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Advanced Mathematics for Engineers 1

Advanced Mathematics for Engineers 1 (Hochschule Ravensburg-Weingarten Univ.). Instructor: Professor Wolfgang Ertel. After a repetition of basic linear algebra, computer algebra and calculus, this course will deal with numerical calculus, statistics and function approximation, which are the most important basic mathematics topics for engineers in the fields of computer science, mechatronics and electrical engineering.

Topics covered in this course, Advanced Mathematics for Engineers 1, include: computer algebra; calculus including sequences, power series, continuity, Taylor series, and differential calculus in many variables; discrete distributions; roots of nonlinear equations, and method of least squares and pseudoinverse.

Image: Advanced Mathematics for Engineers 1, Hochschule Ravensburg-Weingarten Univ.


Lecture 01 - Computer Algebra
Lecture 02 - Sequences, Introduction to Mathematica
Lecture 03 - Introduction to Octave, Series
Lecture 04 - Power series, Continuity, Discontinuity
Lecture 05 - Continuity, Discontinuity, Taylor Series
Lecture 06 - Differential Calculus in Many Variables
Lecture 07 - The Total Differential, Extrema without/with Constraints
Lecture 08 - Extrema, Statistics and Probability
Lecture 09 - Discrete Distributions: Binomial Distribution, Hypergeometric Distribution
Lecture 10
Lecture 11
Lecture 12 - Roots of Nonlinear Equations: Fixed Point Iteration, Banach Fixed Point Theorem
Lecture 13 - Banach Fixed Point Theorem, Convergence Speed and Convergence Rate, Newton's Method
Lecture 14 - Polynomial Interpolation, Spline Interpolation
Lecture 15 - Spline Interpolation: Correctness and Complexity, Interpolation of Arbitrary curves
Lecture 16 - Method of Least Squares and Pseudoinverse
Lecture 17 - Method of Least Squares and Pseudoinverse: Multidimensional Least Squares
Lecture 18 - Application of the Pseudoinverse for Function Approximation

References
Advanced Mathematics for Engineers | Hochschule Ravensburg-Weingarten
Instructor: Professor Wolfgang Ertel. Demos and Course Material. Octave Exam Programs. Previous Examinations. Video Lectures from Previous Semesters.