Essential Mathematics for Chemical Engineers

by Michael P. Howard

This is a digitized collection of course notes and problems developed for CHEN 2650 Chemical Engineering Applications of Mathematical Techniques at Auburn University.

Table of contents

• 1. Calculus
  • 1.1. Derivatives
  • 1.2. Product, quotient, and chain rule
  • 1.3. Series expansion
  • 1.4. Integration
  • 1.5. Integration using substitution
  • 1.6. Integration by parts
  • 1.7. Partial fraction decomposition
• 2. Multivariable calculus
  • 2.1. Derivatives
  • 2.2. Total differential
  • 2.3. Manipulating Partial Derivatives
  • 2.4. Series expansion
  • 2.5. Integration
  • 2.6. Line integral
• 3. Linear algebra
  • 3.1. Matrices and vectors
  • 3.2. Systems of linear equations
  • 3.3. Gauss–Jordan elimination
  • 3.4. Determinants
  • 3.5. Matrix inversion
  • 3.6. Eigenvalue problem
• 4. Nonlinear equations
  • 4.1. Quadratic and cubic polynomials
  • 4.2. Root finding methods
  • 4.3. Linearization
• 5. First-order ordinary differential equations
  • 5.1. Separable differential equations
  • 5.2. Exact differential equations
  • 5.3. Linearity
  • 5.4. Undetermined coefficients
  • 5.5. Laplace transform
  • 5.6. Integrating factor
  • 5.7. Numerical solution methods
• 6. Systems of first-order ordinary differential equations
  • 6.1. Linearity
  • 6.2. Homogeneous linear first-order ODEs with constant coefficients
  • 6.3. Numerical solution methods
• 7. Second-order ordinary differential equations
  • 7.1. Reduction of order
  • 7.2. Linearity
  • 7.3. Homogeneous linear second-order ODEs with constant coefficients
  • 7.4. Undetermined coefficients
  • 7.5. Variation of parameters
  • 7.6. Numerical solution methods
• 8. Credits