Workshop 2 Math Functions Builtin mathematical functions Operators

Workshop 2: Math Functions

Built-in mathematical functions Operators Precedence +, -, *, / • Math operators: have different execution priorities • What would you expect from the following calculation: =1+2– 3*4/8 ? • Excel assigns priority to operators as follows: 1. 2. 3. (, ) * , / +, - highest priority lowest priority • Mathematics expressions are evaluated using these priorities Example: 1 + 2 – 3 * 4 / 8 = 1. 5 --> using priority 1 + 2 – 3 * 4 / 8 = 0 -- > left to right

Useful mathematical functions Balloon Behavior • The height and velocity of a hot-air balloon are described as: h(t) = - 0. 12 t 4 + 12 t 3 – 380 t 2 + 4100 t + 220 v(t) = - 0. 48 t 3 + 36 t 2 - 760 t + 4100 where t is a number of hour after launch, h(t) is in meter, v(t) is in m/hr • Create a table showing height (m) and velocity (m/s) of balloon in a period of 0 – 8 Hrs. Hr(s) Height (m) Velocity (m/s) 0 1 2 3 4 5 6 7 8

Useful mathematical functions Balloon Behavior • When will the balloon reach its highest altitude? Hr(s) Height (m) Velocity (m/s) 0 220 1. 14 1 3951. 88 0. 94 2 6994. 08 0. 76 3 9414. 28 0. 59 4 11277. 28 0. 45 5 12645 0. 32 6 13576. 48 0. 20 7 14127. 88 0. 11 8 14352. 48 0. 02 • This type of question usually arises, but how can we efficiently answer that? • Excel provide “Goal seek ” tool to help us • Goto main menu: Tool Goal seek…

Useful mathematical functions Balloon Behavior • At an altitude of 10000 m, how fast is the balloon climbing ? and how long does it take to reach that altitude? Hr(s) Height (m) Velocity (m/s) 0 220 1. 14 1 3951. 88 0. 94 2 6994. 08 0. 76 3 9414. 28 0. 59 4 11277. 28 0. 45 5 12645 0. 32 6 13576. 48 0. 20 7 14127. 88 0. 11 8 14352. 48 0. 02

Built-in mathematical functions Logarithmic & exponential functions

Built-in mathematical functions Logarithmic & exponential functions n Log 2 Loge Log 3 Log 10 en sinh(n) cosh(n) tanh(n) 1 0 0 2. 71828 1. 175201194 1. 543080635 0. 761594156 2 1 0. 693147181 0. 630929754 0. 301029996 7. 389056099 3. 626860408 3. 762195691 0. 96402758 3 1. 584962501 1. 098612289 1 0. 477121255 20. 08553692 10. 01787493 10. 067662 0. 995054754 4 2 1. 386294361 1. 261859507 0. 602059991 54. 59815003 27. 2899172 27. 30823284 0. 9993293 5 2. 321928095 1. 609437912 1. 464973521 0. 698970004 148. 4131591 74. 20321058 74. 20994852 0. 999909204 6 2. 584962501 1. 791759469 1. 630929754 0. 77815125 403. 4287935 201. 7131574 201. 7156361 0. 999987712 7 2. 807354922 1. 945910149 1. 771243749 0. 84509804 1096. 633158 548. 3161233 548. 3170352 0. 999998337 8 3 2. 079441542 1. 892789261 0. 903089987 2980. 957987 1490. 478826 1490. 479161 0. 999999775 9 3. 169925001 2. 197224577 2 0. 954242509 8103. 083928 4051. 541902 4051. 542025 0. 99999997 10 3. 321928095 2. 302585093 2. 095903274 1 22026. 46579 11013. 23287 11013. 23292 0. 99996

Built-in mathematical functions Trigonometry functions Also available: = RADIANS(degree) to convert deg. rad. = DEGREES(radian) to convert rad. deg. = PI( ) Pi constant

Built-in mathematical functions Matrix calculations Important: - The result appears on an active cell only - Use CTRL-SHIFT <ENTER> to copy array formula

Introduction to Microsoft Excel Solving linear equations [A][x] = [B] [x] = [A]-1[B] A = 3 2 -1 2 -2 4 -1 0. 5 -1 B = 1 -2 0