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.
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September 23, 2023
English
English [CC]
Description
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.
Course Curriculum
- Lecture 01 – Computer Algebra Unlimited
- Lecture 02 – Sequences, Introduction to Mathematica Unlimited
- Lecture 03 – Introduction to Octave, Series Unlimited
- Lecture 04 – Power series, Continuity, Discontinuity Unlimited
- Lecture 05 – Continuity, Discontinuity, Taylor Series Unlimited
- Lecture 06 – Differential Calculus in Many Variables Unlimited
- Lecture 07 – The Total Differential, Extrema without/with Constraints Unlimited
- Lecture 08 – Extrema, Statistics and Probability Unlimited
- Lecture 09 – Discrete Distributions: Binomial Distribution, Hypergeometric Distribution Unlimited
- Lecture 12 – Roots of Nonlinear Equations: Fixed Point Iteration, Banach Fixed Point Theorem Unlimited
- Lecture 13 – Banach Fixed Point Theorem, Convergence Speed and Convergence Rate Unlimited
- Lecture 14 – Polynomial Interpolation, Spline Interpolation Unlimited
- Lecture 15 – Spline Interpolation: Correctness and Complexity Unlimited
- Lecture 16 – Method of Least Squares and Pseudoinverse Unlimited
- Lecture 17 – Method of Least Squares and Pseudoinverse: Multidimensional Least Squares Unlimited
- Lecture 18 – Application of the Pseudoinverse for Function Approximation Unlimited
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