diff --git a/HW3/README.md b/HW3/README.md
new file mode 100644
index 0000000..494e0d5
--- /dev/null
+++ b/HW3/README.md
@@ -0,0 +1,74 @@
+# Homework #3
+## due 2/15/17 by 11:59pm
+
+
+1. Create a new github repository called 'roots_and_optimization'.
+
+ a. Add rcc02007 and pez16103 as collaborators.
+
+ b. Clone the repository to your computer.
+
+ c. Copy your `projectile.m` function into the 'roots_and_optimization' folder.
+ *Disable the plotting routine for the solvers*
+
+ d. Use the four solvers `falsepos.m`, `incsearch.m`, `newtraph.m` and `mod_secant.m`
+ to solve for the angle needed to reach h=1.72 m, with an initial speed of 1.5 m/s.
+
+ e. The `newtraph.m` function needs a derivative, calculate the derivative of your
+ function with respect to theta, `dprojectile_dtheta.m`. This function should
+ output d(h)/d(theta).
+
+
+ f. In your `README.md` file, document the following under the heading `#
+ Homework #3`:
+
+ i. Compare the number of iterations that each function needed to reach an
+ accuracy of 0.00001%. Include a table in your README.md with:
+
+ ```
+ | solver | initial guess(es) | ea | number of iterations|
+ | --- | --- | --- | --- |
+ |falsepos | | | |
+ |incsearch | | | |
+ |newtraph | | | |
+ |mod_secant | | | |
+ ```
+
+ ii. Compare the convergence of the 4 methods. Plot the approximate error vs the
+ number of iterations that the solver has calculated. Save the plot as
+ `convergence.png` and display the plot in your `README.md` with:
+
+ ``
+
+ iii. In the `README.md` provide a description of the files used to create the
+ table and the convergence plot.
+
+2. The Newton-Raphson method and the modified secant method do not always converge to a
+solution. One simple example is the function f(x) = x*exp(-x^2). The root is at 0, but
+using the numerical solvers, `newtraph.m` and `mod_secant.m`, there are certain initial
+guesses that do not converge.
+
+ a. Calculate the first 5 iterations for the Newton-Raphson method with an initial
+ guess of x_i=2.
+
+ b. Add the results to a table in the `README.md` with:
+
+ ```
+ ### divergence of Newton-Raphson method
+
+ | iteration | x_i | approx error |
+ | --- | --- | --- |
+ | 0 | 2 | n/a |
+ | 1 | | |
+ | 2 | | |
+ | 3 | | |
+ | 4 | | |
+ | 5 | | |
+ ```
+
+ c. Repeat steps a-b for an initial guess of 0.2. (But change the heading from
+ 'divergence' to 'convergence')
+
+3. Commit your changes to your repository. Sync your local repository with github. Then
+copy and paste the "clone URL" into the following Google Form [Homework
+#3](https://goo.gl/forms/UJBGwp0fQcSxImkq2)
diff --git a/lecture_07/.newtraph.m.swp b/lecture_07/.newtraph.m.swp
new file mode 100644
index 0000000..9759dd2
Binary files /dev/null and b/lecture_07/.newtraph.m.swp differ
diff --git a/lecture_07/lecture_07.ipynb b/lecture_07/lecture_07.ipynb
index d7ff495..08d29c4 100644
--- a/lecture_07/lecture_07.ipynb
+++ b/lecture_07/lecture_07.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": 13,
"metadata": {
"collapsed": true
},
@@ -40,12 +40,12 @@
"\n",
"$x_{i+1}=x_{i}-\\frac{f(x_{i})}{f'(x_{i})}$\n",
"\n",
- "Use Newton-Raphson to find solution when $e^{x}=x$"
+ "Use Newton-Raphson to find solution when $e^{-x}=x$"
]
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": 2,
"metadata": {
"collapsed": false
},
@@ -54,7 +54,8 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "error_approx = 1\r\n"
+ "x_r = 0.50000\n",
+ "error_approx = 1\n"
]
}
],
@@ -63,13 +64,14 @@
"df= @(x) -exp(-x)-1;\n",
"\n",
"x_i= 0;\n",
+ "x_r = x_i-f(x_i)/df(x_i)\n",
"error_approx = abs((x_r-x_i)/x_r)\n",
- "x_r=x_i;\n"
+ "x_i=x_r;\n"
]
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 3,
"metadata": {
"collapsed": false
},
@@ -78,8 +80,8 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "x_r = 0.50000\n",
- "error_approx = 1\n"
+ "x_r = 0.56631\n",
+ "error_approx = 0.11709\n"
]
}
],
@@ -91,7 +93,7 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 4,
"metadata": {
"collapsed": false
},
@@ -100,8 +102,8 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "x_r = 0.56631\n",
- "error_approx = 0.11709\n"
+ "x_r = 0.56714\n",
+ "error_approx = 0.0014673\n"
]
}
],
@@ -113,7 +115,7 @@
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 5,
"metadata": {
"collapsed": false
},
@@ -123,7 +125,7 @@
"output_type": "stream",
"text": [
"x_r = 0.56714\n",
- "error_approx = 0.0014673\n"
+ "error_approx = 2.2106e-07\n"
]
}
],
@@ -149,7 +151,7 @@
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 6,
"metadata": {
"collapsed": true
},
@@ -176,12 +178,14 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "ans = 142.74\r\n"
+ "root = 142.74\n",
+ "ea = 8.0930e-06\n",
+ "iter = 48\n"
]
}
],
"source": [
- "newtraph(f_m,df_m,140,0.00001)"
+ "[root,ea,iter]=newtraph(f_m,df_m,140,0.00001)"
]
},
{
@@ -217,7 +221,7 @@
},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 11,
"metadata": {
"collapsed": false
},
@@ -226,17 +230,24 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "ans = 142.74\r\n"
+ "root = 142.74\n",
+ "ea = 3.0615e-07\n",
+ "iter = 7\n"
]
}
],
"source": [
- "mod_secant(f_m,1e-6,50,0.00001)"
+ "[root,ea,iter]=mod_secant(f_m,1,50,0.00001)"
]
},
+ {
+ "cell_type": "raw",
+ "metadata": {},
+ "source": []
+ },
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": 15,
"metadata": {
"collapsed": false
},
@@ -245,23 +256,159 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "error: 'plot_bool' undefined near line 12 column 6\n",
- "error: called from\n",
- " car_payments at line 12 column 3\n",
- " mod_secant at line 22 column 8\n",
- "error: 'Amt' undefined near line 1 column 14\n",
- "error: evaluating argument list element number 1\n"
+ "ans = 1.1185e+04\r\n"
]
+ },
+ {
+ "data": {
+ "image/svg+xml": [
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
}
],
"source": [
- "Amt_numerical=mod_secant(@(A) car_payments(A,30000,0.05,5),1e-6,50,0.001)\n",
- "car_payments(Amt,30000,0.05,5)"
+ "car_payments(400,30000,0.05,5,1)"
]
},
{
"cell_type": "code",
- "execution_count": 11,
+ "execution_count": 17,
"metadata": {
"collapsed": false
},
@@ -270,12 +417,195 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "error: 'Amt' undefined near line 1 column 1\r\n"
+ "Amt_numerical = 5467.0\n",
+ "ans = 3.9755e-04\n"
+ ]
+ },
+ {
+ "data": {
+ "image/svg+xml": [
+ ""
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "Amt_numerical=mod_secant(@(A) car_payments(A,700000,0.0875,30,0),1e-6,50,0.001)\n",
+ "car_payments(Amt_numerical,700000,0.0875,30,1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ans = 1.9681e+06\r\n"
]
}
],
"source": [
- "Amt*12*5"
+ "Amt_numerical*12*30"
]
},
{
@@ -287,7 +617,7 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 19,
"metadata": {
"collapsed": false
},
@@ -398,7 +728,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 20,
"metadata": {
"collapsed": false
},
@@ -428,7 +758,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 23,
"metadata": {
"collapsed": false
},
@@ -611,7 +941,7 @@
"\t\n",
"\n",
"\n",
- "\t\n",
+ "\t\n",
"\t\n",
"\tmod-secant\n",
"\n",
@@ -667,19 +997,20 @@
"ea_fp=zeros(1,N); % appr error false point method\n",
"ea_bs=zeros(1,N); % appr error bisect method\n",
"for i=1:length(iterations)\n",
- " [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,200,0,iterations(i));\n",
+ " [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,300,0,iterations(i));\n",
" [root_ms,ea_ms(i),iter_ms]=mod_secant(f_m,1e-6,300,0,iterations(i));\n",
" [root_fp,ea_fp(i),iter_fp]=falsepos(f_m,1,300,0,iterations(i));\n",
" [root_bs,ea_bs(i),iter_bs]=bisect(f_m,1,300,0,iterations(i));\n",
"end\n",
- " \n",
+ "\n",
+ "setdefaults\n",
"semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))\n",
"legend('newton-raphson','mod-secant','false point','bisection')"
]
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 22,
"metadata": {
"collapsed": false
},
@@ -688,34 +1019,30 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "ea_ms =\n",
- "\n",
- " Columns 1 through 6:\n",
+ "ea_nr =\n",
"\n",
- " 2.3382e+03 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14\n",
+ " Columns 1 through 8:\n",
"\n",
- " Columns 7 through 12:\n",
+ " 6.36591 0.06436 0.00052 0.00000 0.00000 0.00000 0.00000 0.00000\n",
"\n",
- " 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14\n",
+ " Columns 9 through 16:\n",
"\n",
- " Columns 13 through 18:\n",
+ " 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000\n",
"\n",
- " 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14\n",
+ " Columns 17 through 20:\n",
"\n",
- " Columns 19 and 20:\n",
- "\n",
- " 1.9171e-14 1.9171e-14\n",
+ " 0.00000 0.00000 0.00000 0.00000\n",
"\n"
]
}
],
"source": [
- "ea_ms"
+ "ea_nr"
]
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 26,
"metadata": {
"collapsed": false
},
@@ -953,7 +1280,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 27,
"metadata": {
"collapsed": false
},
@@ -962,30 +1289,26 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "ea_bs =\n",
+ "ea_nr =\n",
"\n",
- " Columns 1 through 6:\n",
+ " Columns 1 through 7:\n",
"\n",
- " 9.5357e+03 -4.7554e-01 -2.1114e-01 6.0163e-02 -2.4387e-03 6.1052e-04\n",
+ " 99.03195 11.11111 11.11111 11.11111 11.11111 11.11111 11.11111\n",
"\n",
- " Columns 7 through 12:\n",
+ " Columns 8 through 14:\n",
"\n",
- " 2.2891e-04 -9.5367e-06 2.3842e-06 8.9407e-07 -2.2352e-07 9.3132e-09\n",
+ " 11.11111 11.11111 11.11111 11.11109 11.11052 11.10624 10.99684\n",
"\n",
- " Columns 13 through 18:\n",
+ " Columns 15 through 20:\n",
"\n",
- " -2.3283e-09 -8.7311e-10 3.6380e-11 -9.0949e-12 -3.4106e-12 8.5265e-13\n",
- "\n",
- " Columns 19 and 20:\n",
- "\n",
- " -3.5527e-14 8.8818e-15\n",
+ " 8.76956 2.12993 0.00000 0.00000 0.00000 0.00000\n",
"\n",
"ans = 16.208\n"
]
}
],
"source": [
- "ea_bs\n",
+ "ea_nr\n",
"newtraph(f,df,0.5,0,12)"
]
},
@@ -1008,6 +1331,99 @@
"df(300)"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "f =\n",
+ "\n",
+ "@(x) tan (x) - (x - 1) .^ 2\n",
+ "\n",
+ "ans = 0.37375\n"
+ ]
+ }
+ ],
+ "source": [
+ "% our class function\n",
+ "f= @(x) tan(x)-(x-1).^2\n",
+ "mod_secant(f,1e-3,1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ans = -3.5577e-13\r\n"
+ ]
+ }
+ ],
+ "source": [
+ "f(ans)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ans = 0.39218\n",
+ "ans = 0.39219\n"
+ ]
+ }
+ ],
+ "source": [
+ "tan(0.37375)\n",
+ "(0.37375-1)^2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ans =\n",
+ "\n",
+ " Columns 1 through 8:\n",
+ "\n",
+ " -1.0000 1.5574 -3.1850 -4.1425 -7.8422 -19.3805 -25.2910 -35.1286\n",
+ "\n",
+ " Columns 9 through 11:\n",
+ "\n",
+ " -55.7997 -64.4523 -80.3516\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "f([0:10])"
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
diff --git a/lecture_07/lecture_07.md b/lecture_07/lecture_07.md
index ffdc48d..3aacefb 100644
--- a/lecture_07/lecture_07.md
+++ b/lecture_07/lecture_07.md
@@ -18,7 +18,7 @@ $f'(x_{i})=\frac{f(x_{i})-0}{x_{i}-x_{i+1}}$
$x_{i+1}=x_{i}-\frac{f(x_{i})}{f'(x_{i})}$
-Use Newton-Raphson to find solution when $e^{x}=x$
+Use Newton-Raphson to find solution when $e^{-x}=x$
```octave
@@ -26,12 +26,14 @@ f= @(x) exp(-x)-x;
df= @(x) -exp(-x)-1;
x_i= 0;
+x_r = x_i-f(x_i)/df(x_i)
error_approx = abs((x_r-x_i)/x_r)
-x_r=x_i;
+x_i=x_r;
```
- error_approx = 1
+ x_r = 0.50000
+ error_approx = 1
@@ -41,8 +43,8 @@ error_approx = abs((x_r-x_i)/x_r)
x_i=x_r;
```
- x_r = 0.50000
- error_approx = 1
+ x_r = 0.56631
+ error_approx = 0.11709
@@ -52,8 +54,8 @@ error_approx = abs((x_r-x_i)/x_r)
x_i=x_r;
```
- x_r = 0.56631
- error_approx = 0.11709
+ x_r = 0.56714
+ error_approx = 0.0014673
@@ -64,7 +66,7 @@ x_i=x_r;
```
x_r = 0.56714
- error_approx = 0.0014673
+ error_approx = 2.2106e-07
In the bungee jumper example, we created a function f(m) that when f(m)=0, then the mass had been chosen such that at t=4 s, the velocity is 36 m/s.
@@ -90,10 +92,12 @@ df_m = @(m) 1/2*sqrt(g./m/c_d).*tanh(sqrt(g*c_d./m)*t)-g/2./m*sech(sqrt(g*c_d./m
```octave
-newtraph(f_m,df_m,140,0.00001)
+[root,ea,iter]=newtraph(f_m,df_m,140,0.00001)
```
- ans = 142.74
+ root = 142.74
+ ea = 8.0930e-06
+ iter = 48
## Secant Methods
@@ -119,32 +123,46 @@ $x_{i+1}=x_{i}-\frac{f(x_{i})(\delta x_{i})}{f(x_{i}+\delta x_{i})-f(x_{i})}$
```octave
-mod_secant(f_m,1e-6,50,0.00001)
+[root,ea,iter]=mod_secant(f_m,1,50,0.00001)
```
- ans = 142.74
+ root = 142.74
+ ea = 3.0615e-07
+ iter = 7
```octave
-Amt_numerical=mod_secant(@(A) car_payments(A,30000,0.05,5),1e-6,50,0.001)
-car_payments(Amt,30000,0.05,5)
+car_payments(400,30000,0.05,5,1)
```
- error: 'plot_bool' undefined near line 12 column 6
- error: called from
- car_payments at line 12 column 3
- mod_secant at line 22 column 8
- error: 'Amt' undefined near line 1 column 14
- error: evaluating argument list element number 1
+ ans = 1.1185e+04
+
+
+
+
```octave
-Amt*12*5
+Amt_numerical=mod_secant(@(A) car_payments(A,700000,0.0875,30,0),1e-6,50,0.001)
+car_payments(Amt_numerical,700000,0.0875,30,1)
```
- error: 'Amt' undefined near line 1 column 1
+ Amt_numerical = 5467.0
+ ans = 3.9755e-04
+
+
+
+
+
+
+
+```octave
+Amt_numerical*12*30
+```
+
+ ans = 1.9681e+06
Amortization calculation makes the same calculation for the monthly payment amount, A, paying off the principle amount, P, over n pay periods with monthly interest rate, r.
@@ -257,12 +275,13 @@ ea_ms=zeros(1,N); % appr error Modified Secant
ea_fp=zeros(1,N); % appr error false point method
ea_bs=zeros(1,N); % appr error bisect method
for i=1:length(iterations)
- [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,200,0,iterations(i));
+ [root_nr,ea_nr(i),iter_nr]=newtraph(f_m,df_m,300,0,iterations(i));
[root_ms,ea_ms(i),iter_ms]=mod_secant(f_m,1e-6,300,0,iterations(i));
[root_fp,ea_fp(i),iter_fp]=falsepos(f_m,1,300,0,iterations(i));
[root_bs,ea_bs(i),iter_bs]=bisect(f_m,1,300,0,iterations(i));
end
-
+
+setdefaults
semilogy(iterations,abs(ea_nr),iterations,abs(ea_ms),iterations,abs(ea_fp),iterations,abs(ea_bs))
legend('newton-raphson','mod-secant','false point','bisection')
```
@@ -281,31 +300,27 @@ legend('newton-raphson','mod-secant','false point','bisection')
-
+
```octave
-ea_ms
+ea_nr
```
- ea_ms =
+ ea_nr =
- Columns 1 through 6:
+ Columns 1 through 8:
- 2.3382e+03 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14
+ 6.36591 0.06436 0.00052 0.00000 0.00000 0.00000 0.00000 0.00000
- Columns 7 through 12:
+ Columns 9 through 16:
- 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14
+ 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
- Columns 13 through 18:
+ Columns 17 through 20:
- 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14 1.9171e-14
-
- Columns 19 and 20:
-
- 1.9171e-14 1.9171e-14
+ 0.00000 0.00000 0.00000 0.00000
@@ -344,32 +359,28 @@ legend('newton-raphson','mod-secant','false point','bisection')
-
+
```octave
-ea_bs
+ea_nr
newtraph(f,df,0.5,0,12)
```
- ea_bs =
-
- Columns 1 through 6:
+ ea_nr =
- 9.5357e+03 -4.7554e-01 -2.1114e-01 6.0163e-02 -2.4387e-03 6.1052e-04
+ Columns 1 through 7:
- Columns 7 through 12:
+ 99.03195 11.11111 11.11111 11.11111 11.11111 11.11111 11.11111
- 2.2891e-04 -9.5367e-06 2.3842e-06 8.9407e-07 -2.2352e-07 9.3132e-09
+ Columns 8 through 14:
- Columns 13 through 18:
+ 11.11111 11.11111 11.11111 11.11109 11.11052 11.10624 10.99684
- -2.3283e-09 -8.7311e-10 3.6380e-11 -9.0949e-12 -3.4106e-12 8.5265e-13
+ Columns 15 through 20:
- Columns 19 and 20:
-
- -3.5527e-14 8.8818e-15
+ 8.76956 2.12993 0.00000 0.00000 0.00000 0.00000
ans = 16.208
@@ -383,6 +394,55 @@ df(300)
+```octave
+% our class function
+f= @(x) tan(x)-(x-1).^2
+mod_secant(f,1e-3,1)
+```
+
+ f =
+
+ @(x) tan (x) - (x - 1) .^ 2
+
+ ans = 0.37375
+
+
+
+```octave
+f(ans)
+```
+
+ ans = -3.5577e-13
+
+
+
+```octave
+tan(0.37375)
+(0.37375-1)^2
+```
+
+ ans = 0.39218
+ ans = 0.39219
+
+
+
+```octave
+f([0:10])
+```
+
+ ans =
+
+ Columns 1 through 8:
+
+ -1.0000 1.5574 -3.1850 -4.1425 -7.8422 -19.3805 -25.2910 -35.1286
+
+ Columns 9 through 11:
+
+ -55.7997 -64.4523 -80.3516
+
+
+
+
```octave
```
diff --git a/lecture_07/lecture_07.pdf b/lecture_07/lecture_07.pdf
index 79b130c..70d8fc2 100644
Binary files a/lecture_07/lecture_07.pdf and b/lecture_07/lecture_07.pdf differ
diff --git a/lecture_07/lecture_07_files/lecture_07_15_1.svg b/lecture_07/lecture_07_files/lecture_07_15_1.svg
new file mode 100644
index 0000000..903c445
--- /dev/null
+++ b/lecture_07/lecture_07_files/lecture_07_15_1.svg
@@ -0,0 +1,131 @@
+
\ No newline at end of file
diff --git a/lecture_07/lecture_07_files/lecture_07_16_1.svg b/lecture_07/lecture_07_files/lecture_07_16_1.svg
new file mode 100644
index 0000000..a3a2125
--- /dev/null
+++ b/lecture_07/lecture_07_files/lecture_07_16_1.svg
@@ -0,0 +1,151 @@
+
\ No newline at end of file
diff --git a/lecture_07/lecture_07_files/lecture_07_24_1.svg b/lecture_07/lecture_07_files/lecture_07_24_1.svg
index a8b614c..b511b10 100644
--- a/lecture_07/lecture_07_files/lecture_07_24_1.svg
+++ b/lecture_07/lecture_07_files/lecture_07_24_1.svg
@@ -43,47 +43,47 @@
-
+
10-14
-
+
10-12
-
+
10-10
-
+
10-8
-
+
10-6
-
+
10-4
-
+
10-2
-
+
100
-
+
102
@@ -98,28 +98,43 @@
-
- 10
+
+ 50
+
+
+
+
+ 100
-
- 20
+
+ 150
-
- 30
+
+ 200
-
- 40
+
+ 250
+
+
+
+
+ 300
+
+
+
+
+ 350
- 50
+ 400
@@ -141,7 +156,7 @@
-
+
mod-secant
@@ -150,7 +165,7 @@
-
+
false point
@@ -159,7 +174,7 @@
-
+
bisection
@@ -168,7 +183,7 @@
-
+
diff --git a/lecture_07/lecture_07_files/lecture_07_26_1.svg b/lecture_07/lecture_07_files/lecture_07_26_1.svg
new file mode 100644
index 0000000..a8b614c
--- /dev/null
+++ b/lecture_07/lecture_07_files/lecture_07_26_1.svg
@@ -0,0 +1,182 @@
+
\ No newline at end of file