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14.3: Determinants
https://chem.libretexts.org/Courses/Grinnell_College/CHM_364%3A_Physical_Chemistry_2_(Grinnell_College)/14%3A_Math_Chapters/14.03%3A_Determinants
Chapter Objectives Learn how to calculate the determinant of a square matrix. Understand how to solve systems of simultaneous linear equations using determinants. Learn the properties of determinants.
14.12.12: Partial Derivatives
https://chem.libretexts.org/Courses/Grinnell_College/CHM_364%3A_Physical_Chemistry_2_(Grinnell_College)/14%3A_Math_Chapters/14.12%3A_Formula_Sheets/14.12.12%3A_Partial_Derivatives
\[ \begin{array}{c} \left ( \frac{\partial u}{\partial r} \right )_\theta=\left ( \frac{\partial u}{\partial x} \right )_y\left ( \frac{\partial x}{\partial r} \right )_\theta+\left ( \frac{\partial u...\[ \begin{array}{c} \left ( \frac{\partial u}{\partial r} \right )_\theta=\left ( \frac{\partial u}{\partial x} \right )_y\left ( \frac{\partial x}{\partial r} \right )_\theta+\left ( \frac{\partial u}{\partial y} \right )_x\left ( \frac{\partial y}{\partial r} \right )_\theta \\ \left ( \frac{\partial u}{\partial \theta} \right )_r=\left ( \frac{\partial u}{\partial x} \right )_y\left ( \frac{\partial x}{\partial \theta} \right )_r+\left ( \frac{\partial u}{\partial y} \right )_x\left ( \frac{…
14.12.8: Fourier Series
https://chem.libretexts.org/Courses/Grinnell_College/CHM_364%3A_Physical_Chemistry_2_(Grinnell_College)/14%3A_Math_Chapters/14.12%3A_Formula_Sheets/14.12.08%3A_Fourier_Series
For a periodic function of period $2L$ : \[\begin{array}{c} f(x)=\frac{a_0}{2}+\sum\limits_{n=1}^{\infty}a_n\cos\left ( \frac{n \pi x}{L} \right )+\sum\limits_{n=1}^{\infty}b_n\sin\left ( \frac{n \pi...For a periodic function of period $2L$ : $\begin{array}{c} f(x)=\frac{a_0}{2}+\sum\limits_{n=1}^{\infty}a_n\cos\left ( \frac{n \pi x}{L} \right )+\sum\limits_{n=1}^{\infty}b_n\sin\left ( \frac{n \pi x}{L} \right ) \\ a_0=\frac{1}{L}\int\limits_{-L}^{L}f(x)dx \\ a_n=\frac{1}{L}\int\limits_{-L}^{L}f(x)\cos{\left(\frac{n \pi x}{L} \right)}dx \\ b_n=\frac{1}{L}\int\limits_{-L}^{L}f(x)\sin{\left(\frac{n \pi x}{L} \right)}dx \end{array} \nonumber$
14.12.5: Complex Numbers
https://chem.libretexts.org/Courses/Grinnell_College/CHM_364%3A_Physical_Chemistry_2_(Grinnell_College)/14%3A_Math_Chapters/14.12%3A_Formula_Sheets/14.12.05%3A_Complex_Numbers
$re^{\pm i\phi}=r\cos{\phi}\pm i r \sin{\phi}=x \pm iy \nonumber$
14.4: Vectors
https://chem.libretexts.org/Courses/Grinnell_College/CHM_364%3A_Physical_Chemistry_2_(Grinnell_College)/14%3A_Math_Chapters/14.04%3A_Vectors
In this chapter we will review a few concepts you probably know from your physics courses. This chapter does not intend to cover the topic in a comprehensive manner, but instead touch on a few concept...In this chapter we will review a few concepts you probably know from your physics courses. This chapter does not intend to cover the topic in a comprehensive manner, but instead touch on a few concepts that you will use in your physical chemistry classes.
10.5: First Order Ordinary Differential Equations
https://chem.libretexts.org/Courses/DePaul_University/Thermodynamics_and_Introduction_to_Quantum_Mechanics_(Southern)/10%3A_Appendix-_Mathematics_for_Physical_Chemistry/10.05%3A_First_Order_Ordinary_Differential_Equations
Be able to identify the dependent and independent variables in a differential equation. Be able to identify whether an ordinary differential equation (ODE) is linear or nonlinear. Be able to find the ...Be able to identify the dependent and independent variables in a differential equation. Be able to identify whether an ordinary differential equation (ODE) is linear or nonlinear. Be able to find the general and particular solutions of linear first order ODEs. Be able to find the general and particular solutions of separable first order ODEs. Understand how to verify that the solution you got in a problem satisfies the differential equation and initial conditions.
10.4.5: Line Integrals
https://chem.libretexts.org/Courses/DePaul_University/Thermodynamics_and_Introduction_to_Quantum_Mechanics_(Southern)/10%3A_Appendix-_Mathematics_for_Physical_Chemistry/10.04%3A_Exact_and_Inexact_Differentials/10.4.05%3A_Line_Integrals
This means that if we want to calculate the work or the heat involved in the process, we would need to integrate the inexact differentials $dw$ and $dq$ indicating the particular path used to take...This means that if we want to calculate the work or the heat involved in the process, we would need to integrate the inexact differentials $dw$ and $dq$ indicating the particular path used to take the system from the initial to the final states:
10.6.2: Second Order Ordinary Differential Equations - Oscillations
https://chem.libretexts.org/Courses/DePaul_University/Thermodynamics_and_Introduction_to_Quantum_Mechanics_(Southern)/10%3A_Appendix-_Mathematics_for_Physical_Chemistry/10.06%3A_Second_Order_Ordinary_Differential_Equations/10.6.02%3A_Second_Order_Ordinary_Differential_Equations_-_Oscillations
We’ll start with the problem of the pendulum, and as we already discussed in Section 3.2, even if the pendulum is not particularly interesting as an application in chemistry, the topic of oscillations...We’ll start with the problem of the pendulum, and as we already discussed in Section 3.2, even if the pendulum is not particularly interesting as an application in chemistry, the topic of oscillations is of great interest due to the fact that atoms in molecules vibrate around their bonds.
10.1: Before We Begin...
https://chem.libretexts.org/Courses/DePaul_University/Thermodynamics_and_Introduction_to_Quantum_Mechanics_(Southern)/10%3A_Appendix-_Mathematics_for_Physical_Chemistry/10.01%3A_Before_We_Begin...
10.4.2: Exact and Inexact Differentials
https://chem.libretexts.org/Courses/DePaul_University/Thermodynamics_and_Introduction_to_Quantum_Mechanics_(Southern)/10%3A_Appendix-_Mathematics_for_Physical_Chemistry/10.04%3A_Exact_and_Inexact_Differentials/10.4.02%3A_Exact_and_Inexact_Differentials
If you are given a function of more than one variable, you can calculate its total differential using the definition of a total differential of a function $u$ : (\(du=\left(\frac{\partial u}{\partial...If you are given a function of more than one variable, you can calculate its total differential using the definition of a total differential of a function $u$ : ( $du=\left(\frac{\partial u}{\partial x_1} \right)_{x_2...x_n} dx_1+\left( \frac{\partial u}{\partial x_2} \right)_{x_1, x_3...x_n} dx_2+...+\left( \frac{\partial u}{\partial x_n} \right)_{x_1...x_{n-1}} dx_n$ ).
10.4.6: Exact and Inexact Differentials (Summary)
https://chem.libretexts.org/Courses/DePaul_University/Thermodynamics_and_Introduction_to_Quantum_Mechanics_(Southern)/10%3A_Appendix-_Mathematics_for_Physical_Chemistry/10.04%3A_Exact_and_Inexact_Differentials/10.4.06%3A_Exact_and_Inexact_Differentials_(Summary)
If the derivatives are identical, we conclude that the differential $df$ is exact, and therefore it is the total differential of a function $f(x,y)$ . It is important to keep in mind that the integ...If the derivatives are identical, we conclude that the differential $df$ is exact, and therefore it is the total differential of a function $f(x,y)$ . It is important to keep in mind that the integration constant in the first case will be an arbitrary function of $y$ , and in the second case an arbitrary function of $x$ . This means that the integral of $df$ along any path is simply the function $f$ evaluated at the final state minus the function $f$ evaluated at the initial state:

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