# Mathematics 252 - Chemistry 302 Mathematics for Chemistry II.

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Mathematics 252 - Chemistry 302 Mathematics for Chemistry II

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%

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 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.

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

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  1×10 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)

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

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

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

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

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

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

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

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

Converting between number systems

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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