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Essential Mathematics for Chemical Engineers
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1. Calculus
1.1. Functions
1.2. Function identities
1.3. Limits
1.4. Derivatives
1.5. Rules for derivatives
1.6. Series expansion
1.7. Integration using substitution
1.8. Integration by parts
1.9. Partial fraction decomposition
2. Multivariable calculus
2.1. Derivatives
2.2. Total differential
2.3. Manipulating partial derivatives
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. Definition
4.2. Quadratic and cubic polynomials
4.3. Root finding methods
5. First-order ordinary differential equations
5.1. Definition
5.2. Separable differential equations
5.3. Exact differential equations
5.4. Laplace transform
5.5. Integrating factor
5.6. Numerical solution methods
6. Systems of first-order ordinary differential equations
6.1. Definition
6.2. Linearity
6.3. Homogeneous linear first-order ODEs with constant coefficients
6.4. Numerical solution methods
7. Second-order ordinary differential equations
7.1. Substitution
7.2. Linearity
7.3. Reduction of order
7.4. Homogeneous linear second-order ODEs with constant coefficients
7.5. Undetermined coefficients
7.6. Variation of parameters
7.7. Numerical solution methods
8. Credits
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Index