Equation Sheets

GitHub

Introduction

This repository contains equations that I learned, used, and/or taught in science and engineering courses at the University of Washington (UW, undergraduate) and University of California, Berkeley (UCB, graduate). Topics include calculus, applied mathematics, chemistry, physics, and chemical engineering.

You can download pdf of the equation sheets in this repository or view them online. The online version is most up-to-date, and it’s also configured to be printable. You may also find the course notes helpful.

If you like this resource, feel free to star, watch, or fork.

If you find any mistake, please feel free to raise an issue.

Chemistry

• UW CHEM 145 Honors General Chemistry I
  • Undergraduate, Year 1
  • Covered gases, thermodynamics, and equilibrium.
  • Taken in Au19 with Professor Joshua Vaughan
  • Textbook: Principles of Modern Chemistry 7e by Oxtoby et al.
• UW CHEM 155 Honors General Chemistry II
  • Undergraduate, Year 1
  • Covered acid-base equilibria, solution equilibria, electrochemistry, kinetics, nuclear chemistry, and quantum mechanics and atomic structure.
  • Taken in Wi20 with Professor David Ginger
  • Textbook: Principles of Modern Chemistry 7e by Oxtoby et al.
• UW CHEM 238 Organic Chemistry II
  • Undergraduate, Year 2
  • Covered alcohol, thiol, ether, sulfide, epoxide, glycol, alkyne, diene, benzene, transition metal catalysis, IR, NMR, UV-Vis spectroscopy, and mass spectrometer.
  • Taken in Wi21 with Professor Michael Gelb
  • Textbook: Organic Chemistry 6e by Loudon et al.
• UW CHEM 455 Physical Chemistry
  • Undergraduate, Year 3-4
  • Covered postulates, particle in a box, finite potential well, barrier scattering, commutator, dimer model, vibrational and rotational spectroscopy, hydrogen atom, spin, many e- atoms, Hartree-Fock orbitals, and chemical bonding.
  • Taken in Au21 with Professor David Masiello
  • Textbook: Quantum Chemistry and Spectroscopy 4e by Engel

Physics

• UW PHYS 121 Mechanics
  • Undergraduate, Year 1
  • Covered kinematics, dynamics, energy, momentum, rotational kinematics and dynamics, and universal gravitation.
  • Taken in Au20
  • Required textbook: Principles and Practice of Physics 1e by Mazur
  • Study textbook: University Physics with Modern Physics 14e by Young and Freedman
• UW PHYS 122 Electromagnetism
  • Undergraduate, Year 1
  • Covered electric force, electric field, gauss’s law, electric potential, capacitance, current, magnetic force, magnetic field, electromagnetic induction, maxwell’s equations, DC circuits, AC circuits, special relativity.
  • Taken in Wi21
  • Required textbook: Principles and Practice of Physics 1e by Mazur
  • Study textbook: University Physics with Modern Physics 14e by Young and Freedman
• UW PHYS 123 Waves
  • Undergraduate, Year 1
  • Covered periodic motion, 1D, 2D, 3D waves, ray optics, wave and particle optics, fluid mechanics, entropy, thermodynamic processes, and degradation of energy.
  • Taken in Sp21
  • Required textbook: Principles and Practice of Physics 1e by Mazur
  • Study textbook: University Physics with Modern Physics 14e by Young and Freedman

Calculus

• UW MATH 124 Calculus I
  • Undergraduate, Year 1
  • Covered limits, continuity, derivatives, extreme values, L’Hospital’s rule, intermediate value theorem, mean value theorem, and applications of differentiation.
  • Taken in Au17 in high school as AP Calculus BC with Mr. Trey
  • Textbook: Calculus Early Transendentals 8e by Stewart
• UW MATH 125 Calculus II
  • Undergraduate, Year 1
  • Covered indefinite and definite integrals, fundamental theorem of calculus, u-substitution, integration by parts, integral approximations, trigonometric integrals and substitutions, improper integrals, and applications of integration.
  • Taken in Sp17 in high school as AP Calculus BC with Mr. Trey
  • Textbook: Calculus Early Transendentals 8e by Stewart
• UW MATH 126 Calculus III
  • Undergraduate, Year 1
  • Covered vectors, equation of lines, planes, cylinders, and quadratic surfaces, vector functions, partial derivatives, tangent plane approximation, extreme values, double integrals on Cartesian and polar coordinates, and Taylor series.
  • Taken in Wi20 with Professor Ebru Bekyel
  • Textbook: Calculus Early Transendentals 8e by Stewart
• UW MATH 324 Calculus IV
  • Undergraduate, Year 2
  • Covered double integral, triple integral, chain rule, directional derivative, gradient vector, line integrals, surface integrals, curl and divergence, Green’s theorem, Stoke’s theorem, and divergence theorem.
  • Taken in Wi21 with Kuan-Ting Yeh
  • Textbook: Calculus Early Transendentals 8e by Stewart

Applied Mathematics

• UW AMATH 301 Beginning Scientific Computing
  • Undergraduate, Year 1-3
  • Covered root-finding, optimization, curve fitting, solving linear systems, singular value decomposition (SVD, PCA), numerical differentiation and integration, solving first-order and higher order ODEs, stability and stiffness of ODEs, phase portraits, chaotic systems, and Fourier transform.
  • Taken in Sp20 with Dr. Craig Gin
• UW AMATH 351 Differential Equations
  • Undergraduate, Year 1-2
  • Covered first order and second order ODEs with applications in mathematical modeling, stability, and mechanical vibrations. Covers systems of differential equations and Laplace transform.
  • Taken in Wi21 with Alanna Gary
  • Optional textbook: Elementary Differential Equations and Boundary Value Problems 11e by Boyce et al.
• [UW AMATH 353 Partial Differential Equations and Waves]
  • Undergraduate, Year 2-3
  • Covered traveling waves, wave equation, d’Alembert’s solution, standing waves, separation of variables, and conservation laws.
  • Taken in Sp22 with Professor Mark Kot
  • Textbook: An Introduction to the Mathematical Theory of Wave 1e by Knobel

Chemical Engineering

Chemical Engineering Fundamentals

• UW CHEM E 310 Material and Energy Balances
  • Undergraduate, Year 2
  • Covered units and process variables, material balances of nonreactive and reactive systems, single- and multi-phase systems, energy balances of nonreactive and reactive systems.
  • Taken in Sp21 with Professor Elizabeth Nance
  • Textbook: Elementary Principles of Chemical Processes 4e by Felder et al.
• UW CHEM E 375 Chemical Engineering Computer Skills
  • Undergraduate, Year 2
  • Covered chemical engineering scientific computing and numerical methods. Topics include curve fitting, balancing chemical equations, solving VLE problems, plotting VLE x/y and Txy diagrams, determining Antoine’s coefficients, chemical kinetics, and time-dependent and -independent heat transfer.
  • Taken in Sp21 with Professor Jim Pfaendtner
• UCB CHM ENG 130 Mathematics and Statistics in Chemical Engineering
  • Undergraduate, Year 3
  • Covered first-, second-order ODEs, coupled systems of ODEs, PDEs, and statistics.
  • Instruction in progress in Au23 with Professor Aditi Krishnapriyan

Thermodynamics and Statistical Mechanics

• UW CHEM E 325 Energy and Entropy
  • Undergraduate, Year 3
  • Covered thermodynamic data, molecular interactions and equations of state, first and second law analysis, process efficiency, and single and multi-component equilibrium.
  • Taken in Au21 with Professor David Bergsman
  • Optional textbook: Engineering and Chemical Thermodynamics 2e by Koretsky
• UW CHEM E 326 Chemical Engineering Thermodynamics
  • Undergraduate, Year 3
  • Covered thermodynamic relations, single- and multi-component phase equilibrium, fugacity-based equilibrium, phase equilibrium applications, and chemical equilibrium.
  • Taken in Wi22 with Professor René Overney
  • Textbook: Engineering and Chemical Thermodynamics 2e by Koretsky
• UW CHEM E 457 Principles of Molecular Engineering
  • Undergraduate, Year 3
  • Covered probability, entropy, Boltzmann’s law, ensembles, chemical and physical equilibrium, solvation and phase transfer, and phase transitions.
  • Taken in Sp22 with Professor Samson Jenekhe
  • Textbook: Molecular Driving Forces: Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience 2e by Dill and Bromberg
• UCB CHM ENG 240 Thermodynamics for Chemical Product and Process Design
  • Graduate
  • In progress in Au23 with Professor Rui Wang

Transport Processes

• UW CHEM E 330 Transport Processes I
  • Undergraduate, Year 3
  • Covered transport fundamentals: rate laws, transport coefficients, shell balance method, and generalization to 3D. Covered fluid mechanics: Navier-Stokes equation, top-down method, turbulence, dynamic similarity, dimensional analysis, Bernoulli analysis, and microfluidics.
  • Taken in Au21 with Professor John Berg
  • Optional textbook: Transport Phenomena Revised 2e by Bird et al.
• [UW CHEM E 340 Transport Process II]
  • Undergraduate, Year 3
  • Covered 1D conduction, 2D conduction, transient heat conduction, convection, boiling and condensation, heat exchangers, and radiation.
  • Taken in Wi22 with Professor David Bergsman
  • Optional textbook: Fundamentals of Heat and Mass Transfer 8e by Bergman et al.
• UW CHEM E 435 Transport Process III
  • Undergraduate, Year 4
  • Covered mass transfer, single equilibrium stages, multistage cascades, absorption and stripping, distillation, and membrane separations.
  • Taken in Au22 with Professor Jorge Marchand
  • Textbook: Separation Process Principles with Applications Using Process Simulators 4e by Seader et al.
• UCB CHM ENG 250 Transport Processes
  • Graduate
  • In progress in Au23 with Professor Kranthi Mandadapu

Chemical Reaction Engineering

• UW CHEM E 465 Reactor Design
  • Undergraduate, Year 4
  • Covered rate law, reactor sizing, stoichiometry, isothermal reactor deign, rate law determination, multiple reactions, enzymatic and catalytic reactions, and nonisothermal reactor design.
  • Taken in Au22 with Professor Alex Prybutok
  • Textbook: Essentials of Chemical Reaction Engineering 2e by Fogler
• UW CHEM E 467 Biochemical Engineering
  • Undergraduate, Year 3-4
  • Covered enzyme and cell growth kinetics, cell reaction stoichiometry, media design, oxygen transfer, sterilization, bioreactor design, bioseparation, mammalian cell culture, immunology, and biologics.
  • Taken in Sp23 with Professor Alex Prybutok
  • Optional textbook: Biochemical Engineering: A Textbook for Engineers, Chemists and Biologists 2e by Katoh et al.
• UCB CHM ENG 244 Kinetics and Reaction Engineering
  • Graduate
  • In progress in Au23 with Professor Alexander Katz

Process Engineering

• [UW CHEM E 480 Process Dynamics and Control]
  • Undergraduate, Year 4
  • In progress Wi23 with Professor James Carothers
  • Textbook: Process Dynamics and Control 4e by Seborg et al.
• UW CHEM E 485 Process Design I
  • Undergraduate, Year 4
  • In progress Wi23 with Professor Vincent Holmberg
  • Textbook: Analysis, Synthesis, and Design of Chemical Processes 5e by Turton et al.
  • Aspen Plus lectures and case studies: NPTEL, Indian Institute of Technology, Guwahati

Nanoscience and Molecular Engineering

• UW NME 220 Molecular and Nanoscale Principles
  • Undergraduate, Year 2-4
  • Covered scaling and transport properties, atomic theory of matter, atomic models, wave functions in quantum mechanics, nanoscience and technology, electronic structures of molecules, and molecular modes and energetic properties.
  • Taken in Sp21 with Professor René Overney
  • Textbook: Custom text