Lectures related to Introduction to MATLAB and Octave

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.

Orthogonality and Distance in Functions

Covers the concept of orthogonality between vectors and the notion of distance between functions.

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Integral Techniques: Integration by Parts

Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.

Piecewise Functions Composition

Covers the composition of piecewise functions and introduces the signum and Heaviside functions.

Programming for Engineers: Advanced MATLAB Techniques

Explores advanced MATLAB techniques, emphasizing vectorization, 'find' function, and plot manipulation.

Continuity of Functions

Covers the concept of continuity of functions and determining continuity at specific points through examples.

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.

Continuous Functions: Integrability and Examples

Explores continuous functions and integrability through practical examples.