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Search found 444 results on 18 pages for 'equation'.

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  • Convert latitude and longitude into northings and eastings

    - by Rippo
    Hi I have the following UK postcode dy8 3xt and know that the latitude and longitude is:- 54.452772 -2.156082 I also know that the Eastings, Northings for the postcode is:- 389490 283880 However I am struggling to find the equation that converts lat/long to northings and Eastings, I would prefer to have the equation in both in jScript and c# (I am being greedy)! Can anyone help? EDIT Thanks for your help so far guys, I am starting to learn something here esp. the terminology... Some more info, if you click on this link you can see the results I am looking for. The postcode I entered projects to lat/lng using WG S84 and the grid ref projects to OSGB. So my question is how is this done? WHAT I LEARNT Thanks to all that answered, I finally got led to here which I can confirm works great

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  • Matlab: how do I force ode45 to take steps of exactly 0.01 on the T axis?

    - by Gravitas
    I'm using Matlab to solve a differential equation. I want to force ode45 to take constant steps, so it always increments 0.01 on the T axis while solving the equation. How do I do this? ode45 is consistently taking optimized, random steps, and I can't seem to work out how to make it take consistent, small steps of 0.01. Here is the code: options= odeset('Reltol',0.001,'Stats','on'); %figure(1); %clf; init=[xo yo zo]'; tspan=[to tf]; %tspan = t0:0.01:tf; [T,Y]=ode45(name,tspan,init,options);

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  • Typesetting a large matrix in LaTeX

    - by Hooked
    I have a 3x12 matrix I'd like to input into my LaTeX (with amsmath) document but LaTeX seems to choke when the matrix gets larger then 3x10: \begin{equation} \textbf{e} = \begin{bmatrix} 1&1&1&1&0&0&0&0&-1&-1&-1&-1\\ 1&-1&0&0&1&1&-1&-1&0&0&1&-1\\ 0&0&1&-1&1&-1&1&-1&1&-1&0&0 \end{bmatrix} \end{equation} The error: Extra alignment tab has been changed to \cr. tells me that I have more & then the bmatrix environment can handle. Is there a proper way to handle this? Also it seems that the alignment for 1's and the -1's are different, is that also expected of the bmatrix?

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  • Finding the intersection of two vector equations.

    - by Matthew Mitchell
    I've been trying to solve this and I found an equation that gives the possibility of zero division errors. Not the best thing: v1 = (a,b) v2 = (c,d) d1 = (e,f) d2 = (h,i) l1: v1 + ?d1 l2: v2 + µd2 Equation to find vector intersection of l1 and l2 programatically by re-arranging for lambda. (a,b) + ?(e,f) = (c,d) + µ(h,i) a + ?e = c + µh b +?f = d + µi µh = a + ?e - c µi = b +?f - d µ = (a + ?e - c)/h µ = (b +?f - d)/i (a + ?e - c)/h = (b +?f - d)/i a/h + ?e/h - c/h = b/i +?f/i - d/i ?e/h - ?f/i = (b/i - d/i) - (a/h - c/h) ?(e/h - f/i) = (b - d)/i - (a - c)/h ? = ((b - d)/i - (a - c)/h)/(e/h - f/i) Intersection vector = (a + ?e,b + ?f) Not sure if it would even work in some cases. I haven't tested it. I need to know how to do this for values as in that example a-i. Thank you.

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  • How to read in a negative double with scanf() in C

    - by rize
    I'm learning basics of C and writing a simple first order equation solver. I want the input to be exactly ax+b=c or ax-b=c, where a, b, c are double type. I'm employing scanf() to read in user input and to check if it's of the correct form. However, if I enter a negative double, -4.6 say, as the "a" in the equation, scanf() won't read the a,b,c correctly. I'm using %lf inside scanf(). How do I read a negative double, then? Many thanks. My code: if (scanf("%lfx+%lf=%lf", &a, &b, &c)) more code If I use as the input "-6.2x+3.4=-5.9", the value 3.4 will be assinged to variable a, while b and c remain as they were and "more code" is run.

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  • getting the value of a filter at an arbitrary time

    - by Andiih
    Context: I'm trying to improve the values returned by the iPhone CLLocationManager, although this is a more generally applicable problem. The key is that CLLocationManger returns data on current velocity as and when it feels like it, rather than at a fixed sample rate. I'd like to use a feedback equation to improve accuracy v=(k*v)+(1-k)*currentVelocity where currentVelocity is the speed returned by didUpdateToLocation:fromLocation: and v is the output velocity (and also used for the feedback element). Because of the "as and when" nature of didUpdateToLocation:fromLocation: I could calculate the time interval since it was last called, and do something like for (i=0;i<timeintervalsincelastcalled;i++) v=(k*v)+(1-k)*currentVelocity which would work, but is wasteful of cycles. Especially as I probably want timeintervalsincelastcalled to be measured as 10ths of a second. Is there a way to solve this without the loop ? i.e. rework (integrate?) the formula so I put an interval into the equation and get the same answer as I would have by iteration ?

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  • How to customize notches in ggplot boxplot

    - by cjy8709
    I had a question on how to change/customize the upper and lower limit of a notch on a boxplot created by ggplot2. I looked through the function stat_boxplot and found that ggplot calculates the notch limits with the equation median +/- 1.58 * iqr / sqrt(n). However instead of that equation I wanted to change it with my own set of upper and lower notch limits. My data has 4 factors and for each factor I calculated the median and did a bootstrap to get a 95% confidence interval of that median. Thus in the end I would like to change every boxplot to have its own unique notch upper and lower limit. I'm not sure if this is even possible in ggplot and was wondering if people have an idea on how to do this? Thanks again!

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  • How to move a directional light according to the camera movement?

    - by Andrea Benedetti
    Given a light direction, how can I move it according to the camera movement, in a shader? Think that an artist has setup a scene (e.g., in 3DSMax) with a mesh in center of that and a directional light with a position and a target. From this position and target I've calculated the light direction. Now I want to use the same direction in my lighting equation but, obviously, I want that this light moves correctly with the camera. Thanks.

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  • What Precalculus knowledge is required before learning Discrete Math Computer Science topics?

    - by Ein Doofus
    Below I've listed the chapters from a Precalculus book as well as the author recommended Computer Science chapters from a Discrete Mathematics book. Although these chapters are from two specific books on these subjects I believe the topics are generally the same between any Precalc or Discrete Math book. What Precalculus topics should one know before starting these Discrete Math Computer Science topics?: Discrete Mathematics CS Chapters 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations 3.1 Algorithms 3.2 The Growths of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.8 Matrices 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.6 Generating Permutations and Combinations 6.1 An Introduction to Discrete Probability 6.4 Expected Value and Variance 7.1 Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.5 Inclusion-Exclusion 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.5 Equivalence Relations 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Ptahs 10.1 Introduction to Trees 10.2 Application of Trees 10.3 Tree Traversal 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits 12.1 Language and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines Precalculus Chapters R.1 The Real-Number System R.2 Integer Exponents, Scientific Notation, and Order of Operations R.3 Addition, Subtraction, and Multiplication of Polynomials R.4 Factoring R.5 Rational Expressions R.6 Radical Notation and Rational Exponents R.7 The Basics of Equation Solving 1.1 Functions, Graphs, Graphers 1.2 Linear Functions, Slope, and Applications 1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression 1.4 More on Functions 1.5 Symmetry and Transformations 1.6 Variation and Applications 1.7 Distance, Midpoints, and Circles 2.1 Zeros of Linear Functions and Models 2.2 The Complex Numbers 2.3 Zeros of Quadratic Functions and Models 2.4 Analyzing Graphs of Quadratic Functions 2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression 2.6 Zeros and More Equation Solving 2.7 Solving Inequalities 3.1 Polynomial Functions and Modeling 3.2 Polynomial Division; The Remainder and Factor Theorems 3.3 Theorems about Zeros of Polynomial Functions 3.4 Rational Functions 3.5 Polynomial and Rational Inequalities 4.1 Composite and Inverse Functions 4.2 Exponential Functions and Graphs 4.3 Logarithmic Functions and Graphs 4.4 Properties of Logarithmic Functions 4.5 Solving Exponential and Logarithmic Equations 4.6 Applications and Models: Growth and Decay 5.1 Systems of Equations in Two Variables 5.2 System of Equations in Three Variables 5.3 Matrices and Systems of Equations 5.4 Matrix Operations 5.5 Inverses of Matrices 5.6 System of Inequalities and Linear Programming 5.7 Partial Fractions 6.1 The Parabola 6.2 The Circle and Ellipse 6.3 The Hyperbola 6.4 Nonlinear Systems of Equations

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  • Layout of mathematical views (iOS)

    - by William Jockusch
    I am trying to figure out the right way to encapsulate graphical information about mathematical objects. It is not simple. For example, a matrix can include square brackets around its entries, or not. Some things carry down to sub-objects -- for example, a matrix might track the font size to be used by its entries. Similarly, the font color and the background color would carry down to the entries. Other things do not carry down. For example, the entries of the matrix do not need to know whether or not the matrix has those square brackets. Based on all of the above, I need to calculate sizes for everything, then frames. All of this can depend on the properties stored above. The size of a matrix depends on the sizes of its entries, and also on whether or not it has those brackets. What I am having a hard time with is not the individual ways to calculate sensible frames for this or that. It is the overall organizational structure of the whole thing. How can I keep track of it all without going crazy. One particular obstacle is worth mentioning -- for reasons I don't want to go into here, I need to calculate the sizes and frames for everything before I instantiate any actual views. So, for example, if I have a Matrix object, I need to calculate its size before I make a MatrixView. If I have an equation, I need to calculate the size of the view for the equation before I create the actual view. So I clearly need separate objects for those calculations. But I can't figure out a sensible class structure for those objects. If I put them all into a single class, I get some advantages because copying then becomes easy. But I also end up with a bloated class that contains info that is irrelevant for some objects -- such as whether or not to include those brackets around the matrix. But if I use a lot of different classes, copying properties becomes a real pain. If it matters, this is all in Objective C, for an iOS environment. Any pointers would be greatly appreciated.

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  • Finding vectors with two points

    - by Christian Careaga
    We're are trying to get the direction of a projectile but we can't find out how For example: [1,1] will go SE [1,-1] will go NE [-1,-1] will go NW and [-1,1] will go SW we need an equation of some sort that will take the player pos and the mouse pos and find which direction the projectile needs to go. Here is where we are plugging in the vectors: def update(self): self.rect.x += self.vector[0] self.rect.y += self.vector[1] Then we are blitting the projectile at the rects coords.

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  • Checking timeouts made more readable

    - by Markus
    I have several situations where I need to control timeouts in a technical application. Either in a loop or as a simple check. Of course – handling this is really easy, but none of these is looking cute. To clarify, here is some C# (Pseudo) code: private DateTime girlWentIntoBathroom; girlWentIntoBathroom = DateTime.Now; do { // do something } while (girlWentIntoBathroom.AddSeconds(10) > DateTime.Now); or if (girlWentIntoBathroom.AddSeconds(10) > DateTime.Now) MessageBox.Show("Wait a little longer"); else MessageBox.Show("Knock louder"); Now I was inspired by something a saw in Ruby on StackOverflow: Now I’m wondering if this construct can be made more readable using extension methods. My goal is something that can be read like “If girlWentIntoBathroom is more than 10 seconds ago” 1st attempt if (girlWentIntoBathroom > (10).Seconds().Ago()) MessageBox.Show("Wait a little longer"); else MessageBox.Show("Knock louder"); So I wrote an extension for integer that converts the integer into a TimeSpan public static TimeSpan Seconds(this int amount) { return new TimeSpan(0, 0, amount); } After that, I wrote an extension for TimeSpan like this: public static DateTime Ago(this TimeSpan diff) { return DateTime.Now.Add(-diff); } This works fine so far, but has a great disadvantage. The logic is inverted! Since girlWentIntoBathroom is a timestamp in the past, the right side of the equation needs to count backwards: impossible. Just inverting the equation is no solution, because it will invert the read sentence as well. 2nd attempt So I tried something new: if (girlWentIntoBathroom.IsMoreThan(10).SecondsAgo()) MessageBox.Show("Knock louder"); else MessageBox.Show("Wait a little longer"); IsMoreThan() needs to transport the past timestamp as well as the span for the extension SecondsAgo(). It could be: public static DateWithIntegerSpan IsMoreThan(this DateTime baseTime, int span) { return new DateWithIntegerSpan() { Date = baseTime, Span = span }; } Where DateWithIntegerSpan is simply: public class DateWithIntegerSpan { public DateTime Date {get; set;} public int Span { get; set; } } And SecondsAgo() is public static bool SecondsAgo(this DateWithIntegerSpan dateAndSpan) { return dateAndSpan.Date.Add(new TimeSpan(0, 0, dateAndSpan.Span)) < DateTime.Now; } Using this approach, the English sentence matches the expected behavior. But the disadvantage is, that I need a helping class (DateWithIntegerSpan). Has anyone an idea to make checking timeouts look more cute and closer to a readable sentence? Am I a little too insane thinking about something minor like this?

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  • fast 3d point -> cuboid volume intersection test

    - by user1130477
    Im trying to test whether a point lies within a 3d volume defined by 8 points. I know I can use the plane equation to check that the signed distance is always -1 for all 6 sides, but does anyone know of a faster way or could point me to some code? Thanks EDIT: I should add that ideally the test would produce 3 linear interpolation parameters which would lie in the range 0..1 to indicate that the point is within the volume for each axis (since I will have to calculate these later if the point is found to be in the volume)

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  • How do you enable webcam support in facebook for ubuntu 10.04?

    - by Jonathan
    I think I have finally arrived at an insolvable equation: Chromium v.7 + Ubuntu 10.04 + Sun Java 6 + Webcam + Facebook + Flash 10 = non-functional All of those items listed above are potential points of failure in this situation, and any help narrowing them down would be fantastic. I am simply trying to enable webcame support directly through Facebooks website. Forum searches and the usual googling turn up few posts related to this specific equation. Two of the major suggestions include: 1) Installing the Sun (I refuse to say oracle sob)-provided Java implementation instead of the OpenJDK normally installed in ubuntu. And yes, after installing it, I did update all my default supports to use the sun commands over the openjdk. 2) Somehow enabling Facebook as a permitted site to access my webcam using Flash settings. I have not been able to explore option 2 because I cannot find a way to adjust the Flash settings in chromium 7. Other factors that do not help include the fact that I am pretty sure facebook changes its webcam interface every 10 seconds just to keep troubleshooters and support personnel on their toes. If anyone has a OTP that informs us of the next shift in the app, a leak would be greatly appreciated! Cheers!

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  • How do you enable webcam support in Facebook for Ubuntu 10.04?

    - by Jonathan
    I think I have finally arrived at an insolvable equation: Chromium v.7 + Ubuntu 10.04 + Sun Java 6 + Webcam + Facebook + Flash 10 = non-functional All of those items listed above are potential points of failure in this situation, and any help narrowing them down would be fantastic. I am simply trying to enable webcame support directly through Facebooks website. Forum searches and the usual googling turn up few posts related to this specific equation. Two of the major suggestions include: 1) Installing the Sun (I refuse to say oracle sob)-provided Java implementation instead of the OpenJDK normally installed in Ubuntu. And yes, after installing it, I did update all my default supports to use the sun commands over the openjdk. 2) Somehow enabling Facebook as a permitted site to access my webcam using Flash settings. I have not been able to explore option 2 because I cannot find a way to adjust the Flash settings in chromium 7. Other factors that do not help include the fact that I am pretty sure facebook changes its webcam interface every 10 seconds just to keep troubleshooters and support personnel on their toes. If anyone has a OTP that informs us of the next shift in the app, a leak would be greatly appreciated!

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  • How much is a subscriber worth?

    - by Tom Lewin
    This year at Red Gate, we’ve started providing a way to back up SQL Azure databases and Azure storage. We decided to sell this as a service, instead of a product, which means customers only pay for what they use. Unfortunately for us, it makes figuring out revenue much trickier. With a product like SQL Compare, a customer pays for it, and it’s theirs for good. Sure, we offer support and upgrades, but, fundamentally, the sale is a simple, upfront transaction: we’ve made this product, you need this product, we swap product for money and everyone is happy. With software as a service, it isn’t that easy. The money and product don’t change hands up front. Instead, we provide a service in exchange for a recurring fee. We know someone buying SQL Compare will pay us $X, but we don’t know how long service customers will stay with us, or how much they will spend. How do we find this out? We use lifetime value analysis. What is lifetime value? Lifetime value, or LTV, is how much a customer is worth to the business. For Entrepreneurs has a brilliant write up that we followed to conduct our analysis. Basically, it all boils down to this equation: LTV = ARPU x ALC To make it a bit less of an alphabet-soup and a bit more understandable, we can write it out in full: The lifetime value of a customer equals the average revenue per customer per month, times the average time a customer spends with the service Simple, right? A customer is worth the average spend times the average stay. If customers pay on average $50/month, and stay on average for ten months, then a new customer will, on average, bring in $500 over the time they are a customer! Average spend is easy to work out; it’s revenue divided by customers. The problem comes when we realise that we don’t know exactly how long a customer will stay with us. How can we figure out the average lifetime of a customer, if we only have six months’ worth of data? The answer lies in the fact that: Average Lifetime of a Customer = 1 / Churn Rate The churn rate is the percentage of customers that cancel in a month. If half of your customers cancel each month, then your average customer lifetime is two months. The problem we faced was that we didn’t have enough data to make an estimate of one month’s cancellations reliable (because barely anybody cancels)! To deal with this data problem, we can take data from the last three months instead. This means we have more data to play with. We can still use the equation above, we just need to multiply the final result by three (as we worked out how many three month periods customers stay for, and we want our answer to be in months). Now these estimates are likely to be fairly unreliable; when there’s not a lot of data it pays to be cautious with inference. That said, the numbers we have look fairly consistent, and it’s super easy to revise our estimates when new data comes in. At the very least, these numbers give us a vague idea of whether a subscription business is viable. As far as Cloud Services goes, the business looks very viable indeed, and the low cancellation rates are much more than just data points in LTV equations; they show that the product is working out great for our customers, which is exactly what we’re looking for!

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  • Efficient Multiple Linear Regression in C# / .Net

    - by mrnye
    Does anyone know of an efficient way to do multiple linear regression in C#, where the number of simultaneous equations may be in the 1000's (with 3 or 4 different inputs). After reading this article on multiple linear regression I tried implementing it with a matrix equation: Matrix y = new Matrix( new double[,]{{745}, {895}, {442}, {440}, {1598}}); Matrix x = new Matrix( new double[,]{{1, 36, 66}, {1, 37, 68}, {1, 47, 64}, {1, 32, 53}, {1, 1, 101}}); Matrix b = (x.Transpose() * x).Inverse() * x.Transpose() * y; for (int i = 0; i < b.Rows; i++) { Trace.WriteLine("INFO: " + b[i, 0].ToDouble()); } However it does not scale well to the scale of 1000's of equations due to the matrix inversion operation. I can call the R language and use that, however I was hoping there would be a pure .Net solution which will scale to these large sets. Any suggestions? EDIT #1: I have settled using R for the time being. By using statconn (downloaded here) I have found it to be both fast & relatively easy to use this method. I.e. here is a small code snippet, it really isn't much code at all to use the R statconn library (note: this is not all the code!). _StatConn.EvaluateNoReturn(string.Format("output <- lm({0})", equation)); object intercept = _StatConn.Evaluate("coefficients(output)['(Intercept)']"); parameters[0] = (double)intercept; for (int i = 0; i < xColCount; i++) { object parameter = _StatConn.Evaluate(string.Format("coefficients(output)['x{0}']", i)); parameters[i + 1] = (double)parameter; }

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  • Accurate least-squares fit algorithm needed

    - by ggkmath
    I've experimented with the two ways of implementing a least-squares fit (LSF) algorithm shown here. The first code is simply the textbook approach, as described by Wolfram's page on LSF. The second code re-arranges the equation to minimize machine errors. Both codes produce similar results for my data. I compared these results with Matlab's p=polyfit(x,y,1) function, using correlation coefficients to measure the "goodness" of fit and compare each of the 3 routines. I observed that while all 3 methods produced good results, at least for my data, Matlab's routine had the best fit (the other 2 routines had similar results to each other). Matlab's p=polyfit(x,y,1) function uses a Vandermonde matrix, V (n x 2 matrix) and QR factorization to solve the least-squares problem. In Matlab code, it looks like: V = [x1,1; x2,1; x3,1; ... xn,1] % this line is pseudo-code [Q,R] = qr(V,0); p = R\(Q'*y); % performs same as p = V\y I'm not a mathematician, so I don't understand why it would be more accurate. Although the difference is slight, in my case I need to obtain the slope from the LSF and multiply it by a large number, so any improvement in accuracy shows up in my results. For reasons I can't get into, I cannot use Matlab's routine in my work. So, I'm wondering if anyone has a more accurate equation-based approach recommendation I could use that is an improvement over the above two approaches, in terms of rounding errors/machine accuracy/etc. Any comments appreciated! thanks in advance.

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  • Attempting my first fortran 95 program, to solve quadratic eqn. Getting weird errors.

    - by Damon
    So, I'm attempting my first program in Fortran, trying to solve quadratic eqn. I have double and triple checked my code and don't see anything wrong. I keep getting "Invalid character in name at (1)" and "Unclassifiable statement at (1)" at various locations. Any help would be greatly appreciated... ! This program solves quadratic equations ! of the form ax^2 + bx + c = 0. ! Record: ! Name: Date: Notes: ! Damon Robles 4/3/10 Original Code PROGRAM quad_solv IMPLICIT NONE ! Variables REAL :: a, b, c REAL :: discrim, root1, root2, COMPLEX :: comp1, comp2 CHARACTER(len=1) :: correct ! Prompt user for coefficients. WRITE(*,*) "This program solves quadratic equations " WRITE(*,*) "of the form ax^2 + bx + c = 0. " WRITE(*,*) "Please enter the coefficients a, b, and " WRITE(*,*) "c, separated by commas:" READ(*,*) a, b, c WRITE(*,*) "Is this correct: a = ", a, " b = ", b WRITE(*,*) " c = ", c, " [Y/N]? " READ(*,*) correct IF correct = N STOP IF correct = Y THEN ! Definition discrim = b**2 - 4*a*c ! Calculations IF discrim > 0 THEN root1 = (-b + sqrt(discrim))/(2*a) root2 = (-b - sqrt(discrim))/(2*a) WRITE(*,*) "This equation has two real roots. " WRITE(*,*) "x1 = ", root1 WRITE(*,*) "x2 = ", root2 IF discrim = 0 THEN root1 = -b/(2*a) WRITE(*,*) "This equation has a double root. " WRITE(*,*) "x1 = ", root1 IF discrim < 0 THEN comp1 = (-b + sqrt(discrim))/(2*a) comp2 = (-b - sqrt(discrim))/(2*a) WRITE(*,*) "x1 = ", comp1 WRITE(*,*) "x2 = ", comp2 PROGRAM END quad_solv Thanks in advance!

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  • LaTex, align alignment characters between align blocks

    - by ccook
    I would like to align two alignment characters between two align blocks so that I can have some text in the middle of a derivation with equations maintaining the horizontal alignment. For example the following excerpt of latex using align \begin{align*} \frac{\delta \phi}{\delta x_1} = {} &\frac{9}{8}\frac{\delta_1\phi}{\delta_1x_1}-\frac{1}{8}\frac{\delta_3\phi}{\delta_3x_1} \\ & \frac{9}{8}\frac{1}{h_1}\left[\phi(x_1+h_1/2)-\phi(x_i-h_1/2)\right]-\frac{1}{8}\frac{1}{3h_1}\left[\phi(x_i+3h_1/2)-\phi(x_1-3h_1/2)\right] \end{align*} some text in the middle \begin{align*} & \frac{9}{8}\frac{1}{h_1}\left[\phi(x_1+h_1/2)-\phi(x_i-h_1/2)\right]-\frac{1}{8}\frac{1}{3h_1}\left[\phi(x_i+3h_1/2)-\phi(x_1-3h_1/2)\right] \end{align*} Ideally I would like the left of the equation in the second block to line up with that of the second equation in the first block. I could do a workaround by not having text in the middle, however, I would like this functionality. EDIT I would like to have a good amount of text between. Say three to four lines that line up as normal paragraphs. Adding text in the alignment block is the workaround I poorly alluded to.

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  • Scheme Infix to Postfix

    - by Cody
    Let me establish that this is part of a class assignment, so I'm definitely not looking for a complete code answer. Essentially we need to write a converter in Scheme that takes a list representing a mathematical equation in infix format and then output a list with the equation in postfix format. We've been provided with the algorithm to do so, simple enough. The issue is that there is a restriction against using any of the available imperative language features. I can't figure out how to do this in a purely functional manner. This is our fist introduction to functional programming in my program. I know I'm going to be using recursion to iterate over the list of items in the infix expression like such. (define (itp ifExpr) ( ; do some processing using cond statement (itp (cdr ifExpr)) )) I have all of the processing implemented (at least as best I can without knowing how to do the rest) but the algorithm I'm using to implement this requires that operators be pushed onto a stack and used later. My question is how do I implement a stack in this function that is available to all of the recursive calls as well?

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