diff --git a/.gitignore b/.gitignore
index adb2aef..089c1bf 100644
--- a/.gitignore
+++ b/.gitignore
@@ -2,4 +2,3 @@
 *.jl.cov
 *.jl.mem
 .DS_Store
-/Manifest.toml
diff --git a/Manifest.toml b/Manifest.toml
new file mode 100644
index 0000000..4f01be6
--- /dev/null
+++ b/Manifest.toml
@@ -0,0 +1,614 @@
+# This file is machine-generated - editing it directly is not advised
+
+[[AbstractFFTs]]
+deps = ["LinearAlgebra", "Test"]
+git-tree-sha1 = "dfaf23dba016254bb0eed6de326510caea2889bf"
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+
+[[ApproXD]]
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+repo-rev = "master"
+repo-url = "https://github.com/floswald/ApproXD.jl.git"
+uuid = "f0e97480-066f-5960-9ba5-e027352bc8af"
+version = "0.1.0"
+
+[[ApproxFun]]
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+
+[[ArnoldiMethod]]
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+[[Base64]]
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+
+[[BasisMatrices]]
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+[[BinDeps]]
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+[[BlockBandedMatrices]]
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+[[Plots]]
+deps = ["Base64", "Contour", "Dates", "FixedPointNumbers", "GR", "JSON", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "Reexport", "Requires", "Showoff", "SparseArrays", "StaticArrays", "Statistics", "StatsBase", "Test", "UUIDs"]
+git-tree-sha1 = "5bcc6dbc8b7fe0823d9a63dde87d7d4542149693"
+uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
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+
+[[Polynomials]]
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+[[PositiveFactorizations]]
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+[[Primes]]
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+
+[[Printf]]
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+
+[[Profile]]
+deps = ["Printf"]
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+
+[[ProgressMeter]]
+deps = ["Distributed", "Printf", "Random", "Test"]
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+version = "0.9.0"
+
+[[PyCall]]
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+git-tree-sha1 = "5a65d9bfd7099c2baa13d2aecf3cde752092a95b"
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+[[PyPlot]]
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+git-tree-sha1 = "3ea391c3211f799df20396d256cee5c8bd755605"
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+
+[[QuadGK]]
+deps = ["DataStructures", "LinearAlgebra", "Test"]
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+uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
+version = "2.0.3"
+
+[[QuantEcon]]
+deps = ["DSP", "Distributions", "FFTW", "LightGraphs", "LinearAlgebra", "Markdown", "NLopt", "Optim", "Pkg", "Primes", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "Test"]
+git-tree-sha1 = "d1f545bef50bbd83b04abbaf3e226e04cde34b9c"
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+[[REPL]]
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+
+[[Random]]
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+[[RecipesBase]]
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+
+[[Reexport]]
+deps = ["Pkg"]
+git-tree-sha1 = "7b1d07f411bc8ddb7977ec7f377b97b158514fe0"
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+
+[[Requires]]
+deps = ["Test"]
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+uuid = "ae029012-a4dd-5104-9daa-d747884805df"
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+
+[[Rmath]]
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+git-tree-sha1 = "9a6c758cdf73036c3239b0afbea790def1dabff9"
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+[[SHA]]
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+
+[[Serialization]]
+uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
+
+[[SharedArrays]]
+deps = ["Distributed", "Mmap", "Random", "Serialization"]
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+
+[[Showoff]]
+deps = ["Compat"]
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+[[SimpleTraits]]
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+version = "0.8.0"
+
+[[Sockets]]
+uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
+
+[[SortingAlgorithms]]
+deps = ["DataStructures", "Random", "Test"]
+git-tree-sha1 = "03f5898c9959f8115e30bc7226ada7d0df554ddd"
+uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
+version = "0.3.1"
+
+[[SparseArrays]]
+deps = ["LinearAlgebra", "Random"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[SpecialFunctions]]
+deps = ["BinDeps", "BinaryProvider", "Libdl", "Test"]
+git-tree-sha1 = "0b45dc2e45ed77f445617b99ff2adf0f5b0f23ea"
+uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
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+
+[[StaticArrays]]
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+
+[[Statistics]]
+deps = ["LinearAlgebra", "SparseArrays"]
+uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[[StatsBase]]
+deps = ["DataStructures", "DelimitedFiles", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "Test"]
+git-tree-sha1 = "435707791dc85a67d98d671c1c3fcf1b20b00f94"
+uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
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+
+[[StatsFuns]]
+deps = ["Rmath", "SpecialFunctions", "Test"]
+git-tree-sha1 = "b3a4e86aa13c732b8a8c0ba0c3d3264f55e6bb3e"
+uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+version = "0.8.0"
+
+[[SuiteSparse]]
+deps = ["Libdl", "LinearAlgebra", "SparseArrays"]
+uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
+
+[[Test]]
+deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
+uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[[ToeplitzMatrices]]
+deps = ["Compat", "FFTW", "LinearAlgebra", "StatsBase"]
+git-tree-sha1 = "5242fdbeafe1f2e0187935bb13a5c651d5626106"
+uuid = "c751599d-da0a-543b-9d20-d0a503d91d24"
+version = "0.5.0"
+
+[[Tokenize]]
+deps = ["Printf", "Test"]
+git-tree-sha1 = "3e83f60b74911d3042d3550884ca2776386a02b8"
+uuid = "0796e94c-ce3b-5d07-9a54-7f471281c624"
+version = "0.5.3"
+
+[[URIParser]]
+deps = ["Test", "Unicode"]
+git-tree-sha1 = "6ddf8244220dfda2f17539fa8c9de20d6c575b69"
+uuid = "30578b45-9adc-5946-b283-645ec420af67"
+version = "0.4.0"
+
+[[UUIDs]]
+deps = ["Random", "SHA"]
+uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
+
+[[Unicode]]
+uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
+
+[[VersionParsing]]
+deps = ["Compat"]
+git-tree-sha1 = "c9d5aa108588b978bd859554660c8a5c4f2f7669"
+uuid = "81def892-9a0e-5fdd-b105-ffc91e053289"
+version = "1.1.3"
diff --git a/Project.toml b/Project.toml
index 516f264..5fba901 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,6 +3,18 @@ uuid = "ce1ef771-b552-5ca6-80e4-7358b8c578e2"
 authors = ["Florian Oswald <florian.oswald@gmail.com>"]
 version = "0.1.0"
 
+[deps]
+ApproXD = "f0e97480-066f-5960-9ba5-e027352bc8af"
+ApproxFun = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
+BasisMatrices = "08854c51-b66b-5062-a90d-8e7ae4547a49"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+FastGaussQuadrature = "442a2c76-b920-505d-bb47-c5924d526838"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
+PyPlot = "d330b81b-6aea-500a-939a-2ce795aea3ee"
+SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
diff --git a/q1.png b/q1.png
new file mode 100644
index 0000000..e49e0f8
Binary files /dev/null and b/q1.png differ
diff --git a/q2.png b/q2.png
new file mode 100644
index 0000000..e16fc41
Binary files /dev/null and b/q2.png differ
diff --git a/q3.png b/q3.png
new file mode 100644
index 0000000..922d69c
Binary files /dev/null and b/q3.png differ
diff --git a/q7.png b/q7.png
new file mode 100644
index 0000000..b8bd338
Binary files /dev/null and b/q7.png differ
diff --git a/src/HWfuncapp.jl b/src/HWfuncapp.jl
index 732fe3f..b60db13 100644
--- a/src/HWfuncapp.jl
+++ b/src/HWfuncapp.jl
@@ -4,34 +4,127 @@ using FastGaussQuadrature # to get chebyshevnodes
 
 # you dont' have to use PyPlot. I did much of it in PyPlot, hence
 # you will see me often qualify code with `PyPlot.plot` or so.
-using PyPlot  
+# using PyPlot
 import ApproXD: getBasis, BSpline
 using Distributions
+using BasisMatrices
+using LinearAlgebra, SpecialFunctions
 using ApproxFun
 using Plots
 
+export q1, q2, q3, q7
+
 ChebyT(x,deg) = cos(acos(x)*deg)
 unitmap(x,lb,ub) = 2 .* (x .- lb) ./ (ub .- lb) .- 1	#[a,b] -> [-1,1]
+abmap(x,lb,ub) = 0.5 .* (ub .+ lb) .+ 0.5 .* (ub .- lb) .* x	# [-1,1] -> [a,b]
+function chebpol(x, n)
+	Φ = zeros(size(x,1),n) # chebyshev polynomials basis
+	for i in 1:size(x,1)
+		for j in 1:n
+			Φ[i,j] = ChebyT(x[i],j-1)
+			# Φ[i,j] = abmap(Φ[i,j], lb, ub)
+		end
+	end
+	return Φ
+end
 
-function q1(n)
-	f(x) = x .+ 2x.^2 - exp.(-x)
 
+function q1(n=15)
+	lb = -3
+	ub = 3
+	x = range(lb, stop = ub ,length = n)
+	# generate Chebyshev nodes
+	S, y = gausschebyshev(n)
+	# Scale Chebyshev nodes on -3 to 3 domain
+	ϕ = abmap(S, lb, ub) # Chebyshev nodes on -3, 3
+	# define function
+	f(x) = x .+ 2x.^2 - exp.(-x)
+	# Evaluate function at chebyshev nodes
+	Y = f(ϕ)
+
+	# Build Function grid
+	Φ = chebpol(S, n)
+
+	# Estimate parameters of approximation
+	c = Φ\Y
+
+	# Evaluate approximation
+	Yhat = Φ*c
+
+	# Test accuracy on larger sample
+	n_new = range(lb, stop = ub ,length = 100)
+	# Evaluate function
+	Y_new = f(n_new)
+	# Build Polynomial grid
+	Φ_new = chebpol(unitmap(n_new,lb,ub), n)
+
+	# Evaluate using fitted coefficients
+	Yhat_new = Φ_new*c
+
+	# Plot
+	p = Any[]
+	push!(p,Plots.plot(n_new, [Y_new, Yhat_new], label=["True value" "Approximation"], marker=([:none :diamond])))
+	err = Y_new .- Yhat_new
+	push!(p, Plots.plot(n_new, err, label="Approximation error"))
+	Plots.plot(p...)
 	# without using PyPlot, just erase the `PyPlot.` part
-	PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q1.png"))
-	return Dict(:error=>maximum(abs,err))
+	Plots.savefig(Plots.plot(p...), joinpath(dirname(@__FILE__),"..","q1.png"))
+	return Dict("error"=>maximum(abs,err))
 end
 
-function q2(b::Number)
+
+function q2(b=4)
 	@assert b > 0
+	n = 15
 	# use ApproxFun.jl to do the same:
+	deg = n - 1
+	ub = b
+	lb = -b
+	S = Chebyshev(lb..ub)
+	p = range(lb,stop=ub,length=n)  # a non-default grid
+	# define function
+	f(x) = x .+ 2x.^2 - exp.(-x)
+	# evaluate function
+	v = f(p)           # values at the non-default grid
+	V = Array{Float64}(undef,n,deg + 1) # Create a Vandermonde matrix by evaluating the basis at the grid
 
-	Plots.savefig(p,joinpath(dirname(@__FILE__),"..","q2.png"))
+	for k = 1:deg+1
+	    V[:,k] = Fun(S,[zeros(k-1);1]).(p) # Evaluate Chebyshev basis at p
+		# [zeros(k-1);1] is the identity matrix, all observations have same k degree Chebyshev basis function, evaluated at a different point
+	end
+	V
+	g = Fun(S,V\v);
+	@show g(1.1)
+	@show f(1.1)
+
+	n_new = range(lb, stop = ub, length = 100)
+	p = Any[]
+	push!(p,Plots.plot(n_new, [f(n_new), g.(n_new)], label=["True value" "Approximation"], marker=([:none :diamond])))
+	err = f(n_new) .- g.(n_new)
+	push!(p, Plots.plot(n_new, err, label="Approximation error"))
+	fig = Plots.plot(p...)
+
+	Plots.savefig(fig,joinpath(dirname(@__FILE__),"..","q2.png"))
 end
 
-function q3(b::Number)
 
+function q3(b=10)
+
+	x = Fun(identity,-b..b)
+	f = sin(x^2)
+	g = cos(x)
+	h = f - g
+	r = roots(h)
+
+	Plots.plot(h, label="h(x)")
+	Plots.scatter!(r,h.(r), label="Roots")
+	Plots.savefig(joinpath(dirname(@__FILE__),"..","q3.png"))
+	# xbis = Fun(identity,-b..0)
+	g = cumsum(h) # indefinite  integral
+	g = g + h(-b) # definite integral with constant of integration
+	integral = norm(g(0) - g(-b)) # definite integral from -b to 0
 	# p is your plot
-	return (p,integral)
+	return (integral)
 end
 
 # optinal
@@ -43,7 +136,7 @@ end
 
 # I found having those useful for q5
 mutable struct ChebyType
-	f::Function # fuction to approximate 
+	f::Function # fuction to approximate
 	nodes::Union{Vector,LinRange} # evaluation points
 	basis::Matrix # basis evaluated at nodes
 	coefs::Vector # estimated coefficients
@@ -79,7 +172,7 @@ function q5(deg=(5,9,15),lb=-1.0,ub=1.0)
 
 	runge(x) = 1.0 ./ (1 .+ 25 .* x.^2)
 
-	
+
 	PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q5.png"))
 
 end
@@ -94,10 +187,42 @@ function q6()
 
 end
 
-function q7()
-
-
-	PyPlot.savefig(joinpath(dirname(@__FILE__),"..","q7.png"))
+function q7(n=13)
+	f(x) = abs.(x).^0.5
+
+	# Regular grid
+	bs = BSpline(13,3,-1,1) #13 knots, degree 3 in [0,1], no multiplicity
+	# 3 knots grid
+	multiknots = vcat(range(-1,stop = -0.1,length = 5),0,0,0, range(0.1,stop = 1,length =5))
+	bs2 = BSpline(multiknots, 3)
+
+	# Evaluate function of interest
+	x = range(-1,stop =1.0, length = 65)
+	Y = f(x)
+
+	# Evaluate basis on grid
+	B = Array(getBasis(collect(x),bs))
+	B2 = Array(getBasis(collect(x),bs2))
+
+	# Solve for parameters
+	c = B\Y
+	c2 = B2\Y
+
+	# Compute fitted values
+	Yhat = B*c
+	Yhatbis = B2*c2
+
+	# Compute fitting errors
+	err = Y .- Yhat
+	errbis = Y .- Yhatbis
+
+	# Plot
+	p = Any[]
+	push!(p,Plots.plot(x, Y, title = "True function"))
+	push!(p,Plots.plot(x, [Yhat, Yhatbis], label = ["uniform" "multiplicity"], title="Approximations"))
+	push!(p,Plots.plot(x, [err, errbis], label = ["uniform" "multiplicity"], title="Errors"))
+	return Plots.plot(p...)
+	Plots.savefig(joinpath(dirname(@__FILE__),"..","q7.png"))
 end
 
 
diff --git a/test/runtests.jl b/test/runtests.jl
index 6453446..9d13d54 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -3,8 +3,10 @@ using Test
 
 @testset "HWfuncapp.jl" begin
 	# test that q1 with 15 nodes has an error smaller than 1e-9
-    
+
     # test that the integral of function h [-10,0] ≈ 1.46039789878568
 
-    @test false  # by default fail
+    @testset "q1" begin
+		out = q1()
+		@test out["error"] < 1e-9
 end