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Mathematical Methods in Chemistry

This text introduces student to mathematical/computational methods in chemical kinetics, thermodynamics, quantum chemistry.

Physical and Theoretical Chemistry Textbook Maps Chemistry

Author: Marcia Levitus
Publisher: Arizona State University
Source: LibreTexts
License: CC BY-NC-SA
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 106 sections

01: Before We Begin...
1.01: Things to review
1.02: Odd and Even Functions
1.03: The Exponential Function
1.04: The Period of a Periodic Function
1.05: Exercises
02: Complex Numbers
2.01: Algebra with Complex Numbers
2.02: Graphical Representation and Euler Relationship
2.03: Complex Functions
2.04: Problems
03: Series
3.01: Maclaurin Series
3.02: Linear Approximations
3.03: Taylor Series
3.04: Other Applications of Mclaurin and Taylor series
3.05: 3.5 Problems
04: First Order Ordinary Differential Equations
4.01: Definitions and General Concepts
4.02: 1st Order Ordinary Differential Equations
4.03: Chemical Kinetics
4.04: Problems
05: Second Order Ordinary Differential Equations
5.01: Second Order Ordinary Differential Equations
5.02: Second Order Ordinary Differential Equations - Oscillations
5.03: Second Order Ordinary Differential Equations with Boundary Conditions
5.04: An example in Quantum Mechanics
5.05: Problems
06: Power Series Solutions of Differential Equations
6.01: Introduction to Power Series Solutions of Differential Equations
6.02: The Power Series Method
6.03: The Laguerre Equation
6.04: Problems
07: Fourier Series
7.01: Introduction to Fourier Series
7.02: Fourier Series
7.03: Orthogonal Expansions
7.04: Problems
08: Calculus in More than One Variable
8.01: Functions of Two Independent Variables
8.02: The Equation of State
8.03: The Chain Rule
8.04: Double and Triple Integrals
8.05: Real Gases
8.06: Problems
09: Exact and Inexact Differentials
9.01: The Total Differential
9.02: Exact and Inexact Differentials
9.03: Differentials in Thermodynamics - State and Path Functions
9.04: A Mathematical Toolbox
9.05: Line Integrals
9.06: Exact and Inexact Differentials (Summary)
9.07: Problems
10: Plane Polar and Spherical Coordinates
10.01: Coordinate Systems
10.02: Area and Volume Elements
10.03: A Refresher on Electronic Quantum Numbers
10.04: A Brief Introduction to Probability
10.05: Problems
11: Operators
11.01: Definitions
11.02: Operator Algebra
11.03: Operators and Quantum Mechanics - an Introduction
11.04: Problems
12: Partial Differential Equations
12.01: Introduction to Partial Differential Equations
12.02: The Method of Separation of Variables
12.03: The Wave Equation in One Dimension
12.04: Molecular Diffusion
12.05: Problems
13: Determinants
13.01: The Solutions of Simultaneous Linear Equations
13.02: Calculation of a 3 3 determinant
13.03: The Determinant as a Volume
13.04: Properties of Determinants
13.05: Problems
14: Vectors
14.01: Introduction to Vectors
14.02: The Scalar Product
14.03: The Vector Product
14.04: Vector Normalization
14.05: Problems
15: Matrices
15.01: Definitions
15.02: Matrix Addition
15.03: Matrix Multiplication
15.04: Symmetry Operators
15.05: Matrix Inversion
15.06: Orthogonal Matrices
15.07: Eigenvalues and Eigenvectors
15.08: Hermitian Matrices
15.09: Problems
16: Formula Sheets
16.01: Some Important Numbers
16.02: Quadratic Equation
16.03: Logarithms and Exponentials
16.04: Trigonometric Identities
16.05: Complex Numbers
16.06: Operators
16.07: Taylor Series
16.08: Fourier Series
16.09: Derivatives and Primitives (Indefinite Integrals)
16.10: Definite integrals
16.11: Differentiation Rules
16.12: Partial Derivatives
16.13: Coordinate Systems