Transcript Mathematics 252 - Chemistry 302 Mathematics for Chemistry II Math 252 – Chem 302 • • • • Instructor: Dr.

Mathematics 252 - Chemistry 302
Mathematics for Chemistry II
Math 252 – Chem 302
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Instructor: Dr. D. Keefe
Office TC-107 / TC-137 (laboratory)
Phone 563-1185 / 1462 (laboratory)
email: [email protected]
Lectures:
T 10:00 – 11:15 am
Th 8:30 – 9:45 am
Laboratories: TBA.
Mark Structure
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Laboratories / Assignments
Term Tests
Final Exam
40%
30%
30%
Math 252 – Chem 302
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Syllabus
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Solutions of nonlinear equations
Solutions of systems of linear equations (matrix inversion)
Interpolation / extrapolation
Integration
Least squares regression
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linear
nonlinear
Differential equations
Matrix eigenvalue-eigenvector problems
Math 252 – Chem 302
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Term Tests
week of Feb 11 – 15
week of Mar 17 – 21
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must be written on the day they are scheduled.
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doctor’s certificate or other supporting document to be eligible for a
rewrite.
Otherwise a mark of 0 (zero) will be given for the test
University closed  test next scheduled lecture period.
Math 252 – Chem 302
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Supplementary Examination
Supplementary Examinations are NOT available for
this course.
Office Hours
TBA
Website
Assignments, copies of lecture transparencies and
other course materials are posted at
http://faculty.cbu.ca/dkeefe/chem302
Introduction
• Many problems in chemistry well suited for
solution on a microcomputer
– Kinetics
– Quantum chemistry
– Spectroscopy
• Complexity
• Repetition
Introduction
• Use
– Maple
• Commercial Mathematics software
– Microsoft Excel
• Spreadsheet with some numerical applications
– C++
• High-level programming language
• Write our own code
• Review Math 187 notes
Number Systems
• Understand how a computer stores information
• Decimal
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10 integers (0,1,2,3,4,5,6,7,8,9)
Decimal point
positive (+) & negative (-) signs
Digits to left of decimal point represent successive positive
powers of ten
– Digits to right of decimal point represent successive negative
powers of ten
– 1234.56
1×103 + 2 ×102 + 3 ×101 + 4 ×100 + 5 ×10-1 + 6 ×10-2
• Not practical for computers – based on binary states
Number Systems
• Binary – Base 2
– 2 integers (0,1)
– Binary point
– positive (+) & negative (-) signs
– Digits to left of binary point represent successive
positive powers of two
– Digits to right of binary point represent successive
negative powers of two
– (1011.01)2
1×23 + 0×22 + 1×21 + 1×20 + 0×2-1 + 1×2-2
Number Systems
• Octal – Base 8
– 8 integers (0,1,2,3,4,5,6,7)
– Octal point
– positive (+) & negative (-) signs
– Digits to left of octal point represent successive
positive powers of eight
– Digits to right of octal point represent successive
negative powers of eight
– (1234.56)8
1×83 + 2×82 + 3×81 + 4×80 + 5×8-1 + 6×8-2
Number Systems
• Hexadecimal – Base 16
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16 integers (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F)
Hexadecimal point
positive (+) & negative (-) signs
Digits to left of hexadecimal point represent successive
positive powers of sixteen
– Digits to right of hexadecimal point represent successive
negative powers of sixteen
– (1AF4.C6)16
1×163 + A×162 + F×161 + 4×160 + C×16-1 + 6×16-2
Number Systems
Decimal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Binary
0
1
10
11
100
101
110
111
1000
1001
1010
1011
1100
1101
1110
Octal
0
1
2
3
4
5
6
7
10
11
12
13
14
15
16
Hexadecimal
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
Number Systems
Decimal
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Binary
10000
10001
10010
10011
10100
10101
10110
10111
11000
11001
11010
11011
11100
11101
11110
Octal
20
21
22
23
24
25
26
27
30
31
32
33
34
35
36
Hexadecimal
10
11
12
13
14
15
16
17
18
19
1A
1B
1C
1D
1E
Converting between number systems
• Binary, Octal, Hexadecimal to Decimal
– Expand the powers of 2,8 or 16 into powers of 10
(1011.01)2
=(1×23 + 0×22 + 1×21 + 1×20 + 0×2-1 + 1×2-2)2
=(1×8 + 0×4 + 1×2 + 1×1 + 0/2 + 1/4)10
=(11.25)10
Converting between number systems
(1234.56)8
=(1×83 + 2×82 + 3×81 + 4×80 + 5×8-1 + 6×8-2)8
=(1×512 + 2×64 + 3×8 + 4×1 + 5/8 + 6/64)10
=(668.71875)10
(1AF4.C6)16
=(1×163 + A×162 + F×161 + 4×160 + C×16-1 + 6×16-2)16
=(1×4096 + 10×256 + 15×16 + 4×1 + 12/16 + 6/256)10
=(6900.7734375)10
Converting between number systems
• Decimal to Binary, Octal, Hexadecimal
– Convert the integer and fraction part separately
– Integer: successively divide by 2, 8 or 16 keeping
track of remainders
– Fraction: successively multiply by 2, 8 or 16 keeping
11.25of
 integer part
track
10
2 11
R
0
.25 2
5
1
0
.50
2
1
1
.00
1
0
0
1
 1 1 .2 5 1 0
  1 0 1 1 .0 1  2
Converting between number systems
 668.71875 10
8 668
R
0
.71875 8
83
4
5
.75
10
3
6
.00
1
2
0
1
 6 6 8 .7 1 8 7 5 1 0
 1 2 3 4 .5 6  8
 6 9 0 0 .7 7 3 4 3 7 5 1 0
R
0
.7734375 16
431
4
12
.375
26
15
6
.000
1
10
0
1
16 6900
 6 9 0 0 .7 7 3 4 3 7 5 1 0
  1 A F 4 .C 6 1 6
Converting between number systems
 1 2 3 4 .5 6 7 1 0
2 1234
R
617
0
308
1
154
0
77
0
38
1
19
0
9
1
4
1
2
0
1
0
0
1
0
.5 6 7 2
1
.1 3 4
0
.2 6 8
0
.5 3 6
1
.0 7 2
0
.1 4 4
0
.2 8 8
0
.5 7 6
1
.1 5 2
 1 2 3 4 .5 6 7 1 0
  1 0 0 1 1 0 1 0 0 1 0 .1 0 0 1 0 0 0 1 ...  2
Converting between number systems
 0 .1 1 0
0
.1 2
0
.2
0
.4
0
.8
1
.6
1
.2
 0 .1 1 0

 0 .0 0 0 1 10 0 1 1... 
2
Converting between number systems
Between Binary, Octal, & Hexadecimal
8=23 (use 3 binary digits for one octal digit)
16=24 (use 4 binary digits for one hexadecimal digit)
1010011100.10111  2
1010011100.10111  2
1 010
10 1001 1100.1011 1000  2
011 100.101 110  2
1234.56  8
 29C .B 8 16