Preparing for University Calculus - Math and Computer Science

More documents

Recommendations

Info

Some useful facts:Algebraic identitiesa 2 − b 2 =(a + b)(a − b) (a + b) 2 = a 2 +2ab + b 2a 3 − b 3 =(a 2 + ab + b 2 )(a − b) a 3 + b 3 =(a 2 − ab + b 2 )(a + b)Exponential identitiesa x b x =(ab) xa x a y = a x+y(a b )(c = a) bc a −b =1/a b =(1/a) ba√ a√ aba =√ ab = b b = b 1/aa log a (b) = b ln(a) = log e (a), e =2.71828 ...log a (b) + log a (c) = log a (bc) log a (b) − log a (c) = log a (b/c)log a (b) log b (c) = log a (c)log a (1/b) =− log a (b)Trigonometric factsLet a triangle have sides of length a, b, c opposite angles A,B,C. ThenPythagoras’ Theorem: If C is right, a 2 + b 2 = c 2 .Sine Law: sin(A)/a = sin(B)/b = sin(C)/cCosine Law: c 2 = a 2 + b 2 − 2ab cos(C)Trigonometric identitiestan(α) = sin(α)/ cos(α)cot(α) = cos(α)/ sin(α)cot(α) =1/ tan(α)sec(α) =1/ cos(α)csc(α) =1/ sin(α)sin 2 (α)+cos 2 (α) =1sec 2 (α) − tan 2 (α) = 1 csc 2 (α) − cot 2 (α) =1sin(A + B) = sin(A) cos(B) + cos(A) sin(B)sin(A − B) = sin(A) cos(B) − cos(A) sin(B)cos(A + B) = cos(A) cos(B) − sin(A) sin(B)cos(A − B) = cos(A) cos(B) + sin(A) sin(B)tan(A + B) =tan(A) + tan(B)1 − tan(A) tan(B)tan(A − B) =tan(A) − tan(B)1 + tan(A) tan(B)
Ordering informationGetting a copy freePlease note, this is the truly cool way to get this booklet (and saves us time).• This document may be downloaded in Adobe PDF or PostScript format fromthe Web, at our websitehttp://cs.smu.ca/apics/calculus/welcome.php .This site also contains links to free software that will allow you to display andprint the document.• Individuals are hereby granted permission to make photocopies of this documentfor their personal use at no charge, provided they include the entire textincluding the cover, title page, and this page. Please verify that the editionyou copy is not out of date.If all else fails, send money• Booklets can be purchased in small quantities (1 to 4) at $2 each fromCALCULUS BOOKLETc/o Department of Mathematics and Computing ScienceSaint Mary’s UniversityHalifax, Nova ScotiaB3H 3C3Please send cheque or money order made out to “Department of Mathematicsand Computing Science, Saint Mary’s University”. We cannot process creditcards or ship COD.• Booklets can be purchased in bulk from the same address for $10 for 10booklets. Please email rdawson@husky1.stmarys.ca for pricing on ordersover 500.
Page 1 and 2: Preparing for University CalculusPr
Page 3 and 4: 1 About First-Year Calculus1.1 What
Page 5 and 6: 1.5 What is taking university calcu
Page 7 and 8: • Your university or student unio
Page 9 and 10: 2 Ordering informationGetting a cop
Page 11 and 12: Problems: (answers on page 40)1. Fi
Page 13 and 14: Problems: (answers on page 40)1. Si
Page 15 and 16: Problems: (answers on page 40)1. If
Page 17 and 18: Problems: (answers on page 40)1. If
Page 19 and 20: Problems: (answers on page 40)1. So
Page 21 and 22: Problems: (answers on page 40)11. S
Page 23 and 24: Problems: (answers on page 40)1. Ra
Page 25 and 26: Problems: (answers on page 40)1. Fi
Page 28 and 29: 3.10 Exponents and rootsYou should
Page 30 and 31: 3.11 LogarithmsLogarithms are extre
Page 32 and 33: 3.12 Geometry and basic trigonometr
Page 34 and 35: 3.13 Trigonometric identitiesThere
Page 36 and 37: 3.14 Problem solvingSolving applied
Page 38 and 39: 3.14159265358979... Harder Problems
Page 40 and 41: Answers to problems:Section 3.1 (1)

Preparing for University Calculus - Math and Computer Science

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?