, path-independence
  • Common set-ups + pitfalls
Calculus IV

Calculus IV — Final Exam Quick Sheet

PDF • Stokes & Divergence Theorems • flux/circulation
  • Orientation & normals, surface/volume choices
  • Coordinate tricks + sanity checks
Fluids

Fluid Mechanics — Bernoulli, Pipe Flow & Drag

PDF • key equations + worked examples
  • Bernoulli equation, continuity, hydrostatics
  • Pipe flow, Moody chart, drag coefficients
✍️

Practice problems

Circuits DC, Statics, Fluid Mechanics, Calculus I–IV

Circuits

Circuits — ECE2150J

Study each topic first before working on the problems! Some solutions might be a bit rough, but the logic is solid :D
  • Set 1: KCL/KVL basics, series/parallel, source transforms, Thevenin and Norton
  • Set 2: AC state analysis for Final
Fluids

Fluid Mechanics — Pipe Flow & Open Channels

PDF • Bernoulli • pipe losses • dimensional analysis
  • Bernoulli applications, manometry, hydrostatic forces
  • Pipe networks, Darcy-Weisbach, Reynolds number practice
Calc I

Calculus I — Midterm and Final Review

Review notes and practice problems for Calculus 1
  • Logic, induction, Root/Ratio test
  • Sequences, derivatives
Calc II

Calculus II — Full Notes and Practice

This PDF contains both notes and practice problems for the whole class — study the topic yourself first!
PDF • integration techniques • series • applications
  • Parts, partial fractions, trig substitutions
  • Improper integrals & series basics
Calc III

Calculus III — Multivariable

PDF • partials • optimization • multiple integrals
  • Gradients, Lagrange multipliers
  • Double/triple integrals, Jacobians
Calc IV

Calculus IV — Vector Calculus

PDF • line/surface integrals • vector theorems
  • Green, Gauss, Stokes — flux & circulation practice

Need more sheets or problem sets?

If you want cheat sheets or practice problems for other classes, email me anytime:

prachmsn@gmail.com

Tell me the course (e.g., Dynamics, Materials, Signals) and the topics you want covered.