Maths in chemistry: numerical methods for physical and analytical chemistry
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2020]
|
| Series: | De Gruyter Graduate
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 184 Seiten Illustrationen, Diagramme 24 cm x 17 cm |
| ISBN: | 9783110695311 |
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MARC
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| 020 | |a 9783110695311 |c pbk. |9 978-3-11-069531-1 | ||
| 035 | |a (OCoLC)1196896481 | ||
| 035 | |a (DE-599)DNB1209414112 | ||
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| 100 | 1 | |a Bansal, Prerna |d ca. 20./21. Jahrhundert |e Verfasser |0 (DE-588)1219971561 |4 aut | |
| 245 | 1 | 0 | |a Maths in chemistry |b numerical methods for physical and analytical chemistry |c Prerna Bansal |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2020] | |
| 264 | 4 | |c © 2020 | |
| 300 | |a XII, 184 Seiten |b Illustrationen, Diagramme |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter Graduate | |
| 650 | 0 | 7 | |a Physikalische Chemie |0 (DE-588)4045959-7 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analytische Chemie |0 (DE-588)4129906-1 |2 gnd |9 rswk-swf |
| 653 | |a Mathematik | ||
| 653 | |a TB: Textbook | ||
| 689 | 0 | 0 | |a Physikalische Chemie |0 (DE-588)4045959-7 |D s |
| 689 | 0 | 1 | |a Analytische Chemie |0 (DE-588)4129906-1 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-032301694 | ||
Record in the Search Index
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/VC 6100 B219 |
| DE-BY-FWS_katkey | 857768 |
| DE-BY-FWS_media_number | 083000508656 |
| _version_ | 1824553952577847296 |
| adam_text | CONTENTS
ACKNOWLEDGEMENT
*
VII
CHAPTER
1
UNITS
AND
MEASUREMENTS
*
1
1.1
1.2
1.3
1.4
1.4.1
1.4.2
1.5
1.6
1.7
1.8
1.8.1
1.8.2
1.8.3
1.9
1.10
INTRODUCTION
*
1
BASIC
ARITHMETIC
OPERATIONS
*
1
HIERARCHY
OF
OPERATIONS
*
2
CLASSIFICATION
OF
UNIT
SYSTEM
*
3
METRIC
SYSTEM
OF
UNITS
*
3
CLASSIFICATION
OF
METRIC
SYSTEM
OF
UNITS
*
4
DEFINITION
OF
BASE
UNITS
*
5
INTERCONVERSION
OF
UNITS
*
8
SIGNIFICANT
FIGURES
*
9
RULES
FOR
PERFORMING
ARITHMETIC
OPERATIONS
*
10
ADDITION
AND
SUBTRACTION
*
10
MULTIPLICATION
AND
DIVISION
*
11
MIXED
MATHEMATICAL
OPERATIONS
*
12
ROUNDING
OFF
SIGNIFICANT
FIGURES
*
13
PROBLEMS
FOR
PRACTICE
*
14
CHAPTER
2
UNCERTAINTIES
AND
ERRORS
*
17
2.1
2.2
2.3
2.4
2.5
2.6
INTRODUCTION
*
17
ABSOLUTE
AND
RELATIVE
UNCERTAINTY
*
20
PROPAGATION
OF
UNCERTAINTY
*
21
ROUNDING
OFF
UNCERTAINTIES
*
28
CLASSIFICATION
OF
ERRORS
*
28
PROBLEMS
FOR
PRACTICE
*
29
CHAPTER
3
SOME
MATHEMATICAL
FUNCTIONS
*
31
3.1
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.2.5
3.2.6
3.2.7
INTRODUCTION
*
31
CLASSIFICATION
OF
FUNCTIONS
*
31
LINEAR
FUNCTION
*
31
EXPONENTIAL
*
32
LOGARITHMIC
FUNCTION
*
34
POLYNOMIALS
*
36
POWER
FUNCTION
-----
37
CIRCLE
*
37
RATIONAL
NUMBER
*
38
X
CONTENTS
3.2.8
PARTIAL
FRACTIONS
-----
39
3.2.9
TRIGONOMETRIC
FUNCTIONS
-----
39
3.2.9.1
INVERSE
TRIGONOMETRIC
FUNCTIONS
----42
3.2.9.2
HYPERBOLIC
TRIGONOMETRIC
FUNCTIONS
-----
42
3.2.10
TAYLOR
*
S
SERIES
-----
42
3.2.10.1
MACLAURIN
SERIES
-----
43
3.2.11
COORDINATE
SYSTEMS
*
43
3.2.12
NUMBER
SYSTEM
-----
45
3.3
PROBLEMS
FOR
PRACTICE
*
48
CHAPTER
4
DESCRIPTIVE
STATISTICS
*
49
4.1
INTRODUCTION
-----
50
4.2
MEAN
-----
50
4.2.1
ARITHMETIC
MEAN
------
51
4.2.2
WEIGHTED
MEAN
-----
51
4.2.3
GEOMETRIC
MEAN
------
51
4.2.4
HARMONIC
MEAN
*
52
4.3
MEDIAN
-----
52
4.4
MODE
-----
53
4.5
STANDARD
DEVIATION
-----
53
4.6
VARIANCE
-----
54
4.7
COEFFICIENT
OF
VARIATION
-----
54
4.8
DATA
ANALYSIS
-----
57
4.8.1
Q-TEST
-----
57
4.8.2
CONFIDENCE
LIMIT
-----
59
4.8.3
T-TEST
-----
59
4.8.4
F-TEST
-----
62
4.9
DISTRIBUTION
OF
ERRORS
------
65
4.9.1
GAUSSIAN
DISTRIBUTION
------
65
4.9.2
BINOMIAL
DISTRIBUTION
------
66
4.9.3
POISSON
*
S
DISTRIBUTION
-----
67
4.10
STATISTICAL
TOOLS
USING
SPREADSHEETS
*
67
4.11
PROBLEMS
FOR
PRACTICE
*
70
CHAPTER
5
NUMERICAL
CURVE
FITTING
*
71
5.1
INTRODUCTION
-----
71
5.2
CORRELATION
-----
71
5.2.1
PEARSON
CORRELATION
COEFFICIENT
*
72
5.2.2
SPEARMAN
*
S
RANK
CORRELATION
COEFFICIENT
*
72
5.3
REGRESSION
-----
73
CONTENTS
*
XI
5.4
5.5
5.5.1
5.5.2
5.5.3
5.6
5.7
INTERPOLATION
VERSUS
CURVE
FITTING
*
74
LEAST
SQUARE
CURVE
FITTING
*
74
LINEAR
REGRESSION
*
76
MULTIVARIATE
LINEAR
REGRESSION
*
85
POLYNOMIAL
REGRESSION
*
87
REGRESSION
AND
CORRELATION
IN
EXCEL
*
90
EXERCISES
FOR
PRACTICE
*
94
CHAPTER
6
NUMERICAL
INTEGRATION
*
97
6.1
6.2
6.2.1
6.2.2
6.2.2.1
6.2.3
6.2.3.1
6.2.4
6.2.5
6.3
INTRODUCTION
-----
97
NEWTON-COTES
FORMULA
*
97
RIEMANN
SUM
-----
98
TRAPEZOIDAL
RULE
*
100
ERROR
OF
TRAPEZOIDAL
RULE
*
105
SIMPSON
*
S
L/3RD
RULE
*
106
COMPOSITE
INTEGRAL
SIMPSON
*
S
RULE
*
108
SIMPSON
*
S
3/8
RULE
*
109
BOOLE
*
S
RULE
*
110
EXERCISES
FOR
PRACTICE
*
115
CHAPTER
7
DIFFERENTIAL
EQUATIONS
*
117
7.1
7.2
7.3
7.3.1
7.3.2
7.3.3
7.4
INTRODUCTION
*
117
EULER
*
S
METHOD
*
118
RUNGE-KUTTA
METHOD
-----
121
RK
2
OR
PREDICTOR-CORRECTOR
METHOD
*
121
RK3
-----
124
RK4-----
124
PROBLEMS
FOR
PRACTICE
*
129
CHAPTER
8
NUMERICAL
DIFFERENTIATION
*
131
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
INTRODUCTION
*
131
DERIVATIVES
USING
NEWTON
*
S
FORWARD
INTERPOLATION
POLYNOMIAL
*
134
DERIVATIVES
USING
NEWTON
*
S
BACKWARD
INTERPOLATING
POLYNOMIAL
*
137
DERIVATIVES
USING
STIRLING
INTERPOLATING
POLYNOMIAL
-----
139
NEWTON
*
S
DIVIDED
DIFFERENCE
POLYNOMIAL-
*
142
LAGRANGE
*
S
POLYNOMIAL
*
144
RICHARDSON
*
S
EXTRAPOLATION
*
147
PROBLEMS
FOR
PRACTICE
*
149
XII
*
CONTENTS
CHAPTER
9
NUMERICAL
ROOT-FINDING
METHODS
*
151
9.1
9.2
9.3
9.4
9.5
9.6
9.7
INTRODUCTION
*
151
NEWTON-RAPHSON
METHOD
*
151
ITERATION
METHOD
*
156
BINARY
BISECTION
METHOD
-----
162
SECANT
METHOD
*
165
REGULA-FALSI
METHOD
*
169
PROBLEMS
FOR
PRACTICE
*
174
APPENDIX
A
-----
175
APPENDIX
B
ANSWERS
TO
THE
PROBLEMS
FOR
PRACTICE
*
179
INDEX
*
181
|
| adam_txt |
CONTENTS
ACKNOWLEDGEMENT
*
VII
CHAPTER
1
UNITS
AND
MEASUREMENTS
*
1
1.1
1.2
1.3
1.4
1.4.1
1.4.2
1.5
1.6
1.7
1.8
1.8.1
1.8.2
1.8.3
1.9
1.10
INTRODUCTION
*
1
BASIC
ARITHMETIC
OPERATIONS
*
1
HIERARCHY
OF
OPERATIONS
*
2
CLASSIFICATION
OF
UNIT
SYSTEM
*
3
METRIC
SYSTEM
OF
UNITS
*
3
CLASSIFICATION
OF
METRIC
SYSTEM
OF
UNITS
*
4
DEFINITION
OF
BASE
UNITS
*
5
INTERCONVERSION
OF
UNITS
*
8
SIGNIFICANT
FIGURES
*
9
RULES
FOR
PERFORMING
ARITHMETIC
OPERATIONS
*
10
ADDITION
AND
SUBTRACTION
*
10
MULTIPLICATION
AND
DIVISION
*
11
MIXED
MATHEMATICAL
OPERATIONS
*
12
ROUNDING
OFF
SIGNIFICANT
FIGURES
*
13
PROBLEMS
FOR
PRACTICE
*
14
CHAPTER
2
UNCERTAINTIES
AND
ERRORS
*
17
2.1
2.2
2.3
2.4
2.5
2.6
INTRODUCTION
*
17
ABSOLUTE
AND
RELATIVE
UNCERTAINTY
*
20
PROPAGATION
OF
UNCERTAINTY
*
21
ROUNDING
OFF
UNCERTAINTIES
*
28
CLASSIFICATION
OF
ERRORS
*
28
PROBLEMS
FOR
PRACTICE
*
29
CHAPTER
3
SOME
MATHEMATICAL
FUNCTIONS
*
31
3.1
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.2.5
3.2.6
3.2.7
INTRODUCTION
*
31
CLASSIFICATION
OF
FUNCTIONS
*
31
LINEAR
FUNCTION
*
31
EXPONENTIAL
*
32
LOGARITHMIC
FUNCTION
*
34
POLYNOMIALS
*
36
POWER
FUNCTION
-----
37
CIRCLE
*
37
RATIONAL
NUMBER
*
38
X
CONTENTS
3.2.8
PARTIAL
FRACTIONS
-----
39
3.2.9
TRIGONOMETRIC
FUNCTIONS
-----
39
3.2.9.1
INVERSE
TRIGONOMETRIC
FUNCTIONS
----42
3.2.9.2
HYPERBOLIC
TRIGONOMETRIC
FUNCTIONS
-----
42
3.2.10
TAYLOR
*
S
SERIES
-----
42
3.2.10.1
MACLAURIN
SERIES
-----
43
3.2.11
COORDINATE
SYSTEMS
*
43
3.2.12
NUMBER
SYSTEM
-----
45
3.3
PROBLEMS
FOR
PRACTICE
*
48
CHAPTER
4
DESCRIPTIVE
STATISTICS
*
49
4.1
INTRODUCTION
-----
50
4.2
MEAN
-----
50
4.2.1
ARITHMETIC
MEAN
------
51
4.2.2
WEIGHTED
MEAN
-----
51
4.2.3
GEOMETRIC
MEAN
------
51
4.2.4
HARMONIC
MEAN
*
52
4.3
MEDIAN
-----
52
4.4
MODE
-----
53
4.5
STANDARD
DEVIATION
-----
53
4.6
VARIANCE
-----
54
4.7
COEFFICIENT
OF
VARIATION
-----
54
4.8
DATA
ANALYSIS
-----
57
4.8.1
Q-TEST
-----
57
4.8.2
CONFIDENCE
LIMIT
-----
59
4.8.3
T-TEST
-----
59
4.8.4
F-TEST
-----
62
4.9
DISTRIBUTION
OF
ERRORS
------
65
4.9.1
GAUSSIAN
DISTRIBUTION
------
65
4.9.2
BINOMIAL
DISTRIBUTION
------
66
4.9.3
POISSON
*
S
DISTRIBUTION
-----
67
4.10
STATISTICAL
TOOLS
USING
SPREADSHEETS
*
67
4.11
PROBLEMS
FOR
PRACTICE
*
70
CHAPTER
5
NUMERICAL
CURVE
FITTING
*
71
5.1
INTRODUCTION
-----
71
5.2
CORRELATION
-----
71
5.2.1
PEARSON
CORRELATION
COEFFICIENT
*
72
5.2.2
SPEARMAN
*
S
RANK
CORRELATION
COEFFICIENT
*
72
5.3
REGRESSION
-----
73
CONTENTS
*
XI
5.4
5.5
5.5.1
5.5.2
5.5.3
5.6
5.7
INTERPOLATION
VERSUS
CURVE
FITTING
*
74
LEAST
SQUARE
CURVE
FITTING
*
74
LINEAR
REGRESSION
*
76
MULTIVARIATE
LINEAR
REGRESSION
*
85
POLYNOMIAL
REGRESSION
*
87
REGRESSION
AND
CORRELATION
IN
EXCEL
*
90
EXERCISES
FOR
PRACTICE
*
94
CHAPTER
6
NUMERICAL
INTEGRATION
*
97
6.1
6.2
6.2.1
6.2.2
6.2.2.1
6.2.3
6.2.3.1
6.2.4
6.2.5
6.3
INTRODUCTION
-----
97
NEWTON-COTES
FORMULA
*
97
RIEMANN
SUM
-----
98
TRAPEZOIDAL
RULE
*
100
ERROR
OF
TRAPEZOIDAL
RULE
*
105
SIMPSON
*
S
L/3RD
RULE
*
106
COMPOSITE
INTEGRAL
SIMPSON
*
S
RULE
*
108
SIMPSON
*
S
3/8
RULE
*
109
BOOLE
*
S
RULE
*
110
EXERCISES
FOR
PRACTICE
*
115
CHAPTER
7
DIFFERENTIAL
EQUATIONS
*
117
7.1
7.2
7.3
7.3.1
7.3.2
7.3.3
7.4
INTRODUCTION
*
117
EULER
*
S
METHOD
*
118
RUNGE-KUTTA
METHOD
-----
121
RK
2
OR
PREDICTOR-CORRECTOR
METHOD
*
121
RK3
-----
124
RK4-----
124
PROBLEMS
FOR
PRACTICE
*
129
CHAPTER
8
NUMERICAL
DIFFERENTIATION
*
131
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
INTRODUCTION
*
131
DERIVATIVES
USING
NEWTON
*
S
FORWARD
INTERPOLATION
POLYNOMIAL
*
134
DERIVATIVES
USING
NEWTON
*
S
BACKWARD
INTERPOLATING
POLYNOMIAL
*
137
DERIVATIVES
USING
STIRLING
INTERPOLATING
POLYNOMIAL
-----
139
NEWTON
*
S
DIVIDED
DIFFERENCE
POLYNOMIAL-
*
142
LAGRANGE
*
S
POLYNOMIAL
*
144
RICHARDSON
*
S
EXTRAPOLATION
*
147
PROBLEMS
FOR
PRACTICE
*
149
XII
*
CONTENTS
CHAPTER
9
NUMERICAL
ROOT-FINDING
METHODS
*
151
9.1
9.2
9.3
9.4
9.5
9.6
9.7
INTRODUCTION
*
151
NEWTON-RAPHSON
METHOD
*
151
ITERATION
METHOD
*
156
BINARY
BISECTION
METHOD
-----
162
SECANT
METHOD
*
165
REGULA-FALSI
METHOD
*
169
PROBLEMS
FOR
PRACTICE
*
174
APPENDIX
A
-----
175
APPENDIX
B
ANSWERS
TO
THE
PROBLEMS
FOR
PRACTICE
*
179
INDEX
*
181 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bansal, Prerna ca. 20./21. Jahrhundert |
| author_GND | (DE-588)1219971561 |
| author_facet | Bansal, Prerna ca. 20./21. Jahrhundert |
| author_role | aut |
| author_sort | Bansal, Prerna ca. 20./21. Jahrhundert |
| author_variant | p b pb |
| building | Verbundindex |
| bvnumber | BV046891891 |
| classification_rvk | SK 950 VC 6100 |
| ctrlnum | (OCoLC)1196896481 (DE-599)DNB1209414112 |
| discipline | Chemie / Pharmazie Mathematik |
| discipline_str_mv | Chemie / Pharmazie Mathematik |
| format | Book |
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| id | DE-604.BV046891891 |
| illustrated | Illustrated |
| index_date | 2024-07-03T15:21:30Z |
| indexdate | 2025-02-20T06:44:03Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110695311 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032301694 |
| oclc_num | 1196896481 |
| open_access_boolean | |
| owner | DE-11 DE-29T DE-92 DE-862 DE-BY-FWS DE-20 DE-19 DE-BY-UBM DE-1102 |
| owner_facet | DE-11 DE-29T DE-92 DE-862 DE-BY-FWS DE-20 DE-19 DE-BY-UBM DE-1102 |
| physical | XII, 184 Seiten Illustrationen, Diagramme 24 cm x 17 cm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter Graduate |
| spellingShingle | Bansal, Prerna ca. 20./21. Jahrhundert Maths in chemistry numerical methods for physical and analytical chemistry Physikalische Chemie (DE-588)4045959-7 gnd Funktion Mathematik (DE-588)4071510-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Statistik (DE-588)4056995-0 gnd Analytische Chemie (DE-588)4129906-1 gnd |
| subject_GND | (DE-588)4045959-7 (DE-588)4071510-3 (DE-588)4128130-5 (DE-588)4056995-0 (DE-588)4129906-1 |
| title | Maths in chemistry numerical methods for physical and analytical chemistry |
| title_auth | Maths in chemistry numerical methods for physical and analytical chemistry |
| title_exact_search | Maths in chemistry numerical methods for physical and analytical chemistry |
| title_exact_search_txtP | Maths in chemistry numerical methods for physical and analytical chemistry |
| title_full | Maths in chemistry numerical methods for physical and analytical chemistry Prerna Bansal |
| title_fullStr | Maths in chemistry numerical methods for physical and analytical chemistry Prerna Bansal |
| title_full_unstemmed | Maths in chemistry numerical methods for physical and analytical chemistry Prerna Bansal |
| title_short | Maths in chemistry |
| title_sort | maths in chemistry numerical methods for physical and analytical chemistry |
| title_sub | numerical methods for physical and analytical chemistry |
| topic | Physikalische Chemie (DE-588)4045959-7 gnd Funktion Mathematik (DE-588)4071510-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Statistik (DE-588)4056995-0 gnd Analytische Chemie (DE-588)4129906-1 gnd |
| topic_facet | Physikalische Chemie Funktion Mathematik Numerisches Verfahren Statistik Analytische Chemie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032301694&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bansalprerna mathsinchemistrynumericalmethodsforphysicalandanalyticalchemistry AT walterdegruytergmbhcokg mathsinchemistrynumericalmethodsforphysicalandanalyticalchemistry |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 VC 6100 B219 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |