- California State Polytechnic University, Pomona
Keivan Navi, Ph.D., Professor
Fundamentals of C programming and Unix environment. File management, communications and process control. Regular expressions. Unix system calls, concurrent, and socket programming. Learn how to program the Arduino for real-world usage, such as to control lights, motors and motion detection sensors. This course assumes the use of real hardware components in a live lab environment (not software-simulated hardware).
Course Detail
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Week# 1
Linear Algebra Concepts and Notation
Representation of Integers
Representation of Fractions
From Binary to Decimal/Octal/Hexadecimal and vice versa
Binary Digit, Ternary Digit, Balanced Ternary Digit, Redundant Ternary Digit Set -
Week#2
Floating-Point Arithmetic
Loss of Significance and Error Propagation
Computational Methods for Error Estimation
Some Comments on Convergence of Sequences
Some Mathematical Preliminaries
Real and Imaginary (complex) numbers -
Week# 3
Fixed-Point Iteration
Convergence Acceleration for Fixed-Point Iteration
Newton
Secant Methods
Bisection -
Week# 4
Properties of Matrices
Conventional Computer arithmetic versus Matrices Arithmetic
Addition (compressors)
Subtraction by addition
Multiplication
Division by Multiplication
Square root and function evaluation
Addition, Subtraction, Multiplication (Direct, Inner, Outer, Tensor) and application -
Week# 5
Approximation Computing
Approximate Arithmetic
Rounding
Truncation
First Exam Feb. 24 -
Week# 6
Conventional Differentiation
The meaning of Differentiation
Numerical Differentiation
Conventional Integration
The meaning of Integration
Numerical Integration: Some Basic Rules -
Week# 7
Numerical Integration: Gaussian Rules
Numerical Integration: Composite Rules
Adaptive Quadrature
Extrapolation to the Limit
Romberg Integration
Trapezoidal Rule of Integration
Simpson -
Week# 8
Ordinary Differential Equations
Numerical Integration by Taylor Series
Euler’s Method
Runge-Kutta Methods
Step-Size Control with Runge-Kutta Methods
Systems of Differential Equations -
Week # 9
Finite Difference Methods
Shooting Methods
Collocation Methods -
Week # 10
How to write a Research Paper
Paper presentation (optional) -
Week # 11
Solution of Linear Systems by Elimination
Pivoting Strategy
The Triangular Factorization
Residual of an Approximate Solution
Norms
Backward-Error Analysis and Iterative Improvement
Determinants -
Week # 12
Eigenvalue Problem
Eigen vector
Application in Quantum Computing -
Week # 13
Residue Number System -
Week # 14
Interpolation -
Week #15
Scientific Metrics
Some Ph.D. and Ms. Project Examples
Paper presentation
Overall conclusion
- Linear Algebra in Twenty Five Lectures - UC Davis Mathematics - PDF By Tom Denton and Andrew Waldron
- A complete (400 page) online Linear Algebra textbook. Well, the actual text is only 200 pages; the other 200 pages are scripts for 79 videos that take the place of most worked exercises that are common in traditional textbooks. The text contains a few Exercises, but also makes use of online homework (and checks that students are doing the reading) via WebWork.