| Students possess foundational mathematical skills in calculus, integration, and Fourier series, essential for understanding and solving AI-related problems. They are able to analyze continuous functions, apply differential and integral calculus in both one-dimensional and multivariate contexts, and use Fourier series for signal processing and function approximation.
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- Analyzing Continuous Functions and Limits (k4)
Students can understand and compute limits of functions, analyze their continuity, and apply this knowledge to assess the behavior of mathematical functions in various contexts.
- Applying Differential Calculus in One Dimension (k4)
Students are able to perform differentiation of one-dimensional functions, applying concepts like derivatives and tangent lines to problems involving rate of change and optimization.
- Understanding Basic Integration Theory (k4)
Students can solve integrals of basic functions, understand the principles of definite and indefinite integration, and apply integration techniques to find areas under curves and cumulative quantities.
- Applying Fourier Series for Function Decomposition (k4)
Students are capable of using Fourier series to represent periodic functions as sums of sines and cosines, understanding the importance of this decomposition in function approximation and signal analysis.
- Performing Multivariate Differential Calculus (k4)
Students can apply differentiation techniques in multiple dimensions, calculating partial derivatives, gradients, and optimizing functions of several variables in various AI-related problems.
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Students have gained knowledge of continuous functions, differential and integral calculus, and their applications in analyzing the behavior of mathematical functions. They also know the basic theory of Fourier series for function decomposition and approximation, as well as the fundamentals of multivariate differential calculus, providing tools for problem-solving in AI and data analysis.
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