C# Numerical Methods for Scientists and Engineers

Course Curriculum

Chapter 1: Introduction

Lecture 1: Introduction

Chapter 2: Solution of Nonlinear Equations

Lecture 1: Visual Studio Solution and Project Setup

Lecture 2: Bisection Method

Lecture 3: Regula Falsi Method

Lecture 4: Secant Method

Lecture 5: Newton Raphson Method

Lecture 6: Unit Test Project Setup

Lecture 7: Nonlinear Unit Tests Part 1

Lecture 8: Nonlinear Unit Tests Part 2

Chapter 3: Solution of Simultaneous Linear Equations

Lecture 1: System of Equations Project and Interface

Lecture 2: Gauss Elimination (Solve Equations)

Lecture 3: Gauss Elimination (Reduced Form)

Lecture 4: Gauss Elimination (Swap Rows)

Lecture 5: Gauss Elimination (Back Substitution)

Lecture 6: Gauss Elimination (Validate Solutions)

Lecture 7: Setup Unit Tests

Lecture 8: Refactor and Debug Unit Test

Chapter 4: Curve Fitting and Interpolation

Lecture 1: Add Project Class and Interface

Lecture 2: Linear Interpolation

Lecture 3: Linear Regression

Lecture 4: Power Regression

Lecture 5: Interpolation Regression Unit Tests

Chapter 5: Numerical Differentiation

Lecture 1: Project Class and Interface

Lecture 2: Forward Difference Method

Lecture 3: Backward Difference Method

Lecture 4: Central Difference Method

Lecture 5: Numerical Differentiation Unit Tests

Chapter 6: Numerical Integration

Lecture 1: Project Class and Interface

Lecture 2: Trapezoidal Method

Lecture 3: Simpson's 1/3 Method

Lecture 4: Simpson's 3/8 Method

Lecture 5: Numerical Integration Unit Tests

Chapter 7: Ordinary Differential Equations

Lecture 1: Project Class and Interface

Lecture 2: Euler's Method

Lecture 3: Runge-Kutta Method

Lecture 4: Ordinary Differential Equations Unit Tests