Solving Problems with Numerical Methods

سرفصل های دوره

This course focuses on conceptually understanding and implementing numerical techniques to solve mathematical problems. Many problems in the real world are hard, or impossible, to solve analytically but easy to solve numerically.

1. Course Overview

1. Course Overview

2. Understanding Numerical Methods

1. Version Check

2. Prerequisites and Course Outline

3. Introducing Numerical Methods

4. Direct and Iterative Numerical Methods

5. Numerical Instability and Errors

6. Interpolation and Extrapolation

7. Constant, Linear, Polynomial, and Spline Interpolation

8. System of Linear Equations

9. Gaussian Elimination and Jacobi Method

3. Applying Numerical Methods to Solve Problems

1. Demo - Linear and Constant Interpolation

2. Demo - Linear and Polynomial Extrapolation

3. Demo - Interpolation Using Spline and Smoothing Techniques

4. Demo - Iterative Techniques - Jacobi Method to Solve Linear Equations

5. Demo - Direct Techniques - Gaussian Elimination to Solve Linear Equations

6. Demo - Discretizing Continuous Data

7. Demo - Rounding Errors and Approximation Errors

8. Demo - Approximating Derivate Calculations

9. Demo - Eulers Method and Numerical Instability

4. Working with Graphs Using Numerical Techniques

01. Graphs and Graph Applications

02. Directed and Undirected Graphs

03. Connected and Unconnected Graphs

04. Graph Representations

05. Shortest Path Algorithms

06. Demo - Defining and Configuring Graphs

07. Demo - Specifying Attributes for Edges and Vertices

08. Demo - Exploring Different Kinds of Graphs

09. Demo - Calculating Shortest Distances

10. Demo - Calculating Shortest Paths

5. Implementing Local Search and Optimizations

01. Solutions Approaches to N-Queens

02. Introducing Local Search Algorithms

03. Simulated Annealing and Threshold Accepting

04. Demo - 8 Queens - Calculating Number of Attacks

05. Demo - 8 Queens - Generating Candidate Solutions

06. Demo - 8 Queens - Solution Using Local Search Techniques

07. Objective Constraints and Decision Variables

08. Wyndor Glass - Framing the Optimization Problem

09. Setting up the Optimization as a Linear Programming Problem

10. Solving the Linear Programming Problem Graphically

11. Demo - Solving Optimization Problems Using Linear Programming

12. Demo - Linear Programming to Solve the Wyndor Glass Problem

6. Implementing Integration and Differentiation

01. Modeling Population Growth

02. Interpreting Derivatives

03. Verhulsts Equation for Population Growth

04. Understanding Integration

05. Demo - Calculating Derivatives

06. Demo - Calculating Velocity and Acceleration Using Derivatives

07. Demo - Performing Integration

08. Demo - Using the ODE Solver to Solve Differential Equations

09. Demo - Solving Verhulsts Equation

10. Summary and Further Study

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تولید کننده: PluralSight