Scientific Computing

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About Course

This Scientific Computing course will provide an introduction to the use of computers in solving problems arising in the physical, biological, and engineering sciences.

Various computational approaches commonly used to solve mathematical problems (including systems of linear equations, optimization, curve fitting, integration, and differential equations) will be presented.  Both the theory and application of each numerical method will be demonstrated.

You should gain mathematical judgment in selecting tools to solve scientific problems through in-class examples and programming homework assignments.

MATLAB will be used as the primary environment for numerical computation.  No previous coding experience is required; an overview of MATLAB’s syntax, code structure, and algorithms will be given.

Although the subject matter of scientific computing has many aspects that can be made rather difficult, the material in this course is meant to be an introduction and will therefore be presented in as simple a way as possible.  Theoretical aspects will be mentioned throughout the course, but more complicated issues such as rigorous proofs will not be presented.  Applications will be emphasized.

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What Will You Learn?

  • Learn the Beginning Scientific Computing

Course Content

Scientific Computing

  • Lecture: Higher-order Integration Schemes
    00:00
  • Lecture: Ordinary Differential Equations and Time-stepping
    00:00
  • Lecture: Data Fitting with Matlab
    00:00
  • Lecture: Linear Programming and Genetic Algorithms
    00:00
  • Lecture: Numerical Differentiation Methods
    00:00
  • Lecture: Eigenvalues and Eigenvectors
    00:00
  • Lecture: Unconstrained Optimization (Derivative Methods)
    00:00
  • Lecture: Iteration Methods for Ax-b
    00:00
  • Lecture: LU Matrix Decomposition for Ax=b
    00:00
  • Lecture: Gaussian Elimination for Ax=b
    00:00
  • Supplement: Using ODE45 & Runge-Kutta methods
    00:00
  • Lecture: PCA for Face Recognition
    00:00
  • Lecture: Eigen-decompositions and Iterations
    00:00
  • Lecture: Least-Squares Fitting Methods
    00:00
  • Lecture: Polynomial Fits and Splines
    00:00
  • Lecture: Higher-order Accuracy Schemes for Differentiation and Integration
    00:00
  • Lecture: Unconstrained Optimization (Derivative-Free Methods)
    00:00
  • Lecture: Error and Stability of Time-stepping Schemes
    00:00
  • Lecture: FFT and Image Compression
    00:00
  • Lecture: General Time-stepping and Runge-Kutta Schemes
    00:00
  • Lecture: Theory of the Fourier Transform
    00:00
  • Lecture: Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT)
    00:00
  • Lecture: The Singular Value Decomposition (SVD)
    00:00
  • Lecture: Principal Componenet Analysis (PCA)
    00:00
  • Supplement: Big systems of ODEs
    00:00
  • Supplement: Indexing equations
    00:00
  • Supplement: Discrete Fourier Transform
    00:00
  • Supplement: Mean Value Theorem
    00:00
  • Lecture: Application of Runge-Kutta to Lorenz Equation
    00:00
  • Lecture: Vectorized Time-step Integrators
    00:00
  • Lecture: Application of Runge-Kutta to Chaotic Dynamics and the Double Pendulum
    00:00
  • Supplement: Vector fields and phase-planes
    00:00
  • Lecture: Vectors & Matrices
    00:00
  • Lecture: Logic, Loops, and Iterations
    00:00
  • Lecture: Vectors & Matrices
    00:00
  • Lecture: Linear Systems of Equations
    00:00

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