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Mathematics 252 - Chemistry 302 Mathematics for Chemistry II

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Math 252 – Chem 302 Instructor: Dr. D. Keefe Office TC-107 / TC-137 (laboratory) Phone 563-1185 / 1462 (laboratory) email: Dale_Keefe@cbu.ca Lectures: T 10:00 – 11:15 am Th 8:30 – 9:45 am Laboratories: TBA. Mark Structure –Laboratories / Assignments 40% –Term Tests30% –Final Exam30%

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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

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Math 252 – Chem 302 Term Tests week of Feb 11 – 15 week 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.

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Math 252 – Chem 302 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

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Introduction Many problems in chemistry well suited for solution on a microcomputer –Kinetics –Quantum chemistry –Spectroscopy Complexity Repetition

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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

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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 1×10 3 + 2 ×10 2 + 3 ×10 1 + 4 ×10 0 + 5 ×10 -1 + 6 ×10 -2 Not practical for computers – based on binary states (on/off)

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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 1×2 3 + 0×2 2 + 1×2 1 + 1×2 0 + 0×2 -1 + 1×2 -2

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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 1×8 3 + 2×8 2 + 3×8 1 + 4×8 0 + 5×8 -1 + 6×8 -2

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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 1×16 3 + A×16 2 + F×16 1 + 4×16 0 + C×16 -1 + 6×16 -2

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Number Systems DecimalBinaryOctalHexadecimal 0000 1111 21022 31133 410044 510155 611066 711177 81000108 91001119 10101012A 11101113B 12110014C 13110115D 14111016E 15111117F

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Number Systems DecimalBinaryOctalHexadecimal 16100002010 17100012111 18100102212 19100112313 20101002414 21101012515 22101102616 23101112717 24110003018 25110013119 2611010321A 2711011331B 2811100341C 2911101351D 3011110361E 3111111371F

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Converting between number systems Binary, Octal, Hexadecimal to Decimal –Expand the powers of 2,8 or 16 into powers of 10 (1011.01) 2 =(1×2 3 + 0×2 2 + 1×2 1 + 1×2 0 + 0×2 -1 + 1×2 -2 ) 2 =(1×8 + 0×4 + 1×2 + 1×1 + 0/2 + 1/4) 10 =(11.25) 10

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Converting between number systems (1234.56) 8 =(1×8 3 + 2×8 2 + 3×8 1 + 4×8 0 + 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 =(1×16 3 + A×16 2 + F×16 1 + 4×16 0 + C×16 -1 + 6×16 -2 ) 16 =(1×4096 + 10×256 + 15×16 + 4×1 + 12/16 + 6/256) 10 =(6900.7734375) 10

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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

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Converting between number systems

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Between Binary, Octal, & Hexadecimal 8=2 3 (use 3 binary digits for one octal digit) 16=2 4 (use 4 binary digits for one hexadecimal digit)

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Number Systems. 2 The total number of allowable symbols in a number system is called the radix or base of the system. Decimal Numbers: radix = 10 (symbols:

Number Systems. 2 The total number of allowable symbols in a number system is called the radix or base of the system. Decimal Numbers: radix = 10 (symbols:

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