Mathematics 252 - Chemistry 302 Mathematics for Chemistry II.

Mathematics 252 - Chemistry 302Mathematics 252 - Chemistry 302Mathematics for Chemistry IIMathematics for Chemistry II

Math 252 – Chem 302• Instructor: Dr. D. Keefe

Office TC-107 / TC-137 (laboratory)Phone 563-1185 / 1462 (laboratory)email: [email protected]

• Lectures: T 10:00 – 11:15 amTh 8:30 – 9:45 am

• Laboratories: TBA. • Mark Structure

– Laboratories / Assignments 40%– Term Tests 30%– Final Exam 30%

Math 252 – Chem 302• Syllabus

– Solutions of nonlinear equations– Solutions of systems of linear equations (matrix inversion)– Interpolation / extrapolation– Integration– Least squares regression

• linear• nonlinear

– Differential equations– Matrix eigenvalue-eigenvector problems

Math 252 – Chem 302

• Term Testsweek of Feb 11 – 15week of Mar 17 – 21

– must be written on the day they are scheduled. • 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

• Supplementary ExaminationSupplementary Examinations are NOT available for this course.

• Office HoursTBA

• WebsiteAssignments, copies of lecture transparencies and other course materials are posted athttp://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

– 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 (on/off)

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

– 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 SystemsDecimal Binary Octal Hexadecimal

0 0 0 01 1 1 12 10 2 23 11 3 34 100 4 45 101 5 56 110 6 67 111 7 78 1000 10 89 1001 11 910 1010 12 A11 1011 13 B12 1100 14 C13 1101 15 D14 1110 16 E15 1111 17 F

Number SystemsDecimal Binary Octal Hexadecimal

16 10000 20 1017 10001 21 1118 10010 22 1219 10011 23 1320 10100 24 1421 10101 25 1522 10110 26 1623 10111 27 1724 11000 30 1825 11001 31 1926 11010 32 1A27 11011 33 1B28 11100 34 1C29 11101 35 1D30 11110 36 1E31 11111 37 1F

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 track of

integer part 1011.25

211 R

5 1

2 1

1 0

0 1

0 .25 2

0 .50

1 .00 10 211.25 1011.01

Converting between number systems 10668.71875

8 668 R

83 4

10 3

1 2

0 1

0 .71875 8

5 .75

6 .00 10 8668.71875 1234.56

106900.7734375

16 6900 R

431 4

26 15

1 10

0 1

0 .773437516

12 .375

6 .000

10 166900.7734375 1AF4.C6

Converting between number systems 101234.567

21234 R

617 0

308 1

154 0

77 0

38 1

19 0

9 1

4 1

2 0

1 0

0 1

0 .567 2

1 .134

0 .268

0 .536

1 .072

0 .144

0 .288

0 .576

1 .152

10 21234.567 10011010010.10010001...

Converting between number systems

100.1

0 .1 2

0 .2

0 .4

0 .8

1 .6

1 .2

10 20.1 0.000110011...

Converting between number systems

Between Binary, Octal, & Hexadecimal8=23 (use 3 binary digits for one octal digit)

16=24 (use 4 binary digits for one hexadecimal digit)

2

2

8

1010011100.10111

1 010 011100.101110

1234.56

2

2

16

1010011100.10111

10 10011100.10111000

29C.B8