What is Scientific Computing?
- Definition: Study of how to solve problems involving real (or complex) numbers using computers
- Focus: Study algorithms for solving problems with real or complex numbers
- Key Issues: Study issues that arise when using computers for such problems
- These issues do NOT arise when dealing with integers or strings
Applications and Fields
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Scientific Fields:
- Engineering
- Physics
- Biology
- Chemistry
- Computational finance
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Computer Science Applications:
- Machine learning and pattern recognition
- Information retrieval
- Image processing
- Multimedia processing
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Historical Note: Previously known as numerical analysis
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Alternative Names: Non CPE/DE people call these algorithms numerical methods
Sample Topics Covered
- Linear and Nonlinear Systems: Solving systems of linear and nonlinear equations
- Data Fitting: Finding the function that best fits a given set of data points
- Calculus Operations:
- Evaluating definite integrals
- Computing derivatives
- Optimization: Finding the maximum/minimum of a given function
- Linear Algebra: Computing eigenvalues and eigenvectors
- Differential Equations: Solving differential equations
Summary: How to solve continuous math problems with computers
Why Use Computers for Math Problems?
- Scale Problem: Math problems in the real world are often too big for humans to solve manually
- Examples of Large-Scale Problems:
- Solving a system of 1,000 linear equations in 1,000 variables
- Finding an eigenvector of a 100-by-100 matrix
- Examples of Large-Scale Problems:
Notes on Proofs
- Coverage: Some proofs will be covered in the course
- Purpose: Mainly for understanding why the methods/algorithms correctly do what we want
Exam Focus: The exams will NOT focus on proofs