Added week 4 blog.

Author: abhiphile

package-lock.json

@@ -13,9 +13,11 @@
   "dependencies": {
     "@ant-design/icons": "^5.3.7",
     "antd": "^5.17.0",
+    "katex": "^0.16.10",
     "react": "^18.2.0",
     "react-dom": "^18.2.0",
     "react-icons": "^5.2.1",
+    "react-katex": "^3.0.1",
     "react-router-dom": "^6.23.0"
   },
   "devDependencies": {

package.json

@@ -26,7 +26,7 @@ const Anchors = () => {
           Phase 2
         </div>
         <div className="ms-3">
-          <Link to="#link-props" className="nav-link text-dark my-1">
+          <Link to="/gsoc24-blog/week4" className="nav-link text-primary my-1">
             Week 4
           </Link>
         </div>

src/assets/Anchors.jsx

@@ -2,9 +2,15 @@ import React from 'react'
 import Navbar from '../Navbar'
 import Anchors from '../assets/Anchors'
 import { Divider, Typography } from 'antd';
-const { Title, Paragraph, Text, Link } = Typography;
+import Footer from '../assets/Footer';
+import { FaCodePullRequest } from 'react-icons/fa6';
+import 'katex/dist/katex.min.css';
+import { InlineMath, BlockMath } from 'react-katex';
+const { Title, Paragraph} = Typography;
 
 const Week4 = () => {
+  const stateEquation = `\\dot{x}(t) = A x(t) + B u(t)`;
+  const outputEquation = `y(t) = C x(t) + D u(t)`;
   return (
     <>
       <Navbar />
@@ -13,20 +19,77 @@ const Week4 = () => {
           <Anchors />
         </div>
         <div className="col m-2">
-          <div className="m-2 border rounded p-2">
+          <div className="m-2 border rounded p-4">
             <Typography>
               <Title>
-                This is the title !
+                Week 3 : Adding support of symbolic matrices to <code>dsolve()</code> in StateSpace.
               </Title>
               <Paragraph className='par'>
-                This is par
+                During the fourth week of my Google Summer of Code (GSOC) journey, In this week I worked on finding symbolic solutions of StateSpace equations.
+                <p>State Equation:</p>
+                <BlockMath math={stateEquation} />
+                <p>Output Equation:</p>
+                <BlockMath math={outputEquation} />
+              </Paragraph>
+              <Title>
+                Implementation
+              </Title>
+              <Paragraph className='par'>
+                <h2>Solving State Space Equations in SymPy</h2>
+                <p>The <code>dsolve</code> method in SymPy solves state space equations of the form:</p>
+
+                <BlockMath math={outputEquation} />
+                <p>Here's a step-by-step breakdown of the <code>dsolve</code> method:</p>
+                <ul>
+                  <li>
+                    <strong>Validate Input Parameters:</strong>
+                    <ul>
+                      <li>Check if <code>var</code> is a Symbol.</li>
+                      <li>Set default <code>initial_conditions</code> and <code>input_vector</code> if not provided.</li>
+                      <li>Validate the dimensions of <code>initial_conditions</code> and <code>input_vector</code>.</li>
+                    </ul>
+                  </li>
+                  <li>
+                    <strong>Solve the State Equation:</strong>
+                    <ul>
+                      <li>Use <code>linodesolve</code> to solve the state equation <InlineMath math={outputEquation} />.</li>
+                      <li>Convert the solution to a matrix form.</li>
+                    </ul>
+                  </li>
+                  <li>
+                    <strong>Apply Initial Conditions:</strong>
+                    <ul>
+                      <li>Evaluate the solution at <code>t = 0</code>.</li>
+                      <li>Identify and solve for the dummy symbols representing initial conditions.</li>
+                      <li>Replace dummy symbols in the solution with solved values.</li>
+                    </ul>
+                  </li>
+                  <li>
+                    <strong>Compute Output Vector:</strong>
+                    <ul>
+                      <li>Compute the output vector <code>y</code> using the state vector solution and the input vector.</li>
+                    </ul>
+                  </li>
+                </ul>
+                <p>This method ensures accurate solutions to state space problems, handling symbolic matrices efficiently.</p>
+              </Paragraph>
+              <Title>
+                Pull Requests
+              </Title>
+              <Paragraph className='par'>
+                <a href='https://github.com/sympy/sympy/pull/26736' className='text-success'><FaCodePullRequest /> (Open) Changed the output_vector to dsolve and added support of symbolic matrices..</a>
+                <div className='gap-3'>
+                  <Divider />
+                </div>
+                Abhishek Kumar
+                <br />
+                GSoC Contributor
               </Paragraph>
             </Typography>
           </div>
         </div>
-        <Footer/>
+        <Footer />
       </div>
-
     </>
   )
 }