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Introduction to MATLAB and Octave
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Matlab 2: Vectorisation and Functions
Covers vectorisation, functions, and flow control in Matlab, emphasizing the importance of avoiding global variables and providing examples of simple plots and debugging techniques.
Introduction to MATLAB and Octave
Covers the basics of MATLAB and Octave for handling scripts, functions, vectors, matrices, and writing interactive programs.
Derivability and Composition
Covers derivability, linear applications, composition of functions, and the gradient vector.
Matlab Functions: Vectorization and Plotting
Covers the 'find' function in Matlab for testing criteria on vectors or matrices.
Implicit Functions Theorem
Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.
Implicit Functions Theorem
Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.
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Integration by Substitution
Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.
Applications of Theorems
Demonstrates the practical application of theorems in calculus through two clever examples.
Morse Theory: Critical Points and Non-Degeneracy
Covers Morse theory, focusing on critical points and non-degeneracy.