Fall Semester 2020

Calculus and Elements of Linear Algebra I (JTMS-09)

Syllabus

Quick Links:

Summary:
This module is the first in a sequence introducing mathematical methods at university level in a form relevant for study and research in the quantitative natural sciences, engineering, Computer Science, and Mathematics. The emphasis in these modules lies in training operational skills and recognizing mathematical structures in a problem context. Mathematical rigor is used where appropriate. However, a full axiomatic treatment of the subject is done in the first-year modules Analysis I and Linear Algebra.

Contact Information:
Instructor:Marcel Oliver
Email:m.oliver@jacobs-university.de
Phone:200-3212
Office hours:  Tu 11:00, We 10:00 in Research I, 107
TA:Denida Blloshmi, d.blloshmi@jacobs-university.de
Bishoy Kaleny, b.kaleny@jacobs-university.de

Time and Place:
Lectures:  Mo, We 14:15-15:30, on Teams

Textbook:

Grading:

Tentative class Schedule (subject to change!)

02/09/2020: Introduction; natural numbers, integers, rational, real numbers
07/09/2020: Complex numbers; polynomials, factorization, fundamental theorem of Algebra
09/09/2020: Long division; intervals, inequalities even/odd, composition
14/09/2020: Equations, graphs, functions (domain, range, inverse); brief review of elementary examples (trigonometric functions, exponential, logarithm)
16/09/2020: Limits of functions
21/09/2020: Continuity, types of discontinuities
23/09/2020: Upper and lower bound theorem, intermediate value theorem, affine functions
28/09/2020: Differentiability, derivative, slope, secant, tangent
30/09/2020: Rules and theorems for differentiation, power rule, product rule, chain rule
05/10/2020: Derivatives of exp, log and trigonometric functions, curvature of a function
07/10/2020: Rolle's theorem, mean value theorem, critical point, maximum/minimum of a function
12/10/2020: First and second derivative tests, inflection points, Isoperimetric problem, Newton's method
14/10/2020: Curve sketching
19/10/2020: Anti-derivative, indefinite integral, integrable, rules for integration
21/10/2020: Approximations to area, partitions of intervals, Riemann sum, definite integral, Fundamental theorem of Calculus
26/10/2020: Second fundamental theorem of Calculus, integration by substitution, integration by parts
28/10/2020: Review
02/11/2020: Mock Midterm Exam
04/11/2020: Applications of the integral I
09/11/2020: Applications of the integral II
11/11/2020: Basic analytic geometry: Lines and circles in cartesian plane, vectors/scalars, basis vectors for cartesian plane, components vs. coordinates, magnitude, scalar product, vector product, orthonormal basis, equations of lines/planes/spheres
16/11/2020: Vector spaces, span, linear dependence, dimension, basis vectors
18/11/2020: Matrix-vector multiplication, vector space of matrices, matrix multiplication, identity matrix, null matrix
23/11/2020: Systems of linear equations, Gaussian elimination
25/11/2020: Solutions of linear systems of equations, rank, nullspace, nullity, homogeneous, inhomogeneous
30/11/2020: Rank plus nullity theorem, examples, matrix inverse, regular/singular matrix
02/12/2020: Row operations of Gaussian elimination as linear opera- tors, matrix inverse with Gaussian elimination
07/12/2020: Review for final exam
TBA: Final Exam




Last modified: 2020/12/19
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2020/CO-583/index.html
Marcel Oliver (m.oliver@jacobs-university.de)