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Mathematics 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 / 1462 (laboratory) 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

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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 – 1× × × × × ×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 –( ) 2 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 –( ) 8 1× × × × × ×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× A× F× × C× ×16 -2

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Number Systems DecimalBinaryOctalHexadecimal A B C D E F

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Number Systems DecimalBinaryOctalHexadecimal A B C D E F

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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 ( ) 2 =(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 ( ) 8 =(1× × × × × ×8 -2 ) 8 =(1× ×64 + 3×8 + 4×1 + 5/8 + 6/64) 10 =( ) 10 (1AF4.C6) 16 =(1× A× F× × C× ×16 -2 ) 16 =(1× × ×16 + 4×1 + 12/16 + 6/256) 10 =( ) 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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