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E-grāmata: Symbolic Mathematics for Chemists: A Guide for Maxima Users

  • Formāts: PDF+DRM
  • Izdošanas datums: 24-Aug-2018
  • Izdevniecība: John Wiley & Sons Inc
  • Valoda: eng
  • ISBN-13: 9781119273233
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Symbolic Mathematics for Chemists: A Guide for Maxima UsersPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 24-Aug-2018
  • Izdevniecība: John Wiley & Sons Inc
  • Valoda: eng
  • ISBN-13: 9781119273233
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An essential guide to using Maxima, a popular open source symbolic mathematics engine to solve problems, build models, analyze data and explore fundamental concepts

Symbolic Mathematics for Chemists offers students of chemistry a guide to Maxima, a popular open source symbolic mathematics engine that can be used to solve problems, build models, analyze data, and explore fundamental chemistry concepts. The author — a noted expert in the field — focuses on the analysis of experimental data obtained in a laboratory setting and the fitting of data and modeling experiments. The text contains a wide variety of illustrative examples and applications in physical chemistry, quantitative analysis and instrumental techniques.

Designed as a practical resource, the book is organized around a series of worksheets that are provided in a companion website. Each worksheet has clearly defined goals and learning objectives and a detailed abstract that provides motivation and context for the material. This important resource:

  • Offers an text that shows how to use popular symbolic mathematics engines to solve problems
  • Includes a series of worksheet that are prepared in Maxima
  • Contains step-by-step instructions written in clear terms and includes illustrative examples to enhance critical thinking, creative problem solving and the ability to connect concepts in chemistry
  • Offers hints and case studies that help to master the basics while proficient users are offered more advanced avenues for exploration 

Written for advanced undergraduate and graduate students in chemistry and instructors looking to enhance their lecture or lab course with symbolic mathematics materials, Symbolic Mathematics for Chemists: A Guide for Maxima Users is an essential resource for solving and exploring quantitative problems in chemistry.

Preface xiii
1 Fundamentals 1(32)
1.1 Getting Started With wxMaxima
1(11)
1.1.1 Input Cells
2(1)
1.1.2 The Toolbar
3(1)
1.1.3 The Menus
3(1)
1.1.4 Command History
4(1)
1.1.5 Basic Arithmetic
5(2)
1.1.6 Mathematical Functions
7(1)
1.1.7 Assigning Variables
8(2)
1.1.8 Defining Functions
10(2)
1.1.9 Comments, Images, and Sectioning
12(1)
1.2 A Tour of the General Math Pane
12(16)
1.2.1 Basic Plotting
13(5)
1.2.1.1 Plotting Multiple Curves
14(1)
1.2.1.2 Parametric Plots
15(1)
1.2.1.3 Discrete Plots
15(2)
1.2.1.4 Three-Dimensional Plots
17(1)
1.2.2 Basic Algebra
18(4)
1.2.2.1 Equations
18(1)
1.2.2.2 Substitutions
18(2)
1.2.2.3 Simplification
20(1)
1.2.2.4 Solving Equations
21(1)
1.2.2.5 Simplifying Trigonometric and Exponential Functions
21(1)
1.2.3 Basic Calculus
22(6)
1.2.3.1 Limits
22(1)
1.2.3.2 Differentiation
23(1)
1.2.3.3 Series
24(1)
1.2.3.4 Integration
25(3)
1.2.4 Differential Equations
28(1)
1.3 Controlling Execution
28(2)
1.4 Using Packages
30(3)
2 Storing and Transforming Data 33(38)
2.1 Numbers
33(14)
2.1.1 Floating Point Numbers
33(4)
2.1.2 Integers and Rational Numbers
37(1)
2.1.3 Complex Numbers
38(4)
2.1.4 Constants
42(1)
2.1.5 Units and Physical Constants
43(4)
2.2 Boolean Expressions and Predicates
47(4)
2.2.1 Relational Operators
47(1)
2.2.2 Logical Operators
48(1)
2.2.3 Predicates
49(2)
2.3 Lists
51(6)
2.3.1 List Assignments
51(1)
2.3.2 Indexing List Items
52(1)
2.3.3 Arithmetic with Lists
52(2)
2.3.4 Building and Editing Lists
54(1)
2.3.4.1 Adding Items
54(1)
2.3.4.2 Deleting Items
55(1)
2.3.5 Nested Lists
55(1)
2.3.6 Sublists
56(1)
2.4 Matrices
57(9)
2.4.1 Row and Column Vectors
57(1)
2.4.2 Indexing Matrices
58(1)
2.4.3 Entering Matrices
59(1)
2.4.4 Assigning Matrices
60(1)
2.4.5 Editing Matrices
61(2)
2.4.6 Reading and Writing Matrices From Files
63(2)
2.4.7 Transforming Data in a Matrix
65(1)
2.5 Strings
66(5)
2.5.1 Using String Functions to Work with Files
67(4)
3 Plotting Data and Functions 71(32)
3.1 Plotting in Two Dimensions
71(20)
3.1.1 Changing Plot Size and Resolution
71(2)
3.1.2 Plotting Multiple Curves
73(1)
3.1.3 Changing Axis Ranges
74(1)
3.1.4 Plotting Complex Functions
74(1)
3.1.5 Plotting Data
74(3)
3.1.5.1 Plotting Data in Separate X, Y Lists
75(1)
3.1.5.2 Plotting Data as Lists of X, Y Points
75(1)
3.1.5.3 Plotting Data in Matrices
76(1)
3.1.5.4 Plotting Data with Units
76(1)
3.1.5.5 Plotting Functions and Data Together
77(1)
3.1.6 Adding Text Labels to Graphs
77(1)
3.1.7 Plotting Rapidly Rising Functions
78(6)
3.1.7.1 Solving Axis Scaling Problems
81(2)
3.1.7.2 Positioning the Legend
83(1)
3.1.8 Parametric Plots
84(3)
3.1.9 Implicit Plots
87(2)
3.1.10 Histograms
89(2)
3.2 Plotting in Three Dimensions
91(12)
3.2.1 Plotting Functions of x, y, and z
91(2)
3.2.2 Plotting Multiple Surfaces
93(1)
3.2.3 Plotting in Spherical Coordinates
94(1)
3.2.4 Plotting in Cylindrical Coordinates
95(1)
3.2.5 Parametric Surface Plots
96(2)
3.2.6 Plotting Discrete Three-Dimensional Data
98(1)
3.2.7 Contour Plotting
99(4)
4 Programming Maxima 103(16)
4.1 Nouns and Verbs
103(3)
4.2 Writing Multiline Functions
106(2)
4.3 Decision Making
108(1)
4.4 Recursive Functions
109(1)
4.5 Contexts
110(4)
4.6 Iteration
114(5)
4.6.1 Indexed Loops
114(2)
4.6.2 Conditional Loops
116(1)
4.6.3 Looping Over Lists
117(1)
4.6.4 Nested Loops
118(1)
5 Algebra 119(30)
5.1 Series
119(5)
5.1.1 Simplifying Sums
120(2)
5.1.2 Reindexing and Combining Sums
122(1)
5.1.3 Applying Functions to Sums and Products
123(1)
5.2 Products
124(2)
5.3 Equations
126(15)
5.3.1 Simplifying Equations
126(1)
5.3.2 Simplifying Trigonometric and Exponential Functions
127(1)
5.3.3 Extracting Expressions From an Equation
128(3)
5.3.4 Expanding Expressions
131(3)
5.3.5 Factoring Expressions
134(1)
5.3.6 Substitution
135(3)
5.3.7 Solving an Equation Symbolically
138(2)
5.3.7.1 Handling Multiple Solutions
139(1)
5.3.8 Solving an Equation Numerically
140(1)
5.4 Systems of Equations
141(3)
5.4.1 Eliminating Variables
141(2)
5.4.2 Solving Systems of Equations Without Elimination
143(1)
5.5 Interpolation
144(5)
5.5.1 Piecewise Linear Interpolation
146(1)
5.5.2 Spline Interpolation
147(2)
6 Differentiation, Integration, and Minimization 149(44)
6.1 Limits
149(4)
6.1.1 Limits for Discontinuous Functions
151(1)
6.1.2 Limits for Indefinite Functions
152(1)
6.2 Differentials
153(1)
6.3 Derivatives
154(10)
6.3.1 Explicit Partial and Total Derivatives
156(1)
6.3.2 Derivatives Evaluated at a Specific Point
157(1)
6.3.3 Higher-Order Derivatives
158(1)
6.3.4 Mixed Derivatives
159(1)
6.3.5 Assigning Partial Derivatives
160(2)
6.3.5.1 Partial Derivatives from Total Differential Expansions
161(1)
6.3.5.2 Writing Total Differential Expansions in Terms of New Variables
161(1)
6.3.6 Implicit Differentiation
162(2)
6.4 Maxima, Minima, and Inflection Points
164(9)
6.4.1 Critical Points of Surfaces
167(2)
6.4.2 Numerical Minimization
169(4)
6.5 Integration
173(13)
6.5.1 Integration Constants
174(1)
6.5.2 Definite Integration
174(1)
6.5.3 When Symbolic Integration Fails
175(3)
6.5.4 Numerical Integration
178(4)
6.5.4.1 Numerical Integration over Infinite Intervals
179(1)
6.5.4.2 Numerical Integration with Strongly Oscillating Integrands
180(1)
6.5.4.3 Numerical Integration with Discontinuous Integrands
181(1)
6.5.5 Multiple Integration
182(1)
6.5.6 Discrete Integration
183(3)
6.6 Power Series
186(1)
6.6.1 Testing Power Series for Convergence
186(1)
6.7 Taylor Series
187(6)
6.7.1 Exploring Function Properties with Taylor Series
188(2)
6.7.2 The Remainder Term
190(1)
6.7.3 Taylor Series for Multivariate Functions
191(1)
6.7.4 Approximating Taylor Series
191(2)
7 Matrices and Vectors 193(34)
7.1 Vectors
193(7)
7.1.1 Vector Arithmetic
194(1)
7.1.2 The Dot Product
195(1)
7.1.3 Vector Lengths and Angles
196(1)
7.1.4 The Cross Product
197(1)
7.1.5 Angular Momentum
198(1)
7.1.6 Vector Algebra
199(1)
7.2 Matrices
200(17)
7.2.1 Matrix Arithmetic
201(1)
7.2.2 The Transpose
201(1)
7.2.3 The Matrix Product
202(1)
7.2.4 Determinants
203(3)
7.2.5 The Inverse of a Matrix
206(1)
7.2.6 Matrix Algebra
207(4)
7.2.7 Eigenvalues and Eigenvectors
211(6)
7.2.7.1 Application: Energies and Molecular Orbitals of Ethylene
212(2)
7.2.7.2 Eigenvalues and Eigenvectors for Symmetric Matrices
214(2)
7.2.7.3 Matrix Diagonalization
216(1)
7.3 Vector Calculus
217(10)
7.3.1 Derivative of a Vector with Respect to a Scalar
217(1)
7.3.2 The Jacobian
218(2)
7.3.3 The Gradient
220(2)
7.3.4 The Laplacian
222(2)
7.3.5 The Divergence
224(1)
7.3.6 The Curl
225(2)
8 Error Analysis 227(30)
8.1 Classifying Experimental Errors
227(3)
8.1.1 Systematic Error
229(1)
8.1.2 Random Error
230(1)
8.2 Probability Density
230(8)
8.2.1 Discrete Probability Distributions
230(2)
8.2.2 The Poisson Distribution
232(3)
8.2.3 Continuous Probability Distributions
235(1)
8.2.4 The Normal Distribution
236(2)
8.3 Estimating Precision
238(3)
8.3.1 Standard Error of the Mean
240(1)
8.3.2 Confidence Interval of the Mean
240(1)
8.4 Hypothesis Testing
241(8)
8.4.1 Comparing a Mean with a True Value
243(1)
8.4.2 Comparing Variances
244(2)
8.4.3 Comparing Two Sample Means
246(3)
8.5 Propagation of Error
249(8)
8.5.1 Propagation of Independent Systematic Errors
249(2)
8.5.2 Propagation of Independent Random Errors
251(2)
8.5.3 Covariance and Correlation
253(4)
9 Fitting Data to a Straight Line 257(42)
9.1 The Ordinary Least-Squares Method
259(15)
9.1.1 Using Built-In Functions
260(3)
9.1.2 Error Estimates for the Slope and the Intercept
263(3)
9.1.3 The Determination Coefficient
266(2)
9.1.4 Residual Analysis
268(3)
9.1.5 Testing the Fit Parameters
271(1)
9.1.6 Testing for Lack-of-Fit
272(2)
9.2 Multiple Linear Regression
274(11)
9.2.1 Matrix Form of Multiple Linear Regression
275(2)
9.2.2 Estimating the Errors in the Fit Parameters in MLR
277(1)
9.2.3 Example: Microwave Rotational Spectrum of HCl
278(3)
9.2.4 Detecting and Dealing with Outliers
281(4)
9.3 WLS
285(4)
9.3.1 The Fit Parameters in WLS
286(1)
9.3.2 Error Estimates for the WLS Fit Parameters
286(1)
9.3.3 Finding the Weights
287(1)
9.3.4 Residual Analysis in WLS
288(1)
9.3.5 Evaluating Goodness-of-Fit
288(1)
9.4 Fitting Data to a Line with Errors in Both X and Y
289(5)
9.4.1 Finding Fit Parameters in TLS
290(2)
9.4.2 Error Estimates for the TLS Fit Parameters
292(1)
9.4.3 Assessing Goodness-of-Fit in TLS
293(1)
9.4.4 Multiple Linear Regression with TLS
293(1)
9.5 Calibration and Standard Additions
294(5)
9.5.1 Error Estimates for Calibrated Values
294(1)
9.5.2 Standard Additions
295(4)
10 Fitting Data to a Curve 299(18)
10.1 Transforming Data to a Linear Form
299(3)
10.2 Polynomial Least-Squares Fitting
302(4)
10.2.1 How Many Fit Parameters Are Needed?
304(2)
10.3 Nonlinear Least-Squares Models
306(4)
10.4 Estimating Error in Nonlinear Fit Parameters
310(7)
10.4.1 Estimating Parameter Errors with the Jackknife Method
311(2)
10.4.2 Estimating Parameter Errors with the Bootstrap Method
313(4)
11 Differential Equations 317(26)
11.1 Symbolic Solutions of ODEs
318(7)
11.1.1 Initial Value Problems
320(2)
11.1.2 Boundary Value Problems
322(3)
11.2 Power Series Solution of ODEs
325(4)
11.3 Direction Fields
329(6)
11.3.1 Direction Fields with Adjustable Parameters
331(1)
11.3.2 Direction Fields and Autonomous Equations
332(3)
11.4 Solving Systems of Linear Differential Equations
335(3)
11.5 Numerical Solution of ODEs
338(2)
11.6 Solving Partial Differential Equations
340(3)
12 Operators and Integral Transforms 343(16)
12.1 Defining Operators
344(3)
12.2 Fourier Series
347(4)
12.3 Fourier Transforms
351(6)
12.3.1 The Fast Fourier Transform
355(2)
12.4 The Laplace Transform
357(2)
Glossary 359(8)
References 367(4)
Index 371
Professor Fred Senese is a computational chemist at Frostburg State University with a particular focus on chemical education. His research interests include applications of artificial intelligence in chemical education, development of web-based narratives and construction kits for chemical education, remote control and access of instrumentation, and environmental chemical analysis applied to problems in ethnobotany.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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